Hollow Cathode Arcs

Hollow Cathode Arcs JEAN-LOU P DELCROIX Laborntoire rle Physique des Plasmas, Universitk de Paris-Surl, Orsay, France AND

A R M A N D 0 ROCHA TRINDADE Instiluto Superior Tkcnico, Uniuersidade de Lisbon, Portugal

88 91 92 93 A. Normal Regime (N Regime) 97 B. Low Gas-Flow Regime (LQ Regime)................................................... 98 C. Low-Current Regime (LI Regime) . 99 D. High-Pressure Regime (HP Regime) E. Concluding Remarks on HCA Operation .... 102 103 IV. Operating Conditions for Low-Pressure HCA (N, LQ, and LI Regimes) ... . . . . . 103 A. Experimental Requirements ................ 5. Working Parameters for the Low-Pressure Regimes .... ... ..... ....... ........... i06 V. Experimental Results for the Normal Regime ..... .. ..... ... . . ... .. ............... ..... i09 A. Current-Voltage Characteristics ........ ...................................... 109

I. Introduction

11. Historical Re view of HCA 111. Working Regimes of HCA .....................................................................

5. The External Plasma ......__._._.... C . Oscillations and Noise in HCA ........... D. The Cathode Region ................ VI. Theory of the HCA in the N Regime A. General Comments ........................................................................ 157 B. The Nature of the "Active Zone" C. Balance of the Current in the Cathode Region .................................... 166 ... .... .. .. _ _ ... . 170 D. The Ionization Term in the IPC E. Prospects of Improving the The0 F. Conclusion .................................................................................... 175 .........._...... VII. Applications of HCA . A. Multichannel HCA .. ................... 175 B. HC Ion Laser C. Ion Sources for Electric Propulsion Systems ........................... .._........ 180 D. HC MPD Thrusters ........................................................................ 182 ................. E. ac Operation of HCA F. Other Applications of . .... ......... .... ............ .. ., ......, ., ............ ..... 184 .... .. .. VIII. Conclusion ... References .., ., .., ....., ...., ......, .. . .. . .. .. . ..., ....... .. ,, ........, ........, ,....., ....... .. I85 ...........................

.

87

88

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

1. INTRODUCTION Hollow cathodes have been used for some years in different discharge devices, working under varying conditions in widely extended ranges. All of these devices have one common feature: the cathode presents a hollow cavity, enclosed or at least partially bound by walls made of conducting, refractory materials kept at the cathode potential. The geometry of such cathodes is such that their open side faces the anode side of the discharge, so that the plasma existing at the interelectrode space can penetrate the hollow cathode, thus assuring a strong interaction between the plasma and the cathode internal surface (Fig. 1). CATHODE

ANODE

I PLASMA POSlflVE SHEATH

CATHODE WALL

FIG. I . Plasma penetration inside the channel of a cylindrical hollow cathode.

In general terms, this interaction affects an extensive area of the cathode wall; a positive space-charge sheath builds up, so that the incoming ions are strongly accelerated before neutralization upon the wall. If the current is large enough (arc regime) the resulting high wall temperature enhances the thermionic emission; on the other hand the emitted electrons inside the hollow cavity, accelerated by the sheath voltage, have a high probability of making several inelastic collisions with the neutral particles before reaching the interelectrode space.

HOLLOW CATHODE ARCS

89

Considering, for instance, a longitudinal discharge between opposing electrodes, the hollow cathode cavity can present plane-parallel, cylindrical, or spherical geometry (Fig. 2 ) . For a transverse discharge, the electrode

w A-

- PLANE

A

PARALLEL

8,- CYLINDRICAL SINGLE CHANNEL

$

1

3

8,- CYLINDRICAL MULTICHANNEL

f i T @ &-

B3- CYLINDRICAL "MACARONI PACKET"

._.-

-

C

- SPHERICAL

CAVITY

FIG.2. Hollow cathode geometry (longitudinal discharge).

arrangements can, in principle, take one of the basic forms shown in Fig. 3 (orthogonal or coaxial electrodes). The performances of this type of discharge are generally better than those where the cathode presents a plain surface to the anode side; for the same gas pressure, discharge voltage, and general geometric parameters, the resulting discharge current in generally higher for hollow cathode discharges than for conventionally shaped ones. This was probably the point that aroused interest about those discharges in early investigations; later, several other advantages were acknowledged when more detailed research was accomplished on the subject. Hollow cathode glow discharges (low current I 6 I A , high cathode voltage drop V, > 100 V, thermal effects relatively small) were first discovered and their remarkable performances recognized as early as 1923 [Guntherschultze (I)]; but more than 30 years elapsed ( 1958) [Luce (Z)] before the same kind of interest arose about hollow cathode arcs (high current I 2 5 A, low voltage drop V , < 50 V, cathode temperature T 2 2000°C).

90

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

t+

A,- P L A N E PARALLEL ANODE; CYLINDRICAL CATHODE

?-

--

.- - - - . - - - - - - *

-

A,- P L A N E PARALLEL CATHODE; R I N G - S H A P E D ANODE

B2- COAXIAL GEOMETRY, E X T E R N A L CATHODE

6,- COAXIAL GEOMETRY. I N T E R N A L SLOTTED CATHODE

FIG.3. Hollow cathode geometry (transverse discharge).

It can be said that HC glows and HC arcs have been, up to now, two independent fields of research; at least, it is difficult to find significant contributions from the studies of one type of discharge to the other. This is most certainly due to the specialization in the experimental setup required for one or the other type of discharges: power supplies, cooling facilities, electrode erosion problems, specific diagnostic methods to be used, etc., depend strongly on the type of discharge in which one is interested. On the other hand, the emission, excitation, ionization, and transport mechanisms of particles, present at the onset and in the steady-state regime of both types of discharge, are again specifically different, and call for different theoretical and experimental methods of approach. These are sound reasons for the tendency of the various research laboratories to specialize either in hollow cathode glow discharges or in hollow

91

HOLLOW CATHODE ARCS

cathode arcs, seldom in both of them. The same reason applies to the present review; it will be concerned only with HC arcs, which we have been studying extensively since 1964 (2-10). A point on nomenclature should now be raised, considering the number of papers in the scientific literature dealing with either hollow cathode glow or arc discharges. Usually in the literature, the term “hollow cathode effect” concerns a glow discharge, while following Lidsky er a/. ( / I ) ’‘ , hollow cathode discharge” is supposed to mean a high-current device. Still, some authors do not take these views; so, the title and even the abstract are sometimes not sufficient for a reader to decide whether a given paper on hollow cathodes concerns a glow or an arc discharge. For the sake of clarity we propose the designation of hollow cathode arc (HCA) to distinguish such a discharge from a hollow cathode glow (HCG). 11. HISTORICAL REVIEW OF HCA

The first results on HCA discharges were reported by Luce in 1958 (2). The experimental device was constituted of a rather large (1-2 cm i.d.), thick-walled tungsten tube as a cathode, with a gas flowing through into the evacuated interelectrode space. It was found that the discharge began in the interior of the cathode tube, several diameters from the open end, and extended to the anode. The same basic arrangement was used in arc discharges studied at the Oak Ridge National Laboratory and the Research Laboratory of Electronics of the Massachusetts Institute of Technology. The research groups concerned published jointly the results of their pioneer work on HCA discharges [Lidsky er al. ( I / ) ]such as various electrode configurations, cathode materials and injected gases, range of the parameters for proper operation. They measured the external plasma density and temperature and studied the current and energy balances at the electrodes. The combination of tantalum cathode-argon gas was found to be the most satisfactory one for good efficiency and proper operation of the discharge. Important features of the discharge have been pointed out: ( 1 ) the discharge creates a very pure external plasma (low contamination by the cathode material), dense (n, 10’3-10’4 ~ m - and ~ ) highly ionized (up to 95%); (2) the cathode presents a reasonably long lifetime, despite high current densities and high cathode wall temperature (higher than 2500°K). Those characteristics were interesting enough to encourage further research on the subject. Reasonably enough, the next few years saw a steady amount of experimental work being performed to improve the knowledge of HCA discharges, mainly concerning the influence of the various parameters (geometry, external pressure, gas flow rate, axial magnetic field strength, electrode temperature, etc.) on the performance of the discharge as an efficient

-

92

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADB

source of dense, highly ionized plasma [see for example, 6, 12-15)]. An important part of this research work dealt with the study of the noise and oscillations of the discharge (16-19) since it was interesting to evaluate the possibilities of using an HCA as a source of quiet plasma for experimental work on wave propagation. The next step of the research o n HCA consisted mainly of a theoretical effort to understand thoroughly the internal mechanisms of these discharges, namely to account for the high current density that can be drawn out of a hollow cathode without serious damage. In spite of the amount of work already produced [see, for example, (15, 20-23)] by a theoretical approach, this problem is still an open one, especially for very high current densities; nevertheless it can be stated that we have now a fair knowledge of the physical processes involved inside the cathode channel and a reasonable understanding of the reasons for the high efficiency of this type of discharge. The research on HCA has now been stimulated by a number of interesting applications; the possibility of delivering high currents with little damage makes these cathodes very useful devices for ion lasers (24-27); ion thrusters (28, 29); flowing afterglows for chemical applications (9); welding; MHD generators and motors (30); and quiescent plasma machines (18, 31). The many applications already in existence should keep interest high in the next few years. 111. WORKINGREGIMES OF HCA

Considering a cylindrical hollow cathode, with the exit hole facing a plane anode (by far, the most extensively used geometry), several arc regimes can occur, depending on the range of the discharge parameters (pressure vessel y,; gas-flow rate Q ; discharge current I ) . A qualitative classification of operating arc regimes is shown in Table I. where the magnitudes of the determining parameters are indicated. TABLE I WORKING REGIMES OF HCA

Name

Code

Normal regime

N

Low gas-flow regime

LQ

Low-current regime

L1

High-pressure regime HP

Pe

Q

I

Low ( i O . 1 Torr) Not too low Not too low cm3 STP) (>10 A) Low (<0.1 Torr) Very low Not too low ( < l o - * cm3 STP) (>10 A) Low ( 0.1i Torr) Indifferent Very low ( < l o A) Moderate, high Indifferent Indifferent (> 1 Torr)

HOLLOW CATHODE ARCS

93

A . Normal Regime ( N Regime) Earlier research reports pointed out that the “proper” regime of operation of HCA was obtained when a gas was injected through the cathode channel into the discharge vessel, kept at low pressure ( ~ 0 . 1Torr). This mode of operation is easily recognized by an extensive hot zone set at some distance from the tip of the cathode (up to a length of several diameters); this diffuse hot zone is clearly different from the extremely hot, localized cathode spot of the classical (plain cathode) arc discharges (Plate I). Further research on the nature of this active zone required the knowledge of the longitudinal profile of the cathode wall temperature. For a very thin cathode wall (e.g., 0.2 mm), optical pyrometry of the outer cathode surface can give the temperature of the inner emitting surface to a very good approximation. Figure 4 presents a typical profile, showing a maximum at some distance 1 of the cathode (measured from the tip). The temperature range is high enough to provide high thermionic emission from an important area of the cathode wall; however, calculations show that electron multiplication by ionization must take place to account for the measured discharge currents. From the very beginning of the research on HCA it was noticed that the location of the maximum wall temperature moved farther from the open tip of the cathode when the gas-flow rate was reduced; increasing the cathode inside diameter for a given flow rate yields the same result (Fig. 5). It is felt therefore, that the neutral gas pressure inside the cathode channel probably would be the determining parameter for the location of the maximum wall temperature. The pressure varies along the cathode channel due to the gas flowing through; and the maximum temperature would occur at a distance where this pressure reaches an optimum value depending on the exact experimental conditions. Estimates of this optimum pressure (at the hottest zone level) are of the order of a few Torr (fl, 3 1 , 3 2 ) . The reasons for the above requirements for the N regime become more obvious when the origin of the extensive hot zone at the cathode wall is considered. It is clear that a plasma must exist inside the channel, and that a strong ion bombardment is necessary to account for the wall heating. Those ions are mostly created inside the cathode channel (if they were created by ionization in the interelectrode space, the discharge would be affected by lowering substantially the vessel pressure, which is not observed), by inelastic collisions of wall-emitted electrons upon the neutral particles. Thus the pressure requirement inside the channel is due simply to the fact that the mean free path of the fast electrons for inelastic collisions must be short enough for significant ionization to take place inside the hollow cathode. “

”

94

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

Plate I. The same cathode situation photographed with different exposures to show the brightness profile of the cathode cylinder (Q: 0.8 atm cm3 sec-', I 20 A, R = 1.9 mm, B = 100 G ) . L , - 7.5 cm, film: llford HP4, I ) - l/SOO. A 1 / 2 2 , green filter; B / / 3 . 5 , green filter; C f / 2 2 ; D f / 3 . 5 . ~

95

HOLLOW CATHODE ARCS

1

CATHODE

7

6

5

4

ANODE --

3

2

1

0

FIG.4. Typical longitudinal profile of wall temperature in the N regime.

In a fully established N regime the plasma inside the channel transfers a positive potential from the anode to the vicinity of the cathode wall; this creates a space-charge sheath that accelerates the walls-emitted electrons and enhances the ionization inside the hollow cathode. It is found that for the same current the overall cathode drop (and the discharge voltage as well) increases strongly as the hottest zone is made to move deeper inside the cathode tube by varying the flow rate (Fig. 6). This increment attains several volts per centimeter, depending on the cathode inside diameter. An overall cathode drop up to about 50 V, can be measured for deep plasma penetration (several centimeters); since the cathode drop equals the maximum sheath voltage, at the tip of the cathode, several ionizations can be produced by every emitted electron. The N regime is very steady and the current density through the channel cross section can be rather high (typically lo2 A cm-2) without significant damage to the cathode wall, since its temperature is everywhere well below the melting point of the metal (T,,,,,, = 3270°K for Ta; 3653°K for W cathodes).

96

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

4

(mm)

50

40

30

20

10

0

1

0

2

3

;;I

Q

4

(at rn c m . 3sec

I)

FIG.5. Abcissa I of the cathode where the maximum wall temperature occurs for various channel radii R, as a function of the argon gas-flow rate, Q (atm ~ m sec-’) - ~(e = 0,2 mm; I : 15 A ; B = 400 G ) . From Delcroix ef al. (6, p. 414).

100

Vd ( V I

I.....

.............

- ------

I ........... --

N regime

_.i.

LQ regime

40

2o

t

01

10.’

I

I

10.‘

I

I

1 P (atm cm3 s e i ’ ~10

FIG. 6. Discharge voltagc as a function of the gas-flow rate showing the transition between the normal regime (right hand branch) and the low flow rate regime (left-hand side) ( I = 15 A ; R = 1.8 nim; L = 2 1 . 5 cni; p r = 2 x Torr; 8 = 4 0 0 G). From Minoo (31, p. 96).

97

HOLLOW CATHODE ARCS

The portion of plasma inside the cathode channel is called (32) the "internal positive column" (IPC), due to the plasma potential polarity respective to the cathode. It is however, rather different from the usual positive columns of glow or arc discharge because in the present case the wall acts as an emitting electrode, and moreover, is at a constant potential, thus producing an ion sheath with a voltage drop increasing toward the tip of the cathode.

B. Low Gas-Flow Regime ( L Q Regime) Let us consider the following experiment: while working with an HCA in the N regime, the gas-flow rate is made to decrease step by step keeping the vessel pressure and the discharge current constant. As stated before, the hottest zone of the cathode wall will recede from the extremity and the curves T(x) become progressively flatter; the discharge voltage will be increasing steadily (Fig. 6 ) . If the gas-flow rate is made to decrease past a certain value we enter a new regime: a sudden disturbance of the wall temperature takes place over the whole length of the cathode and evolves during some ten seconds. After that time, a new temperature distribution can be observed, where T(x)is decreasing monotonically from the tip of the cathode to the holder (Fig. 7). The new discharge voltage is lower than the extrapolation of the V ( Q )curve for the N regime would indicate (Fig. 6 ) .

1500

1000 I

4

x(cm)

I

I

I

T

3

2

1

0

FIG.7. Transition from the normal regime to the low gas-flow regime, decreasing progressively the gas injection through the cathode channel ( I = 15 A ; R = 0.18 cm; B = 400 G ; p E = l o - * Torr). From Delcroix er oi. (5, p. 267).

98

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

If the gas-flow is further reduced, down to complete cutoff, the discharge voltage and the T ( x ) curve remain unchanged. This low gas-flow operation ( L Q regime) is characterized by the monotonic variation of the temperature with distance along the cathode wall, showing that the plasma does not penetrate significantly inside the cathode channel. This is mainly due to the fact that the gas flow is too low to impose an important pressure gradient along the channel; the pressure is then substantially the same as in the vessel. Under these conditions, the mean free path for the ionization of the neutral gas by the thermionic electrons is too long for significant ionization to take place inside the channel.? This regime is not very interesting for it requires a higher voltage than the normal one. The hottest part of the cathode is less extensive, and so less efficient, as a thermionic source than in the N regime, with the same maximum cathode temperature; furthermore, since the ionization rate inside the channel is very low, the thermionic emission must be completed by ionization in the external plasma to provide for the required discharge current. The LQ regime was first reported in 1968 ( 5 ) ; later articles (21, 26, 31,32) provided additional information on the subject. The transition from this mode of operation to the “ high-pressure regime” (Section IV) has been analyzed by Minoo (31) who studied the external plasma, the magnetic confinement effect when the vessel pressure is increased from to 10 Torr and measured the longitudinal electric field under those conditions (Fig. 8). \

C. Low-Current Regime (LI Regime)

This other low-pressure regime of an HCA will be analyzed very briefly, as it is an undesirable one. It occurs when an attempt is made to ignite the N regime of an HCA with a current that is too low. The easiest way to achieve ignition is to set the correct pressure requirements (Section 111, A) and create afterward an abnormal glow discharge between the electrodes (Section IV). When the cathode begins to get rather hot, an increasing current causes an arc to ignite; the current is at first provided by the ionization in the external plasma and the thermionic emission from a cathode hot spot. If the discharge current (determined by the external circuit) is high enough, this hot spot mode evolves quickly into an N regime with a diffuse cathode active zone; the externally created ions enter the cathode channel, impinge upon the wall, and heat a large area of it up to thermionic temperatures, and a plasma is created inside the hollow cathode.

-

t Taking for instance, p e = lo-’ Torr, estimated gas temperature To 2500’K and for typical electrons having 20 eV kinetic energy, the mean free path for ionization is 50 cm; even taking into account their elastic collisions upon the neutrals (mfp 15 cm), those electrons will leave the channel without producing ionization. N

N

99

HOLLOW CATHODE ARCS E/p ( V/cm Tori

10’

CONFINED. HIGHLV IONIZED PLASMA

i

,

CONFINED. “INTERMEDIATE” PLASMA

NONCONFIHEO ~

PLASMA

10

1

10’

10.~

10.l

lo-’

1

10 P (Torr)

FIG.8. Experimental values of € / p in the external plasma column as a function of the vessel pressurep. From Minoo (31, p. 29). ( I = 15 A; R = 0.18 cm; Q = 0; B = 400 G). * For the definition of “intermediate” plasma see Delcroix (33, p. 92).

However, if the ion current is too low, it is unable to heat the cathode wall enough to create an internal positive column. The hot spot remains at the periphery of the cathode end, moving around it, or it may run erratically along the cathode outer surface, causing strong fluctuations of the discharge voltage. In either case, vaporization and damage to the cathode is expected. This unsteady mode of operation is called the low current (LI) regime (21) and must be avoided during ignition, when it is most likely to occur. Reduction of the discharge current when an N regime is in operation does not usually produce a typical hot spot LI regime. The discharge voltage increases progressively up to the point when it cannot be provided by the power supply; then, the discharge is simply cut off.

D . Higli-Pressure Regime ( H P Regime) If the vessel pressure in an HCA working in the normal regime is made to increase past some lo-’ Torr, the cathode wall temperature maximum is observed to approach the electrode tip. For an external pressure of the order of 1 Torr, a monotonic axial variation of the wall temperature is observed (Fig. 9). Reducing or cutting of the gas injection through the channel does not affect the regime significantly, provided that the vessel pressure is not allowed to change. This cathode mode of operation in the moderate pressure range (up to some 10 Torr) is similar to the LQ regime, in the sense that a plasma is not formed inside the cathode channel in either case. An arc-type cathode spot

100

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

is still not observed; this is, obviously, a distinct advantage of HC over the plain, conventional cathode for low and moderate pressures. Unfortunately, if the vessel pressure in this arc discharge is made to increase further, past some tens of Torr up to atmospheric pressure and beyond, the cathode no longer behaves like a hollow cathode should, that is, with an extensive hot zone and low metal evaporation. As the pressure increases, the hot zone is observed to contract and finally it becomes a localized hot spot at the tip of the cathode; very high spot temperatures cause fierce local vaporization, quick cathode damage and metal contamination of the external plasma. The hollow cathode now behaves like a plain refractory cathode in the hot spot mode. For applications imposing high vessel pressures with strong discharge currents (for instance, MHD devices and chemical reactors) it would be most interesting to achieve typical hollow cathode behavior as in the normal, low pressure regime. Study of the energy balance at the cathode has shown that it is not possible to achieve the heating of an extensive area of the cathode wall by the discharge itself (34). The simplest solution found was an auxiliary heating of the cathode wall by an external circuit. Curves showing the cathode behavior when imposing an external current along the wall are presented in Fig. 10 (8).

x(crn)

7

6

5

4

3

2

1

0

FIG.9. Transition from the normal regime to the high-pressure regime by increasing the vessel pressure. ( I = 20 A ; R = 0.145 cm; Q = 6 x lo-* atm cm3 sec-'; B = 0). From Trindade (21, p. 16).

101

HOLLOW CATHODE ARCS

-5 I

a

Q-

-- L A+

c -

X

i

{-

2400

I

I

FIG.10. High pressure behavior of the HCA: wall temperature profile. (a) Without auxiliary heating (Ih= O), (b) with auxiliary heating in absence of the discharge ( I = 0); (c) working as a “cathotron.” I-Cuthode channel (tantalum wall); 2, tantalum disk; 3, tantalum outer cylinder; 4, insulator; 5, cathode holder. From Delcroix er crl. (34, p. 19).

102

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

The main conclusion of these experiments is that, when the cathode wall temperature reaches the thermionic range over a significant area, the hot spot disappears and a steady discharge is obtained, without significant damage to the cathode. Delcroix, Minoo, and Popovici (34) found the performances of this device to be better when a strong gas flow is injected through the cathode channel. They named the arrangement “ cathotron” (35), since it is (under a conceptual point of view) something like the association of a plasmatron with a hollow cathode. E. Concluding Reniarks on HCA Operation 1, Low-Pressure Discharges ( p E< 0.1 Torr)

a. N regime. Characteristic features of the N regime are extended cathode hot zone and internal positive column. This is the most interesting regime of low-pressure HCA operation, for it provides high arc currents with the lowest discharge voltages. As a drawback, a gas injection must be running through the cathode, imposing a continuous pumping of the discharge vessel. The best way to obtain this regime is to increase the discharge current sufficiently, starting from an abnormal glow discharge. The convenient ignition current density is about 1 A/mm2 through the tube cross section; once the N regime is fully established the current can be reduced about threefold without cutoff. b. LQ regime (including Q = 0). Characteristic features of the LQ regime are extended hot zone, cathode temperature decreasing monotonically from the tip to the cathode holder, and absence of an internal column. This regime requires a higher voltage than the N regime for the same discharge current. Since gas injection is unnecessary, it can operate in a sealed vessel; however, some difficulties must be expected for ignition in those conditions, since the easiest way to establish the LQ regime is through the normal one by reducing gradually the gas flow rate (which is not possible in a sealed vessel). c. LZ regime. Characteristic features of the L1 regime are unsteady operation, hot spot mode, and low cathode lifetime. A suitable choice of the supply voltage and the charge resistor is necessary to avoid this regime during ignition. It is possible that a steady operation with low current density, without cathode spot, could be obtained by providing an external heating of the cathode wall. There are no published data concerning this experiment to insure that a proper operation can be obtained. 2. Moderate and High-Pressure Discliarges a. Moderate range (pE 5 10 Torr). Characteristic features of the moderate range are extended hot zone, cathode temperature decreasing monotonically

HOLLOW CATHODE ARCS

103

from the tip, and absence of an internal column. The absence of a hot spot insures fair cathode lifetime. This regime is easier to establish departing from a N regime by increasing the pressure vessel. A gas injection is not necessary afterward. b. High-pressure range (pE > 10 Torr). A characteristic feature of the high-pressure range is the hot spot mode unless cathode auxiliary heating is provided (cathotron). The best operation is obtained with high gas flow through the cathode. Lack of further published data, either experimental or theoretical on the HP regime, causes the remainder of this work to concentrate in the lowpressure operation of HCA.

IV. OPERATING CONDITIONS FOR LOW-PRESSURE HCA ( N , LQ, A N D LI REGIMES) A . Experimental Requirements

a. Cathode assembly. For a cylindrical geometry, hollow cathodes are usually made of a thin-walled tube of a refractory metal (Ta, W, Mo, the first being the most extensively used), either isolated or as a bundle assembly of tubes (multichannel cathodes, Section VlI, A). The thick-walled or drilled rod variety is not very interesting, for it increases the heat conduction to the cathode holder and consequently lowers the wall temperature. To make the substitution of cathode tubes easier they are not usually welded to the cathode holder; a vacuum-tight and good heat-conducting contact between cathode and holder is obtained by compressing an intermediate washer or ring of soft metal (indium, gold, lead). To prevent the vaporization of this material, the holder is usually water cooled. On the other hand, it is interesting to maintain a high cathode wall temperature at the active (emitting) region, and a radiation shield is quite useful. It may take the form of one or several refractory metal tubes simply put around the cathode, without any type of clamping device (Fig. 11). A ceramic arc stop (alumina or zirconia) is useful to prevent the initial arc (during ignition) from starting at the wrong place, and eventually damaging the cathode holder. 6 . Anode. Anodes are usually cooled, to take away the high power dissipation that occurs there [more than 50 of total input power ( 6 ) ] .They may be shaped as a large ring (sometimes larger than the cathode diameter) or as end-anodes, either plain disks or hollow cylinders. The latter are found to lower the anode drop when they work at high temperatures, and simultaneously reduce plasma oscillations and noise (36). Gas injection through the anode was reported to have a similar effect (37,18); it may also be useful to reduce pressure gradients that could exist along the column.

104

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

CATHODE CHANNEL

I \

t

RADIATION SHIELDS

ARC STOP

FIG. 11. Typical cathode assembly with two radiation shields.

c. Discharge vessel. Vessel dimensions and geometry are determined by the purpose of the discharge; the length of the column does not affect strongly the discharge voltage since the external plasma is almost field-free (12), although a long column may make arc ignition more dificult. For such a long column, an auxiliary anode is sometimes used to make ignition easier. Slender columns such as those used in lasers are, of course, different since the axial electric field is much higher and the discharge voltage increases accordingly (38). The use of baffles inside the vessel may strongly modify the column behavior, introducing local gradients of pressure. This is a common arrangement used in some plasma experiments to separate the source region (cathode region) from a high-vacuum region where the external plasma is allowed to diffuse (18). Differential pumping is used in those cases. Protection of the vessel walls against excessive heating may be obtained by appropriate cooling facilities or, most efficiently by an axial field, confining the plasma in the central part of the vessel. It is also found that the axial magnetic field makes arc ignition easier in the N regime, for it collimates the externally created ions into the hollow cathode. However, a magnetic field is strictly not necessary for HCA operation, even if it generally lowers the discharge voltage for a given current (see Section V, A , 1). d. Vacuum system. As a steady gas injection is usually present, high pumping speed is necessary to maintain the vessel volume at a low pressure. Even at moderately low pressures ( p E Torr), it is normally necessary to provide a high-speed secondary pump (Rootes or diffusion type) of some lo2 1 sec-' pumping speed, backed by a suitable rotary pump. e. Electrical circuit. Two straightforward circuits are presented in Fig. 12 for ignition and operation of a HCA. Ignition is obtained through the abnormal glow regime.

-

105

HOLLOW CATHODE ARCS CATHODE

ANODE

sw2

IHdX= SOA V,

5

1.2 K V

IHix: SOA

FIG.12. Typical circuit arrangements for arc ignition (through abnormal glow discharge) and for steady-state operation. (a) Parallel circuit: ( I ) close Swl, Sw2 is kept open; (2) after cathode heating, close Sw2; (3) after arc starts, open Swl. Swl must take full abnormal glow current; Sw2 must take full arc current. (b) Series circuit: ( I ) close S w l ; Sw2 is kept open; (2) after cathode heating, close Sw2. Swl and Sw2 must take full arc current.

I06

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

3. Working Parameters for the Low-Pressure Regimes

To compare thoroughly the results obtained by various authors, it would be necessary to know the exact conditions of the experimental setup, i.e., working gas; interelectrodes conditions (column length L, pressure pE and pressure gradients, arc confinement situation and vessel geometry, heat exchanges); anode conditions (geometry, material, heat transfer conditions); cathode conditions (cathode material and geometry, heat transfer conditions, gas-flow rate Q); discharge current I and voltage V ; magnitude and geometry of the external magnetic field B. Unfortunately a great number of articles in the literature lack complete information about many of the above parameters, making the actual comparison of results difficult. Nevertheless, most of the authors working on HCA deal with the same general type of discharge described as follows: longitudinal discharge (opposing electrodes); cylindrical geometry, (one hollow cylindrical cathode channel, along the discharge axis); gas-fed cathode, usually made of tantalum, with a flow of a rare gas, usually argon; strong longitudinal magnetic field ( B > 100 G) or no magnetic field applied; external pressure (at the interelectrode space) lower than 0.1 Torr. For this type of discharge the principal independent parameters to be considered are the channel radius R , the gas flow rate Q, and the discharge current I ; while the T(x) curve of the cathode temperature and the discharge voltage Vare the most readily available dependent variables. The cathode and anode drops (V, and VA),the longitudinal electric fields inside and outside the cathode channel ( X , and X,) and the external plasma parameters (n,, n, ,n o , T, , T i , To) involve more elaborate measurements. The principal independent variables R , Q , I , can be varied a priori within very wide limits: R = 0.05 cm to several centimeters; I = 1 A to several 10' A up to several 10' atm-cm3 sec-'. (permanent regime); Q = 0 through However, if an N regime is sought, with rather high efficiency and a fair cathode lifetime, those parameters are not completely unrelated. This point is emphasized in Fig. 13, where we have represented the working conditions of some reported experiments as the loci of composite coordinates Q/Sand I/S ( S being the area of the cathode channel cross section ). The parameter I / S (current density through the cathode cross section) is related to the cathode temperature; Q/Sis the characteristic parameter of the pressure drop inside the channel, having an obvious effect on the phenomena occurring in this region. The choice of the points represented was rather arbitrary and their number limited for the sake of clarity. As a matter of fact, large portions of the diagram ( Q / S ,I / S ) have been extensively studied, mostly in the N regime with argon, but also with other gases [H,(13), N2(43), D2(44, Kr and Ne ( 4 3 , He (53)], and in the LQ regime (31).

107

HOLLOW CATHODE ARCS 102

r

!

i*

INCREASING GAS COOLING EFFECT

0

I

I

L I REGIME (UNSTABLE)

I I I *

I

0

I I

N REGIME

I I

0

I)

10.’

10

’

I

10 2

I / S (A/cm2)

DECREASING CATHODE LIFETIME

’

I

1

10

10

FIG. 13. Working conditions in some reported experiments on low-pressure HCA: Delcroix et a / . (6); Lidsky et N / . (I/); Ahsmann and Van Benthein (12); Kretschnier et cil. (17); Brunet (39); Gritzniacher e / d . (40); Chung (41); Lorente-Arcas (42); Gerry (50).

The experiments show that there are two fairly well-defined forbidden zones for the operation of HCA in the N regime, corresponding to the lower values of the parameters Q / S and t / S . Q / S being too small, the discharge works in the LQ regime (see Section 111, B) and the cathode wall temperature presents a monotonically decreasing longitudinal profile. If the current density is too small, either the discharge is unstable upon ignition, working in a hot spot mode (LI regime), or when evolving from a normal regime by decreasing the discharge current the arc suddenly cuts off. The N regime corresponds to higher values of both parameters; however, one should notice that too big ;1 current density at the cathode channel will impair the cathode lifetime by excessive wall temperature. 500 A/cm2 seems to be a good compromise between a high thermionic current and a fair lifetime. The high gas-flow, low-pressure upper part of the diagram has not yet received much attention, for there seems to be no point in increasing the gas

108

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

consumption while maintaining low vessel pressure by intense pumping. However, some modifications may occur in the discharge behavior in this range, due to important changes in the gas-flow regime, as follows: (i) Flow velocity approaching the speed of sound. Let us take for instance a channel cross section of area S , a local gas pressure equal to 1 Torr (order of magnitude of the pressure at the abscissa where the wall temperature is maximum), and a gas temperature supposed to be at thermal equilibrium with the cathode wall (say, T = 2500°K). The veIocity of sound at this abscissa is then for argon us = 9 x lo4 cm-sec-', while the local gas velocity is numerically given by usas(cm-sec-')

=7 x

103

Q (STP cm3-sec-') S(cm)2

So, a gas flow such that Q / S N 13 cm-sec-' is an upper limit for the flow to remain subsonic at the active zone level (Mach number M < 1). This limit is represented in Fig. 13. (ii) Possibility of a turbulent flow. The limit for a turbulent regime to occur is given numerically for Ar at 1 Torr, 2500"K, by the inequality

N R = 0.59

Q (STP cm3-sec-l) R (cm)

> 1000

This condition is never attained at the active zone level. (iii) Extreme cooling of the cathode wall. This point, which has not been thoroughly studied, concerns the cooling effect of a high gas-flow rate on the cathode wall. Qualitatively it is expected that in these conditions, no extensive portion of the cathode wall can attain thermionic temperatures; then, only by evolving to a hot spot mode can the current requirements be met, and the normal regime probably disappears. The relatively small latitude allowed for variation of the parameters Q and Z for the normal regime (when a cathode of a given diameter is chosen), is one of the drawbacks of the system. If, for instance, a 100 A maximum current must be drawn from an HCA and a high cathode lifetime is desired, choice must be made of a cathode having at least 0.8 cm i.d., imposing a minimum consumption of argon of about 1 atm-cm3-sec-', and a minimum steady-state discharge current of around 20 A (roughly 60 A ignition current). The need for a wider current range and a n economic consumption of gas in every circumstance has been at the origin of multichannel hollow cathodes (7) (see Section VII, A). One could also investigate the effect of an auxiliary heating of the cathode to extend, toward low flow rate values, the domain of existence of the N regime; there are no publications on this subject at the present time.

HOLLOW CATHODE ARCS

v.

109

EXPERIMENTAL RESULTSFOR THE NORMALREGIME A . Current- Voltage Cliaracteristics

1. Comporzents of the Discharge Voltngi>

For a given experimental setup of a n HCA, the V ( I )characteristics depend mainly on the gas-flow rate Q, on the presence and magnitude of the external magnetic field B, and on the vessel pressure p k . Because the total discharge voltage is the sum of three terms (overall cathode drop V c , voltage drop at the external column VE, and anode drop V,), we must evaluate the relative weight of those terms and their dependence on the parameters, in order to understand the behavior of the hollow cathode itself. Considering first the influence of 5 and Q, let us analyze a low pressure discharge where the vessel pressure is kept constant (irrespective of the gasflow rate) at a typical value of Torr. The relative importance of Vc against V , depends both on the depth of penetration of the plasma inside the cathode channel and on the length of the interelectrode space L. Assuming that the length of the internal positive column is I, X , the average field strength in the IPC, and that Y o is the residual value of the cathode voltage drop at the limit of the IPC (x = I ) , one can write (Fig. 14)

FIG.14. Schematic diagram of the potential distribution at the axis of an HCA (N regime).

110

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

Typical values are (6) V , = 12 V ,

,'A

= 0.1

V/cm,t

X I = 8 V/cm, VA = 20 V/cm.

Due to its much higher electric field strength, an IPC some centimeters long clearly dominates the external column influence on the discharge voltage, even in a rather long discharge. For the latter to be dominating, the IPC must really be very short (very high flow rates). As a general rule, for low gas-flow rates the effect of the external column may be neglected; for high gas-flow rates, the IPC is too short, and a long external column may influence strongly the discharge voltage. The V(1)characteristics of HCA in the N regime are typically arc-type; in the range of the lower currents, the voltage is a decreasing function of the current. The V ( I )characteristic goes through a somewhat flat minimum and then acquires a positive slope for the remaining, high-current range. The exact shape of the curves and the current values for the minimum voltage depend strongly on the discharge parameters (p,, R, Q, B), and on the anode geometry and temperature (6, 36, 466). 2. Magnetic Field Effect

To extract coherent information from published experimental data concerning many different discharges, it is necessary to select arbitrarily three kinds of magnetic field effects on HCA. a. Conjinement of the external plasma. This effect starts at relatively low values of B (10-100 G). It changes a diffusion-type external plasma into a well-defined cylindrical column; but the radius of this column is still larger than the cathode channel radius, due to collisional effects. The net result is a substantial reduction of the charged particle loss due to recombination upon the vessel walls. Consequently, a lower electric field X , is expected in these conditions. b. Constriction of the external column. A further increase of B will reduce the radius of the plasma column down to the cathode dimension. For this effect to be apparent, higher values of the magnetic field are necessary. c. Effects on tlie internal column. The net result of the B action is difficult to predict, but the following considerations can be made; (i) the conditions

t Does not apply to wall-confined, small diameter columns.

HOLLOW CATHODE ARCS

111

for plasma confinement vary along the channel, as the pressure gradient makes the collision frequency dependent on the distance along the channel; (ii) the effect of the magnetic field on the sheath near the cathode wall should be taken into account; (iii) the radial diffusion of charged particles is affected by the magnetic field strength; (iv) the magnetic field effect on the IPC is emphasized for low gas-flow rates (longer IPC). Figure 15A presents the V(Z)characteristics for a long discharge (14) with a high gas-flow rate (very short IPC). Thus, the magnetic field acts mostly on the external column; the rather high values of the magnetic field strength insure that column confinement is well achieved. The V ( I ) characteristics are seen to displace upward as B increases. We consider this effect to be mainly due to the constriction of the external column. The field X , in this column varies as l / o R 2( I , total discharge current; R , column radius; o, external plasma conductivity). The conductivity is not affected by variations of electron density and the B effect on T, is not expected to be important (46b); then X, should vary as 1/R2. In the present case the phenomenon is emphasized by a very long column (3 m), but it is still a rather small effect, since the observed 20 V increase in the discharge voltage represents only a 0.07 V/cm increase in the axial electric field. It must be noted that in this case the current for minimum voltage is lower than 100 A, and is not represented in these characteristics. Figure 15B represents the V(2)characteristics for the same discharge, now for a very low flow rate (long IPC). First of all we notice a global increase in the discharge voltage (as compared with the former, high flow rate conditions), due to the voltage drop in the IPC. In this case, too, the V(Z)characteristics are generally displaced upward for increasing B ; however, the curves have changed their shape and the magnetic field effect is in this region strongly dependent on the discharge current. This may be considered as a consequence of the phemonena occurring in the IPC; however, their intrinsic complexity does not allow for a convincing explanation of this effect. Finally, Fig. 16 shows, forlow values of B, the transition between the diffusion-type external plasma and a well-confined plasma column. It occurs at B 50 G for this experiment; when transition takes place, the Ar plasma changes color from pale pink [(Ar I) dominant], to bright blue (Ar 11) as the column takes shape. In general, when the plasma becomes confined the discharge voltage will decrease; in some cases, a change in the anode drop may reverse this phenomenon. The onset of magnetic confinement can be observed by imposing an alternating current on the magnetic coils and recording simultaneously the variation of the discharge voltage and current (for a given external circuit

-

v (V) 100 1510 G 90 1330 C 80

940 G

70

570 G 360 G

60

o = ~ .a tcm cm'sec'

50

0

0

100

200

300

I(A)

V(V) 150

140

1510 G

130

1330 G

120

940 G 360 G

110

100

0 '0

I

I

100

200

, *

300

1(A)

FIG. 15. V ( I )characteristics as a function of the magnetic field strength for two gas-flow rates ( R = 20 mm, L = 300 cm). From Can0 er a[. (14).

113

HOLLOW CATHODE ARCS

a0

-

60

-

20

-

20

-

0

/

B=50G

B=1OOC B=4OOC B = 200 G

20

0

B=o

40

60

[(A)

FIG.16. Effect of the magnetic field in the range where confinement occurs, for deep plasma penetration inside the cathode channel. ( Q = 0.2 atm cni3 sec-’, R = 1.45 mm, L = 21.5 an). From Delcroix ef 01. (6, p. 405).

and fixed supply voltage). The result of one of these experiments is presented in Fig. 17. It shows that minimum voltage and maximum current occur when the magnetic induction reaches a certain critical value B,. For a given maximum current and fixed gas-flow rate, B, was found to vary inversely

125 G 0

25 A

13 6 A

( 5 r n sec/dlvision)

FIG.17. Alternating magnetic field effect on the V U ) characteristics. Urnax = 25 A, R = 1.05 mm, Q = 0.14 atni cm3 sec-’,f- 50 Hz). From Delcroix et nl. ( 6 , p. 415).

114

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

with the cathode channel radius; its order of magnitude corresponds to Larmor radii of a few millimeters, for electrons of 2-5 eV (3).

3. Efect of the Vessel Pressure (pE < 0.1 Torr) For large diameter vessels and magnetically confined plasmas, the V ( I ) discharge characteristics are not affected significantly by changes in the vessel pressure provided it is kept below a few tenths of Torr ( N regime). The reason for this is that the neutral gas density is not higher than a few times 10'' cm-3 in these conditions? and so the external plasma behaves like a highly ionized one. Its parameters are then determined by the Coulomb collisions, and the electric field is almost independent of the gas pressure. The situation is slightly different if no external magnetic field is present. The plasma fills the vessel volume, and the electron density at the axis may drop to 10'1-10'2 cm-3 (46), depending on the discharge current and vessel diameter. The external plasma is then an " intermediate " one (33, p. 92), and the electron temperature now depends on the neutral density. Increasing the gas pressure in the interelectrode space enhances the radial diffusion and consequently the recombination upon the vessel surface increases; a higher electric field should result. The impact of this effect on the total discharge voltage depends on the interelectrode length and on the overall cathode fall; it may be totally negligible for short arcs. 4. EfSect of the Gas-Flow Rate and of the Cathode Diameter

Increasing the gas flow rate in the N regime while the gas pressure is kept constant generally causes the discharge voltage to decrease for a given current (Fig. 18). The same effect is observed for decreasing cathode diameters (6, p. 417). The very important dependence of the discharge voltage on the gas-flow rate and on the cathode diameter, must be ascribed to the varying length of plasma penetrating inside the cathode channel [which is very sensitive to those two parameters (see Fig. 5 ) ] . Obviously, the external plasma and the anode fall cannot play an important role in the matter. Further confirmation lies in the saturation of this effect for higher gas-flow rates (Fig. 19). When the active zone is located at the tip of the cathode, the overall cathode fall is minimum for that cathode and a further increase in the flow rate yields no change in the discharge voltage.

t The temperature of the gas in the vessel is something between 300 K (wall temperature) and 2500°K (cathode temperature). The corresponding densities for pt = 0. I Torr are 3 x 1015 and 4 x ~ m - ~ .

115

HOLLOW CATHODE ARCS 180

-

'*,

v (V)

140 160

J

'2,

'< z ,.

\I

~-

+?--x-*-a+

100 80 120

60

-

20 -

40

0

1

1

I

L

I

1

I

1

I

1

I

1

FIG.18. Influence of the gas flow rate Q on the V ( I ) characteristics. ( R 7 mm, B = 8 7 5 0 G , L = lOOcm,deuteriuni).* 5.0ati1lCm3seC-', ( . ' 4.0atnicm3sec-', 0 3 . 0 a t m 1.5 atm cni3 s e c - ' . From Gibbons and Mackin (44, 2.5 atm cm3 sec-I, cm3 sec-', p. 1775).

r

70

lo

-

0

t

0

0.5

I

I

I

1

1.5

2

a (otm

cm'sec')

FIG.19. Influence of the gas-flow rate Q and thc cathode radius R on the discharge voltage ( I - 15 A, E = 400 G ) . From Minoo (31, p. 79).

I16

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

In the lower limit of gas-flow rates, the N regime changes into the LQ mode, without an external positive column (maximum wall temperature at the tip of the cathode). It presents a higher voltage than the N regime for the same current. B. The External Plasma

1 . Releoant Parameters From the point of view of the external plasma, a hollow cathode can be considered to behave simply as a high-density plasma source; the outside positive potential is only needed for an electron current to be drawn. The mechanism of plasma production is irrelevant for the time being; it may be reasonable to postulate that no ion current is supplied by the external plasma tothecathode region once the N regime is properlyworking (see SectionV, C). Thus the first logical parameter to consider is the magnitude of the electron current drawn from the cathode itself, which roughly equals the total discharge current. The second relevant parameter is the gas pressure in the cessel, supposed to be low in the N regime (pE < 0.1 Torr); its exact value is determined both by the total flow rate injected into the vessel and the pumping capacity of the vacuum system. The mean free path for collisions between neutral particles is, for this pressure range, greater than 1 cm and possibly as large as several meters. In these conditions strong pressure gradients are not expected inside the vessel, unless deliberately introduced by baffles and differential pumping. The plasma density at the discharge axis and its radial gradient depend strongly on the confining situation; an axial rnagnetic$eld is either present, producing a confined plasma column, or is not (diffusion-type plasma). In a less pronounced way, the density at the axis depends on the anode geometry jointly with the arc length (a short arc with a ring-shaped anode, or a distant end-anode, are two extreme situations). As the external plasma column in an HCA is not fundamentally different from plasmas created by other devices (47), we shall limit ourselves to brief comments on the reported data.

2. Electron Densify The electron density for HCA in the N regime is found to vary between

10" and 10" cm-3 for nonconfined plasmas at moderate discharge currents ( I < 100 A); for confined columns, n, reaches from 10" up to some ~ m - ~ .

Table I1 shows a summary of the results obtained by various authors. The

TABLE I1 SUMMARY OF

Ref.

Authors

(12) Ahsmann et al. (51) Aldridge and Keen (13) Boulassier et a / . (14) Can0 et a/. (52) Flannery et ai. (50) Gerry et a/. (44) Gibbons (40) Gritzmacher et al. (15) Hudis et a/. (17) Kretschmer et al. (53) Leonard (53) Leonard (11) Lidsky er al. (54) McCormick (16) Morse (55) Noon e f al. (56) Roberts and Benett (46) Van der Sijde (57) Silk a

PE (Torr)” 10- 4-1 0 - 2

-

10-4

* 10- 4-2.10-

1

10-3 2 x 10-4 10-5**

I(A)

T, (eV)

TI (eV)

Diagnostic method

7-8

25

1000-2350

1013

5.5

30-50

700-2800 360-1510

1-6 X lo‘.’ 1.2 x 10-14

2.5-7 1-5.5

-

Microwaves; probe Microwaves; emission; probe

> 1013

2-15 L 8 50

0.2

15-20

Double probe; emission Thomson scattering Emission ; microwaves

3-5 3.8

0.40.8

250 5

IN0 150

150

-10-3 ,10-3***

-

n, (cm-j)

-

5 x 10-4

several 10-3 1-2 x 10-3

EXTERNAL PLASMA

-

20

10-3-10-4

B(G)

THE

60-80

4 x 10-5 3.15 x 10-4

1.2 x 10-4 10-3-10-4

MEASUREDDATAON

530 25M50 7000

14x 1-2 x

1013

1014

<0.5

0.25

-

600 1400-2800

2 x 101*-2 X l O I 3

70

4OOO -700

3.4 x 1014

2 4 3.9

50 2-300

4.2

100-1OOO

30

400

2.5 x 1014 1013-10’4 5 x 1013

10 2.3 2.5

3-10 4-8

-

10

-

-700

5-20 20

800 750

3-70

260 100-1500 600

20-75 10

AH measurements in argon gas except * hydrogen;

1.8 x 1014

-

> 10’2

1013

1-2 x 1013

** deuterium; *** h e l i h .

-1 4

Spectroscopy ; power balance at the anode

I -2

-

-

0.2-2 0.3-0.6

Spectroscopy; double probe

Plasma scanner Spectroscopy; probes Microwaves; emission; probe Spectroscopy Spectroscopy Probe Probe Probe Probe Retarding potential Spectroscopy; microwaves Spectroscopy

118

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

electron density increases with the discharge current. (It would be proportional to it (16), if the drift velocity were independent of the current.) Likewise, increasing the magnetic field causes the plasma density to increase at the axis; however, a saturation effect is observed for higher values of B. Figure 20 presents typical results of Van der Sijde (46a), obtained by

0 E N D ANODE 2 0 A 0 E N D ANODE GOA

*

lo'L

10"'

'

210

do

6tO

8;:"

,*:lo

RING ANODE 2 5 A RING ANODE 1 5 6

1 2 : J O ; T ( . - ; )

FIG.20. Electron density vs. magnetic field strength, for different values of the discharge current and anode geometries. ( R = 1.25 mm, p s = 1.25 Torr, vessel diameter 30 cm). From Van der Sidje (460, p. 1533).

phase-shift measurements with a 70 GHz interferometer. Two anode geometries have been studied: plain end-anode, and ring-shaped anode. In this figure the effect of confinement by the magnetic field is observed to set in at about 100 G, where the plasma density grows steeply by two orders of magnitude; the saturation effect begins around 400 G . The effect of the discharge current is also apparent in this figure. The radial profile of the electron density is represented in Fig. 21, by the same author (46b);the constricting effect of the magnetic field is very important at the onset of confinement, becoming less so as B increases. The efolding radius for the electron density is in this case around 18 m m for the higher magnetic fields. The effect of the vessel pressure on the plasma density (and on the plasma temperature as well) may be observed in Fig. 22 [from Hamawi and Lidsky (@)I. It concerns a magnetically confined, differentially pumped HCA in argon; 11, and T, were determined at various radial distances r from the axis to by probe measurements, for vessel pressures varying from 2 x 7x Torr. As the pressure increases the electron temperature is observed

119

HOLLOW CATHODE ARCS

"0

5

10

15

20

25

r(rnrn)

30

FIG.21. Radial profile of the electron density for different values of the axial magnetic Torr). From Van der Sijde (466, field (plain-end anode) ( I = 60 A, pE -:= 1.25 Y p. 1512).

to reduce; this may partly account for the corresponding increase in plasma density on the basis that radial diffusion in a highly ionized plasma is an increasing function of the electron temperature. This point of view is supported by the higher density gradients observed on the constant-p curves, on the left-side of the diagram. External ionization (enhanced at higher vessel pressures) may contribute also to increase the electron density. The factors that caused T, to be a decreasing function of the vessel pressure are dealt with in the next section.

3. Particle Temperatures The external plasma of HCA in the N regime at low vessel pressures displays electron temperatures commonly ranging from 1 to 10 eV, while the ion and neutral temperatures are somewhat lower, typically some tenths of electron volts for Tit and T o .Figures 22-25 and Table I I present some typical results concerning these three temperatures and their dependence on the experimental parameters: discharge current, magnetic lield strength, and vessel pressure.

t In the very high current (150 A), high magnetic field (4 kG) HCA reported by Kretschmer et a / . [17], TI was found to reach 10 eV; even if strong instabilities were present, causing abnormal ion heating, this value seems much too high.

120

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

i pE= 7 0 ~ 1 0torr -~

f

I

"

0

2

I

4

6

8

(0

'.

(8V)

FIG.22. Dependence of n, and T. on vessel pressure; results from probe measurements at fixed radial distances r from the column axis (magnetically confined HCA in argon). From Hamawi and Lidsky (48, p. 134).

The effect of the discharge current upon T, , T i , and To is represented in Fig. 23. T, is observed to present a small increase for growing currents, while Ti and To are obviously most influenced by this parameter, presenting in this current range a steady increase without any tendency to saturate. Figure 24 shows the effect of the magnetic field strength. Comparison with Fig. 20 (17, vs. B in the same conditions) shows that the region between 100 and 400 G corresponds to a sharp increase of the electron density; in this range, T, decreases by about 30%, while Ti a n d To both increase at a much larger rate. In the higher magnetic field range, To stabilizes, Ti and T, increase with about the same slope. Figure 25 concerns the effect of the vessel pressure pE upon the ion temperature at constant discharge current and for two values of the magnetic field strength. It shows that the pressure does not affect Tisignificantly in the range considered.

121

HOLLOW CATHODE ARCS T

( OK:

50x10’

LO x 10’

30x10’

*’ *‘

20x10’

10 x103

0

0

L

1

I

1

I

20

LO

60

80

100

I (A)

FIG.23. Effect of the discharge current o n T,, T i , T o . ( B = 900 G , pa = 1.6 x Torr, ring-shaped anode). From Van der Sijde (46c, p. 718).

Returning now to Fig. 22 we see that, at constant I and B, the electron temperature at a given distance from the discharge axis, decreases when the vessel pressure is increased; it must be kept in mind that the plasma density varies in the opposite sense. The above experimental results are not easy to account for in a quantitative way, as all the measured quantities are interdependent; however, some additional considerations may clarify this problem. Following Hudis et af. (IS)the three temperatures T, , T i , T o , are related through the energy balance equation for the ions. Postulating that the ion temperature is the result of their heating by the Coulomb collisions with the electrons (considering the external plasma to be a highly ionized one), and the cooling effect due to kinetic energy transfer during charge-exchange collisions with neutral particles, one can write, in steady state:t IIi(d/dt)(Ei)

=

R,i - Rio 1 0 ,

t The validity of this equilibrium is insured by the long lifetime of the ions in the column, as they are repelled at the anode by the space charge and pushed away from the cathode by the gas flow.

122

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

44 -

LO

-

32

-

24 -

16 -

8-

17-

0

500

1000

1500 B(G)

FIG.24. Effect of the magnetic field on T,, Ti, To. ( I = 75 A, pr: = I .25 x ring-shaped anode). From Van der Sijde (460, pp. 1533, 1534).

Torr,

where Eiis the average energy of the ion population, and R e i t Ri,are the energy exchange term for electron-ion and ion-atom collisions. It is, or course, surmised that other independent heating processes for the ions are not present (like ion cyclotron resonance, for instance). In those conditions T, > Ti > T o . This problem cannot be solved in a self-consistent way without determining the electron and neutral particle temperatures. With an almost field-free external plasma, the electron temperature is mostly determined by processes in the internal positive column ; there the electrons emitted by the cathode wall are accelerated by the cathode sheath potential (in a long IPC it can reach 40-50 V). Their energy decays afterward

G

123

HOLLOW CATHODE ARCS

1 0.71 A

(ev)

0.8

-

=2'akG

0 6

k

4

'

1

2

:

0.4 0.3

-

o0.10

.

3

5

7

z

9

11

13

15

P, (los4 Torr)

FIG.25. Effect of the vessel pressure on the ion temperature, for two values o f the magnetic field ( I = 40 A, differential pumping, hollow anode). From Hudis et al. (U, p. 3298).

through successive elastic and inelastic collision with the neutrals inside the cathode channel. At the beginning of the interelectrode space, the electrons present a thermal energy between 2 and 10 eV; possibly, a population of fast electrons up to 50 eV is still present. This high-energy tail will wear off along the plasma column, due to inelastic collisions with the neutrals and Coulomb collisions. The latter achieve the Maxwellianization of the distribution function with high efficiency, for the corresponding mean free path is typically 1 cm, smaller than the plasma dimension. In those conditions, it is expected that the value of T , in the external plasma does not differ strongly from its value in the cathode region, even if somewhat lower; its exact value depends on the losses by collisions and on the lifetime of the electrons in the column before collection at the anode, or surface recombination on the vessel walls. As to the neutral particle temperature its radial profile is determined by a radial heat conduction equation, taking into account the boundary condition To = Twa,,for r = R,,,,,, , and the heat-transfer processes in the central region of the discharge, mainly, charge-exchange collisions with ions in the column,

124

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

longitudinal heat conduction along the discharge axis, and gas heating inside the cathode channel. Gas-injection conditions into the vessel and neutral gas pressure are obviously relevant parameters for the radial profile of T o . Commonly accepted values of To include (a) ambient temperature, as it would be imposed by the vessel walls (15) (300”-400”K), which seems too low a value for the central region of the discharge; (b) around 2500”K, as it would result from thermal equilibrium with the cathode wall-which is reasonable for cathode-fed HCA of short length, at low vessel pressure (32); and (c) up to the order of 1 eV (46b) if strong heating from ion collisions is expected. If, on the other hand, T, and To are considered to be known through measurements, the ion energy balance equation may be used to do a n independent check of Ti. Referring now to the ion energy balance equation, the terms corresponding to the electron-ion and ion-neutral energy transfer, respectively, may be written as (49, 58) qc2qi2 n, ni me In A ( 1 - Ti/Tc) R CI. = ‘ 271 cO2(2nm, K TJ“’ mi Rio N (8/n)’i2n, no ci0[(KTo+ KT,)/mi]”2(kT, - kTo),

where oio is the charge-transfer collision cross section between ions and neutral atoms. For steady-state

where T, is a reference temperature for comparison of the Coulomb cross section with the nearly hard-sphere cross section for the neutral-ion collision; T, is given by

or, in more practical form

lo4

T, (”K) = 6.6 x

where A is the atomic mass of the gas (40 for argon). On the basis of the preceding discussion, let us consider To and Te to be determined independently so that their ratio ( a = To/Te< I ) is a “known” quantity; we calculate Ti= x T, from the equation 1-x

(s- a)(..

+

which we solved numerically (Fig. 26).

2

125

HOLLOW CATHODE ARCS

'

P=Ti'Tp

:To / T , = 0.5

0 '

0

I

5

I

10

I

15

FIG.26. Diagram for the theoretical prediction of the ion temperature and the ionization degree are known.

I

)

20

c ,when T,,T o ,

Considering In A to have only a small dependence on n, and T,, we take In A = 10 (59) and, for the argon gas c,"= 7 x lo-'' cm2 for Ti < 10 eV (60); then T, N 104"K, of the same order of magnitude as the electron temperature in HCA, even if somewhat lower ( T , -2-5 eV). Then, the interpretation of the curves of Fig. 26 is straightforward. When the plasma in the external column is highly ionized (low vessel pressure, magnetically confined column), the situation fits the left-hand regions of the plot where T , approaches T, (.Y -+ I ) , becoming significantly higher than To (x > a); in the opposite situation (higher vessel pressure, nonconfined arc) Ti To (x a), being much smaller than T,. Finally, let us remark that the ion temperature is extremely sensitive to small variations of the vessel pressure, in the highly ionized region of the diagram [small values of (n,/n,) (T,/Tc)2],while for lower ionization degrees it must be almost independent of the vessel pressure. These conclusions are consistent with the experimental data presented in Figs. 22-25; however, a poor accuracy is expected if T , were evaluated from

- -

126

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

the balance equation.7 I t should further be noticed that the neutral gas temperature is the most difficult to evaluate experimentally and is subject to large uncertainty (46b);obviously thevalues we have been considering concern the gas temperature in the plasma region, as it would be measured spectroscopically. To conclude this section, we must remark that several authors (f2,14, 46, 61) have studied the influence of the gas-flow rate on the external plasma parameters. Unfortunately, as far as we could ascertain from the reported data, those experiments were made without the precaution of keeping the vessel pressure constant while the gas injection was varied; thus, it is difficult to ascribe the reported effects to the gas-flow rate variation, or to the joint effect of changing the vessel pressure.

C. Oscillations and Noise in HCA 1. General Coninients

Let us now review the reported data on the noise and oscillations in an HCA. Generally speaking, the external plasma may display different kinds of spontaneous density fluctuations such as plasma rotation, possibly with deformation of the cylindrical shape of the column, coherent oscillations, possibly nonsinusoidal (discrete spectrum), incoherent oscillations in some frequency bands (continuous spectra due to random fluctuation of phase and amplitude, causing uncertainty in frequency definition), wide spectrum, random oscillations (white noise). The study of these different kinds of oscillations has been the subject of many reports in the literature, dealing mostly with the description and identification of the nature of the observed fluctuations and trying to find their origin. If one succeeds by proper means to damp nearly all kinds of oscillations, then a quiescent plasma can be obtained with an HCA. The experiments are generally conducted by picking up the fluctuations of density with adequately biased Langmuirprobes. Direct frequency measurements are possible for quasimonochromatic oscillations, or with a wave analyzer for coherent oscillations, but only if the background noise is not too high; otherwise, autocorrelation of the measured signal yields the corresponding power spectrum through Fourier transform. Central frequency and linewidth measurements are then straightforward. Proper identification of

t Such a n attempt is reported by Hudis ei ol. (15). with qualitative agreement between experimental and calculated values of T , . I t should however, be noticed that the authors considered To == 400 K , which seems too low a value in the plasma region. The balance equation presented here is believed to be niore accurate for computing T , .

HOLLOW CATHODE ARCS

127

modes requires the use of adequately placed probes along the plasma; cross correlation techniques provide detection of phase shifts between different points. This way, the propagation path, the direction of propagation, and the azimuthal mode number of a given wave can be inferred. Rotation velocity of a fluid of ions can be measured spectroscopically as the corresponding lines will be Doppler-shifted with respect to reference emission; deflection of a movable device and streak photography can also be useful to measure rotational velocity (5f). 2. Arc Rotation Although arcs are known to display rotating instability, generally associated with hot spot motion, HCA plasmas have been reported to rotate, even if a localized hot spot is absent. The aximuthal macroscopic motion of the charged particles may deform the cylindrical shape of the column, so that a “Jlutelike” rotating vane may develop as in the experiment described by Morse (16). In this experiment, probe measurements in the region outside the central core of a magnetically confined HCA showed rotation for B > 350 G; at the same time, the plasma grew eccentric in relation to the axis, as shown in Fig. 27 A. The angular velocity was found to be an increasing function of the magnetic field strength, corresponding to about 2 kHz. The author suggests this motion to be due to an E x B drift which is compatible with an outward directed radial electric field; evidence of this is presented in Fig. 27B, showing an inversion of E, outside the plasma core, as compared to the inward E, before the instability appeared. Previous theory by the same author predicted that, for the calculation of the rotation period

T,

= 2nBz/E,

one should take E, = 0.9 E,, where E, is a “corrected” field given by:

where Eo is the measured (outward) radial field; r o the e-folding distance for the unperturbed density gradient; W T is the product of the cyclotron frequency with the collision time of the relevant charged particle upon the neutrals. In Fig. 27C the calculated period is seen to agree fairly well to the measured one. It is interesting to note that in this experiment the plasma did not rotate in the central core of the column, while a somewhat similar instability reported by Hudis ei al. (62) behaves differently. Again a rotating azimuthal rn = 1

128

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRlNDADE

“1

1000

CALCULATED

I

MEASURED

t

012

300

400

500

1

600

700

-

B(G)

FIG.27. Plasma rotation in two experiments. From Morse (16, pp. 51 8,519) ( I = 10.5 A, Torr, R = 1/16 in., L = 13 in). A. Lines of constant density ( m = I ) ; B. space potential before and during unstable regime (f= 2 kHz); C . measured and calculated rotation period. From Hudis et. a1(62, p. 199 63). D, E. Sense of rotation and corresponding space potential (f=8.4 kHz, in = 1); F. Sense of rotation for a smaller magnetic field ( m = 2, f= 2 X 25.4 kHz).

p ~ 6= X

HOLLOW CATHODE ARCS

I29

instability (f=8.4 kHz) is observed but in the opposite direction, only compatible with a Hall drift if E, is pointing inward (space potential increasing with radius). As a matter of fact, this situation occurs in this case (63, with the further detail that inversion of the field in the plasma core causes it to rotate in a reverse sense with respect to the periphery. Figure 27 D,E provides data for comparison of both experiments. Furthermore Hudis et al. (62) report that an m = 2 azimuthal rotation ofthe core of the column occurs a t f = 2 x 25.4 kHz for a threefold reduction of the magnetic field strength without apparent rotation of the plasma periphery (Fig. 27 F). The sense of rotation would again be compatible with E, pointing inward. However, as stated in another report on the same experiment (64) the authors believe the instability to be caused by a drift wave due to a radial density gradient; Hall rotation would be, with this point of view, a superimposed effect, increasing the measured frequency (see Section V, C, 3). Quite the opposite point of view is taken by Aldridge et al. (51). Theory by these authors shows how a Hall-induced rotation can create growing instability, with a frequency and a growth rate closely related to the rotational E x B velocity. This angular velocity is given by [see also Boeschoten and Demeter (61)] wR =

- V,/r

I

+ (I/%’) + ( VE/rw,)’

where Y E is the azimuthal drift (Hall) velocity due to the radial electric field, and a is the product w ,T ,(gyromagnetic frequency and collision time pertaining to ions). This expression is only accurate for w , < 0,.Using a plasma slab model ( B = B Z ,density gradient parallel to OX, drift along OY), with the assumptions that k, = 0, kZ = 0 (no “radial” or “axial” propagation), a I , k, = 177/r0 of the order of the inverse scale length for gradient of the unperturbed density, a, given by a = l / t i o (dn’ijax) one obtains an instability of complex frequency w with

which presents a positive growth rate if Im (0) < 0 ; this requires w,/a < 0 or, which is the same, EJa > 0 (density and space potential increasing in opposite radial senses). Experiments with a HCA yielded satisfactory agreement between theoretical predictions and measured data, as it is seen in Fig. 28.

130

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

12

-

-

0 -

-

4 -

-

0 .

f(kHz)' 25

PREDIC?ED VALUES

20

-

15

-

10

-

11

5' 0

I

0.5

EXPERIMENTAL VALUES

I

1.0

I

1.5

1

2.0

I

2.5

I

3.0 B ( k G )

(b)

FIG.28. Comparison between theory and experiment for an azimuthal instability induced by a radial electric field [I=25 A; Q ==2.5 atm cm3 sec-' (cathode) and 0.3 atm cm3 sec-' (anode)]. W , T ~G 1 in the cathode region, W ' T ~> 1 in the drift tube. (a) Rotational velocity at various radii vs. magnetic field strength, -__ theoretical predictions, . . . . measured data. (b) Frequency of the m = 1 instability vs. magnetic field strength. From Aldridge and Keen (51, pp. 10, 14).

Another experiment with a much denser plasma (2 x loL4cmP3) higher current ( I = 150 A) and magnetic field strength up to 5 kG, is reported by Krestschmer et al. (17). Plasma rotation is observed at a frequency of 137 kHz at 3.3 kG. However, the authors do not identify this rotation with the presence

HOLLOW CATHODE ARCS

131

or an E, x B drift, for the hollow anode they use is supposed to prevent important radial electric fields from building up in the plasma column. Instead they show, by means of the single-particle fluid theory, that the ion diamagnetic drift frequency wd corresponds to one-half the ion cyclotron frequency in the conditions when a maximum radial gradient of density is compatible with magnetic confinement. The value of this gradient (for w = coi/2) is given by (KTln

17

+ ycp) = $nrwi2.

This mechanism is only possible if the ion Larmor diameter is compatible with the arc radius (limited by the electrode dimensions); these conditions occur for this plasma. The most abundant species in this discharge is the ion A r f + ; the corresponding value of wi/2 matches the rotational velocity measured by the Doppler shift technique. Plasma rotation in the absence of an external magnetic field can also occur in HCA outside the N regime of operation; in the high-pressure regime, when pE > 10 Torr, an anode spot is observed to form. If a hollow anode is used, this spot rotates about the anode tip and the plasma column turns accordingly around the column axis (36); this is a known type of instability which is not characteristic of HCA (65, 66), and is more apparent at high current. The low-current regime, when a hot spot appears on the cathode tip, provides another example of rotational motion due to spot movement (21). 3 . Ion Acoustic Waces ldentification of ion acoustic waves is thoroughly convincing in the experiment reported by Gunshor et al. ( 4 5 ) . Probe measurements and cross correlation techniques have shown the following propagation characteristics of the oscillations in He, Ne, Ar, and Kr: (i) Frequencies (in the range of 2-12 kHz, depending on the gas) are inversely proportional to the arc length (Fig. 29A). Detection of no phase shift between probes at constant azimuth and radius, spaced along the arc, confirm the character of axially standing waves. (ii) Cross correlograms of signals from two orthogonally spaced radial probes at fixed abscissa display a rr/2 phase shift, thus showing an 111 = 1 azimuthal propagation, in the sense of the electron diamagnetic drift (axial B, inward it-gradient). The authors consider this to be a propagation at an angle to the axial field, possibly influenced by the plasma rotation. As the radial electric field is directed inward in this experiment, rotation occurs in the direction of the electron diamagnetic drift; allowance for ion diamagnetic " slip " must be considered.

132

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

A

f (kHr)

14

-

12

-

10

-

oo”o N e

8 -

0 246 I

20

-

10

-

I

I

1

I

I

c

I

5 -

Kr

2 -

1

I

I

I

I

1

1

D

FIG.29. Identification of an ion acoustic wave in an HCA: wave frequency vs. the reciprocal arc length and the atomic mass (I=20-30 A , R = 1/16 in., Q 0.11 atm cm3 sec- I , p e Torr). From Gunshor et a / . (45, p. 1764).

-

133

HOLLOW CATHODE ARCS

(iii) The oscillation frequency is found to be a decreasing function of the ion atomic mass M ; logarithmic plot offvs. M shows good agreement with a theoretical straight line with slope - 1/2 (Fig. 29B). (iv) Finally, the frequency is found to be almost insensitive to variations of the discharge current. As this is roughly proportional to the plasma density, a drift wave (density dependent) must be excluded. Experimental data quite agree with theory. The frequency for an ion acoustic wave propagation in these conditions is given by w = k , oD

+ (1 + kk,’, ,(ykTe/mi)”2 y kTe/miwi)

2 112’

where T, is the electron temperature, y the ratio of specific heats, wi the ion cyclotron frequency, k , , = n/L, k, = rn/ro, where m is the mode number (azimuthal) and L , y o , the characteristic arc length and radius. So, the rotational velocity is the net result of a Hall rotation in the E x B sense, deducting the ion diamagnetic velocity (which is in the opposite sense because E is inward). With the proper values (measured) of B and ro (where the density gradient is maximum), and with an accommodating factor 1/2 for the measured radial electric field, kLt>Dis found to be about 1.5 kHz, in good agreement with the ordinate at the origin on Fig. 29A. The ion acoustic waves appear at relatively low vessel pressures. If pE is increased, the line profile is observed to broaden and a drift wave appears instead (45, 55). 1lD

4. D r f t Waves

In the experiment reported by Chung et al. (64) already mentioned, identification of an unstable drift wave follows from the evidence: (i) The wave is localized near the region of maximum density gradient ( y o = 2.2 cm) and the fluctuations decrease exponentially toward the axis ( r = 0). Figure 30A shows the mean square potential fluctuation vs. the radial coordinate. The result of a cross correlogram at constant abscissa shows an m = 1 azimuthal mode to occur, in the direction of the electron diamagnetic drift. (ii) The measured frequency falls within the range predicted by theory. Neglecting axial propagation in an inhomogeneouscollisionless plasma with an axial magnetic field B,, the frequency of oscillation of the drift wave (w 4 mi) rotating in the sense of the electron diamagnetic drift is given by w = u d with

134

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

(arb. units)

1

0

0 (

I

I

1

I

1

2

3

4

5

p h - ' Torr) E

b)

FIG.30. Identification of a drift wave ( m = 1) in an HCA ( B = 2 kG, T, = 3 eV; (l/n)(an/ar)= 0,5 cm-I). (a) Mean square value of space potential fluctuation and azimuthal wave number m, for different radial distances. (b) Measured wave frequency and electron temperature vs. vessel pressure p E. From Chung and Rose (64, p. 248).

The fact that this wave is superposed on a Hall drift with the same direction (E, inward) causes the measured frequency to be somewhat larger than the calculated wd = 5.5 kHz (for Bo = 2 kG, T, = 3 eV, k1-' = 2.2 cm, (l/n) (an/&) = 0.5 cm-'). The effective measured frequency of 8.4 kHz shows quite an acceptable agreement betweeen theory and experiment. (iii) As the plasma column is more constricted when B, is increased, the quantity [ ( k , dn/ar)/nB,] is expected to be almost independent of the magnetic field; wave frequency measurements at different values of B without

135

HOLLOW CATHODE ARCS

significant differences, support this point of view. However, one would expect the measured frequency to be affected by different values of Hall drift unless EJB, is (again) almost constant with B, . (iv) Dependence of the drift wave frequency on T, as predicted by the equation above was checked by independent measurements of o and T, while the vessel pressure was made to change. Figure 30B shows again satisfactory agreement as to this point.

5 . Coexistence of Ion Acoustic and Drft Waves Several authors (17,45, 55) have observed ion acoustic and drift waves in HCA either coexisting or changing into the other, by suitable (sometimes slight) variations of the experimental conditions. In an article by Noon et al. (55) a detailed study of conditions of existence was reported. The fundamental parameters were found to be the vessel pressure and the magnetic field, their effects being strongly related. Figure 31 illustrates this point. As can be seen, for a fixed magnetic field of 1 150 G, ion acoustic waves exist at the lower vessel pressures. Their amplitude drops quickly in the range 1-2 x Torr, while the drift wave amplitude is at first an increasing function of pressure, decreasing again beyond about 6 x Torr. At constant vessel pressure ( Torr) ion acoustic waves appear for B > 250 G reaching maximum amplitude for B 500 G. At the higher (6 x Torr) vessel pressure, drift waves are dominating, their amplitude increasing with the magnetic field strength. These results were theoretically predictable. Increasing B causes the plasma diamagnetism to be reinforced, as well as reducing the ion Larmor radius. Both effects are known to enhance conditions for instability of dissipative drift waves [see Kadomtsev (67),p. 991. On the other hand, both waves can be unstable at the lower values of gas pressure and magnetic field: the ion acoustic wave is damped for increasing pEand B (both parameters leading to higher plasma densities).

-

6. Other Types of Coherent Oscillations

Besides the oscillations reported in the previous sections, some other results are worth mentioning. Kretschmer et al. ( 1 7 ) (see Section V, C, I ) describe a hollow cathode, hollow anode arc at high magnetic field (4 kG) and discharge current ( I50 A). The high ion temperature measured in those conditions is related to the presence of important instabilities, namely an azimuthal m = 2 mode, corresponding to a traveling wave along the magnetic field. The wave propagates in the direction of the electron diamagnetic drift, with a wide spectrum and

I36

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

1

/

S

3

FIG.31. Simultaneous excitation of drift (D)and ion acousitc ( A ) waves in a HCA; amplitude (arbitrary units) vs. B and p e . From Noon el a / . (55, pp. 10, 14).

broad band of frequencies centered at 45 kHz; it is independent of the magnetic field strength. This is identified asadeceleratedAlfvPn wave(67,p. 84). This oscillation occurs with cathode gas feed. With anode gas feed only, a coherent oscillation, nonsinusoidal (eight largeamplitude harmonics) isobserved a t f = 14 kHz. It is an azimuthal m = I mode propagating in the same direction as the former wave, but its frequency is proportional to the magnetic field strength. It is identified as the driftresistiue wave compatible with finite plasma conductivity (67, p. 84). Again with gas feed through the anode a radiallypropagatingrn = Omode, axial standing wave is observed. It is the slow AlfvPn waue excited by the

HOLLOW CATHODE ARCS

137

B, x Vn radial diamagnetic drift ( B , is induced by the intense longitudinal current). With combined anode-cathode gas feed the coherent oscillations disappear, except in the range = I kG, where a m = I ion cyc/otron wave is observed. In a report by Chung ( 4 )axial , propagation of a n , f = 75 kHz wave (almost exactly the ion cyclotron frequency for the value of B used) was observed. This oscillation was nonsinusoidal, with a large amplitude of harmonics and was more intense in the central core of the plasma column. However, a small addition of gas feed through the anode reduced considerably the amplitude of the harmonics. For a magnetic field in the cathode region beyond a critical value (keeping constant B in the column), the oscillation disappeared. For values of B in the cathode region, far beyond this critical value, fluctuations were observed near the plasma edge. Both oscillations are identified as electrostatic rriodes propagating axially. The higher frequency wave ((0 wi) was found to have a phase velocity close to that of the ion acoustic wave. In a n HCA experiment reported by Minoo ( 3 0 , without magnetic field, coherent oscillations in the range 2-4 kHz were observed when a hollow anode heated by the discharge current was used. The oscillation frequency is a linear function of the discharge current and (approximately) of the vessel pressure, up to about 4 x lo-* Torr (where the oscillation disappears). The frequency varies inversely with the anode channel diameter which suggests that this electrode plays a n important part in the instability. Although it is not directly related to this section, where only self-excited oscillations were described up to now. we shall mention that several authors have studied wave propagation in HCA excited by external means. Ceglio ef al. (68) accomplished wave generation by means of a coil wound around the plasma column. using frequencies in the rf range t o perturb locally the applied steady-state B field. Waves were observed in the range near and above the ion cyclotron frequency; normally two superposed waves, a n ion acoustic and a fast wave were observed, propagating along the discharge axis and with n o phase structure in the transverse direction. N o cyclotron resonance effects were noticed. in spite of the product w i t i 2 5 being rather too large to d a m p the effects of resonance. I t is worthwhile mentioning the important work of Keen and Aldridge ( / 9 . 5 / . 69-72) in the field of nonlinear wave mixing in a n HCA. By means of a n externally applied electromagnetic wave. o r using a feedback technique with a suitably amplified part of a self-excited wave, reinserted in the plasma with an adequate phase shift, these authors were able t o enhance o r subdue plasma oscillations in the column and to determine experimentally the dispersion curve for drift waves in an HCA plasma. To excite density oscillations

-

I38

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

in the plasma, either magnetic field coils at different azimuthal positions or symmetrical plates around the periphery of the column, were used. When oscillations with suitable phase shifts are imposed at those points, different m modes can be excited easily. 7. Incoherent Noise Let us now examine the wide-spectrum noise in HCA. In an exhaustive study of oscillations in an HCA column, Noon et al. (55) present the result of a measurement performed in the situation when the coherent oscillations are unimportant (intermediate magnetic field strength, B = 770 G). The signal is picked up by a floating probe; its frequency spectrum is shown in Fig. 32A, for two values of the cathode gas-flow rate. Ascan be seen, the noise amplitude for this value of the magnetic field depends strongly on the vessel pressure, which in this experiment is determined by Q : a 20 dB decrease of the to 7 x 10-4Torr. noise amplitude is observed whenp, ( Q )increases from The amplitude of this turbulent noise spectrum shows a n f - ’ dependence for the most part of the frequency range. The dependence of the noise amplitude on the magnetic field strength is not explicitly described in this report; it is only mentioned that the incoherent noise level increases about 30%, in the conditions where the coherent oscillations are suppressed. This is done by a reinforcement of the magnetic field strength in the cathode region only. The same effect of the vessel pressure on the noise amplitude is described by Minoo (.?I), in an HCA without confining magnetic field. In the pressure range where coherent oscillations are absent, the white noise level is a decreasing function of the vessel pressure (Fig. 32B). 8. Noise and Radial Diflusion

Studies on instabilities in a magnetically confined plasma column are closely related to the problem of determining the radial diffusion regime. A collisional (“ normal ”) diffusion yields a transverse diffusion coefficient proportional to B - * ; with the onset of turbulence, radial losses increase and D, becomes proportional to 1/B (“enhanced” or Bohm diffusion) (72a). For a fully ionized plasma of different ionic and electronic temperatures, the radial ion flux Tr may be written (52), for the normal diffusion regime

ev .

a

r r =-el - [n,(T, - Ti)] new,’ ar

(Spitzer)

or

eve,

rr= - new,’ -(? ar [ n e ( T e- Ti)]- 12 n

’-“I ar

(Kauffman),

HOLLOW CATHODE ARCS

I39

NOISE R M S AMPL. (dB)

+ 20

i: 0.15

FIG.32. Epiect of the vessel prcssure o n the white noise amplitude. (a) White noise spectrum ( I - 20 A, B 770 G , R - I .58 nini). From Noon er rrl. (55, p. 481). (b) Relative amplitude of incobcrent plasma fluc[lS?tions ( B 0 , I IS A, R = 1.3 mm, L - IS cni). From Minoo (31, p. 45). ~

~

~

where ( J I ~is the electron cyclotron frequency. These expressions differ by a corrective term, the second one being in principle more accurate. The c~rihar~cetl iori ra(lialLflirx is given by

where the numerical factor

ct

is taken as 1/16 in the theory by Bohm (72m),

I40

JEAN-LOUP DELCROIX A N D A R M A N D 0 ROCHA TRINDADE

while Yoshikawa et af. (73) considers it as a function of the relative mean square density fluctuation, S CI =

$ITS

with

S

=

( ( n - no)2)/no2,

no denoting the unperturbed (quiescent) plasma density. The latter author establishes a criterion for the existence of one of the two possible regimes of diffusion. If one assumes that the mean square relative deviation of the density fluctuation, S, is independent of the magnetic field (which is not often the case, as we have seen in the preceding section), one compares it with the nondimensional quantity a, defined as the ratio of the collision and gyromagnetic frequencies a = v/w,

and one gets the desired criterion S % a -+ Bohm diffusion, S @ a -+ normal (collisional diffusion).

The validity of the above equations for an HCA depends on the degree of ionization, because they neglect the ion-neutral collisions. In a highly ionized plasma the equations apply and the diffusion is ambipolar. Otherwise, a radial electric field may exist or not, depending on exact experimental conditions (52). Several experiments report an inward-directed radial field or some volts per centimeter, although its exact value is not very accurately known, due t o the perturbing effect of the magnetic field (52, 55, 62). Indirect measurements of the radial diffusion rate are complicated by lack of accurate knowledge of other losses of charged particles (axial drift, volume recombination, charge-exchange collisions); on the other hand, the direct measurements are complicated since they tend t o introduce perturbations in the diffusion regime. However, some results are worth mentioning. Flannery ef a/. (52) use a diffusion wave technique to study the secondary plasma around the central core of the plasma column. The waves are excited by means of an alternating current superimposed on the discharge current (74). Measurements of the spatial distribution of the phase and amplitude of the radial traveling (diffusion) wave yielded data for comparison with the theoretical predictions of the various diffusion regimes. The collisional theory (Spitzer) seems the one t o best fit the experiment, when the plasma is quiescent (R = 0.318 cm; I = 5 A ; p E = Torr; B = 530 G ; L N 30 cm). In those conditions, the difference between the theoretical and (indirectly) measured diffusion coefficient is only 20% (D,= 2.8 lo3cm2 sec-' for the latter). When the magnetic field strength was different from this optimum value so that the plasma was no longer quiescent, measurements yielded a smaller phase shift of the radial wave, showing a higher diffusion velocity, consistent with a transition to an enhanced (Bohm-type) diffusion regime.

141

HOLLOW CATHODE ARCS

Hudis and Lidsky (75) used a one-sided, rotating probe t o evaluate the radial ion velocity in an HCA column (5 = 1.1-1.8 kG) ni(r = 3.5 cm) = 5 x 10" ~ m - T, ~ = ; 1-2 eV). The probe was positioned eccentrically ( r = 3.5cm), orthogonal to the column axis, so that its active side faced alternatingly upstream and downstream relative t o the radial ion current. From the difference AZsi between the extreme values of the ion saturation current, the electron temperature, and the plasma density, an appropriate relation yields the ion radial velocity ui A],' (L'(Ul/Uo)' - e-(Ux/Uo)2) u0 = ( 2 k T , / t ~ ~ ) ' ' ~ .

Using this technique, the radial diffusion rate is observed t o decrease strongly when the magnetic field strength is higher than a critical value ( B = 1.54 kG) (Fig. 33), showing a definite change in the diffusion regime. Simultaneous

3.9

-

3.3

-

2.7

-

2.1

-

1.5

-

0.9

-

-5 - L

- 3

FIG.33. Radial velocity and plasma density in the secondary region ( r = 3.5 cm) of an HCA column, as a function of the magnetic field strength. Radial velocity, 0 plasma velocity. From Hudis and Lidsky (75,p. 146).

measurements of the density fluctuations have shown, by spectral analysis, that the higher diffusion rate region was associated with the presence of a coherent, f = 12 kHz instability, strongly damped past that critical value of the magnetic field strength. For the quiescent situation, the calculation of the diffusion coefficient agrees with the predictions of the collisional theory. A similar conclusion is drawn by Noon et al. ( 5 3 , ascribing the situation of enhanced diffusion to coherent fluctuations of the plasma density, rather than t o wide-spectrum turbulence. In their HCA experiment (R = 3.85 mm; I = 2 0 A; p E= Torr; B=200-2000 G), they found that the local

142

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

variation of the magnetic field strength at the cathode region determined the amplitude of an observed coherent oscillation identified as an ion acoustic wave. Variations in that amplitude were concomitant with substantial changes in the density radial profile, without significant differences of the incoherent noise level. Calculating the transverse coefficient D, from the knowledge of the e-folding distance, q, of the density profile, supports the viewthat enhanced diffusion is present. Since this coefficient is proportional to y 2 (SS), a q dependence on B - ' / 2 as they observed, means that D , is inversely proportional t o the magnetic field as in Bohm diffusion. Moreover, the magnitude of the calculated coefficient is considerably higher than collisional diffusion predicts, again suggesting an enhanced diffusion. Can0 and Mattioli (76),working with an arc of higher density and higher neutral pressure (I = 250 A ; Q = 8.5 atm cm3 sec- I ) and without the presence of instabilities, calculate the diffusion coefficient in the two hypotheses of normal and enhanced diffusion and find them to be, for their experimental conditions, of the same order of magnitude. They raise an interesting point: since in some conditions the plasma density can increase almost linearly with the magnetic field strength, the normal diffusion coefficient, proportional t o n/B2, can present a n overall dependence as B - ' , yielding the misleading conclusion that an enhanced diffusion might be present. Working with lower gas-flow rates ( Q < 1.4 atm-cm3-sec-'), these authors found that the density fluctuations increase substantially and that in those conditions Bohm diffusion might be present, under Yoshikawa's criterion (S/a %- I ) . Direct measurement of the radial current can be made by means of a suitably biased auxiliary annular electrode placed around the plasma column. Extrapolation of data obtained with variable bias, in the very low bias range, can yield information on the diffusion regime. Yoshikawa and Rose ( 7 3 ) report such an experiment; the ratio I/Vfor the auxiliary ring electrode should be proportional to either n / B or n 2 / B 2 , according to the regime of radial diffusion. The authors find that classical diffusion is present in the lower range of magnetic field strength. and approaches the theoretical predictions of Bohm diffusion when the magnetic field is increased. This is in accordance with the already mentioned criterion t o distinguish between Bohm-type and normal diffusion (S/a % I =+. large magnetic fields correspond t o enhanced diffusion). Figure 34A illustrates the results of this experiment. A similar experiment was performed by Chung and Huang (77) using a ring collector composed of four identical parallel thin rings, the two inner ones being biased with respect to each other, and the outer ones floating so that the diffusion regime is not disturbed. Figure 34B shows the collected current; a transition is observed to occur at a magnetic field of about 1.2 kG. I n the same figure the relative rms density fluctuation is plotted as measured by probes at I .25 cm distance from the column axis. Clearly, the transition in the

143

HOLLOW CATHODE ARCS

o

-

I, (mA)

- n* “0

18

10

0.2

0.1

TRANSITION I

0 700

1200

1700

-

2200

B(G)

(b) FIG.34 Direct measurement of radial diffusion. (a) Voltage-current ratio for a ring collector; solid curves represent theoretical predictions. (Q= 1 atm cm3 sec- I, p c several 10 Torr, L 12 crn, I = 20-50 A S I , = 30mA). From Yoshikawa and Rose (73, p. 338). (b) Collected radial current and relative rms density fluctuation (Q= 1 atm cm3 sec-‘, p F - 2 i. Torr, L = 2 m, I = 20-40 A). From Chung and Huang (77, p. 35). ~

144

JEAN-LOUP DELCROIX A N D A R M A N D 0 ROCHA TRINDADE

diffusion regime is related to the onset of an instability, in this case identified as an m = 1 ion cyclotron instability (f= 70 kHz). 9. The Quiescent Plasma Machine

Let us recall briefly some useful information about suppressing or subduing oscillations in an HCA, as it was presented in the preceding sections: ion acoustic waves, which may originate in the cathode region (55), are damped by a suitable increase of the magnetic field strength of the neutral gas pressure at the cathode region; drift waves can be suppressed by lowering the magnetic field strength or the vessel pressure at the column region(see Fig. 31); cyclotron waves do not exist at too low or too high magnetic fields ( 1 7 ) ; combined anode-cathode feed of the discharge tends to damp or even suppress some instabilities (17, 41). All these points are relevant to understanding the remarkable performance of the device designed by Woo et al. (18, 78) for the production of a quiescent plasma (Fig. 35). The machine is composed of a cathode region ( I ) and a drift REGION

REGION

- D R I F T TUBE R

E

t

l

O

N

d

CATHODEp FEED

ANODE

FEE0

FIG.35. Diagram of the HCA quiescent plasma machine. From Woo ef a / .(78, p. 13 I ) ,

tube region (3) separated by a short baffle region (2). The relevant parameter for the design is the product w i * t i(ion cyclotron frequency times collision time), which is made much higher than unity in the drift tube by means of an energetic pumping; in those conditions, the plasma tends to run quiescently. In the cathode region, when the gas flow imposes a moderate pressure, O ~ @ T ~1 is the normal situation. However, changing the local value of the magnetic field can suppress most of the instabilities. The transition between

HOLLOW CATHODE ARCS

145

the two zones is assured by an intermediate step in a region where mi T~ z 1 ; in this baffle region a universal instability can, in principle, exist (79),for long axial wavelengths. Thus, a short length of this region is unsuitable for this type of oscillation and we can expect the plasma to be quiescent in the drift tube. In such a device, relative density fluctuations as low as lo-’ were observed experimentally in the drift tube. Construction details can be found in Woo et a/. (78); a similar device is described by Aldridge and Keen (51).

D. The Cathode Region 1. Cathode Wall Temperature

The cathode wall presents a maximum temperature at some distance (measured from the tip), in the N regime. This distance is strongly dependent on the gas-ffow rate and on the cathode internal diameter (see Fig. 5); in a less pronounced way, it depends also on the discharge current. As t o the dependence on other experimental parameters: 1 is found to be independent of the vessel pressure p E provided it i s lower than about 0.1 Torr; a slight decrease i n the distance occurs in the case of a magnetically confined discharge, as compared to the case B = 0 (31, p. 74). This effect is only detected when I is long enough. Referring to Fig. 7 (Section 111, B). it will be noticed that the T(x) curves become flatter when 1 is made to increase at constant discharge current by gas-flow rate reduction; simultaneously. the absolute value of T,,, decreases slightly. This effect is qualitatively explained by the effect of a more extended ion bombardment of the cathode wall, compatible with a longer internal positive column. The higher sheath potential and corresponding enhanced ionization rate in the IPC balances the lower thermionic emission associated with the T,,, reduction. As to the influence ofthe discharge current upon the T(x) curves, lappears as a slowly decreasing function of I , while T,,, is observed t o be rather sensitive to increasing the discharge current density across the channel section, as is seen in Fig. 36 [(from Minoo (31)].In this figure T,,,ispresented as a function of 1 for various values of Q and various discharge current (longitudinal) densities (corresponding to constant I across cathode channels of different diameters). The cathode wall temperature is an important parameter for HCA in the N regime: its influence on the discharge voltage is very marked, as it can be seen in Fig. 37 (7). In the conditions of these experiments, the cathode wall temperature was varied as an independent parameter. by altering the heat balance at the cathode without changing the other experimental independent

146

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

Tmox

“C 1 240c

230(

220

210

FIG.36. Effect of the gas-flow rate and of the longitudinal current density (1,’s)on the cathode wall maximum temperature ( I = 1 5 A, B = 0,R = 1.8 to 3.3 mm). From Minoo (31, p. 81).

variables (vessel pressure, gas-flow rate, discharge current). This was done by means of tantalum tubular shields placed around the cathode to prevent cooling by radiation. The increase of cathode wall temperature produces enhanced thermionic emission, making operation at a lower voltage possible, as the figure shows.

2. Power Dissipation in the Cathode Region The total power dissipation in an HCA can be written as

w,=VZ=(W,+ w,+We),+(Wr+ WJ,+ w,,, where the capital subscripts refer to the discharge regions (cathode, external plasma, anode), and W,, W , , and We are, respectively, the radiation, the

147

HOLLOW CATHODE ARCS

60

V(V)

40 A

20

n

0

I

I

I

10

20

30

I

I(A)

40

FIG.37. Current-voltage characteristics, showing the effect of reducing the radiative loss (pyronietric measurement of temperature at the cathode orifice shows 10% increase for the shielded cathode). From Delcroix e/ trl. (7, p. 1560).

thermal conduction, and the electron emission dissipative losses. The latter concerns exclusively the cathode region. As the anode is. in most cases, a water-cooled one and is not emissive, the corresponding power loss is mostly caused by thermal conduction toward its holder. It was found by calorimetric measurements (6) that the power dissipation at the anode by this process represented about 607: of the total input power,? this value being almost independent of the gas-flow rate and of the discharge current (Fig. 38). I n the same figure is presented the result o f a similar calorimetric measurement for the cathode. Again its value ( 5':(; W , )is found to be independent of Q and I, keeping, of course, the same cathode geometry (thin-walled, unshielded cathode, R = 1.45 nim for this experiment). As t o the other terms of the above equation, it is easy to evaluate the cathode radiation loss

-

f Conditions for this experiment were: 1 20-50 A; B 400 G ; plain anode. A similar measurement i n an HCA with very different parameters (1- 150 A; B - 1.5 kG; hollow anode) yielded W,, 70%W, (17).

-

1

~

148

* 0.6

-

0.4

-

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

o

* O

Y

,t 0

0 0

. * 0

*

* *

*-*

WCA ’W!

0

* 0

0.2

I=20A

30A LOA 50A

-

FIG.38. Fractional power transferred at the cathode and anode regions, toward the electrode holders (thermal conduction), as a function of the gas-flow rate ( I = 20-50 A, B = 400 G , R =: 1.45 mni, e = 0.3 mni; plane end anode). From Delcroix et nl. (6, p.407).

where (Iext is the cathode external diameter, ~7the Stefan-Boltzmann constant and E ( T )the metal emissivity. This calculation, based on the experimental T ( x )curves, yielded a power dissipation by radiation of around 15-20 W , , which is a slowly decreasing function of the gas-flow rate. This result is quite understandable, as the cathode becomes more extensively hot as the gas-flow rate is made to decrease. As to the calhode wall cooling by electron emission a nai’ve approach would lead one to ascribe this effect to the thermionic current only; indeed, those electrons produced by wall emission require an energy ecp to be freed from the cathode material. However, it should be noted that every electric charge going through the cathode region causes a cooling effect on the cathode wall, the electrons produced by ionization in the channel being balanced by an equal number of ions which require the energy ecp to recombine upon the wall. Thus we,= Icp, cp being the work function of the cathode metal (4.35 V for tantalum); this amounts to about 10 ”/, W , ,

HOLLOW CATHODE ARCS

-

149

The remaining part of the dissipated power ( 10% W,) concerns the external plasma region, and is the most difficult to obtain by direct measurement. There, radiation occurs in the visible and ultraviolet range due to neutral deexcitation, radiative recombination, and e-i and e-o Bremsstrahlung radiation; calculations are, therefore, too complicated to be reliable. On the other hand, heat conduction toward the entire vessel surface is difficult to measure accurately enough, and we must not forget that neutral gas at a temperature higher than ambient is pumped away, without an obvious method of measuring the corresponding heat loss.

3. Cathode Voltage Drop V,; Minimuni Cathode Fall Vo It is possible to evaluate the overall cathode voltage drop Vc, either by subtracting from the discharge voltage the more readily measurable values of the anode fall ( VA) and of the external plasma voltage drop ( VE); or by the heat balance of the cathode region. The anode fall and the external plasma voltage drop are measured readily enough by Langmuir probe techniques; V, can also be accurately measured by changing the interelectrode distance, which provides a direct measurement of the axial electric field. The power balance at the anode WA = ( VA cp)I yields an independent measure of VA. The vicinity of the cathode region is not healthy to Langmuir probes, due to its high temperature; however, the heat dissipation at the cathode region is accurately known (see the preceding section) and yields the overall cathode drop v, = WJI.

+

Both techniques (difference and heat balance) yield comparable results (6, 21, 31, 32); the overall cathode voltage drop is observed to vary between 12 and 50 V, depending on the gas-flow rate; the higher values correspond to a deeper penetration of plasma inside the cathode channel (higher values of the distance I). It is reasonable to ascribe the increase of Vc to an axialvoltage drop in the internal positive column, corresponding to a longer IPC. Due to the geometry of the cylindrical hollow cathode, the equipotential surfaces must have the approximate shape shown in Fig. 39. Along the axis the electric field is purely longitudinal; in the vicinity of the cathode wall the field is radial and its value increases as /approaches zero (tip of the cathode). The effective length of the IPC is, of course, not accurately known; however, it must be related to the value of I at the maximum wall temperature (see Section VI), and we may take / as a reference length of the IPC. Thus, postulating an axial electric field of average magnitude X I along the IPC. and a "residual" voltage drop Vo in the extreme limit of the IPC ( x I), one can write vc = v o X , l

-

+

150

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE CATHODE

V.

I

4

I

X.1,

+i

vo/

t

X'L,

vc :vo

I ' \ ~~

~~

~

~

~~~~

1, = O (c1

FIG.39. Model for the equipotential surfaces inside the cathode channel, as a function of the flow rate Q. (a) Low Q, (b) moderate Q,(c) high Q.

with 1 '

and

L, being the total cathode length.

151

HOLLOW CATHODE ARCS

V , can be measured when 1 4 0 (high gas-flow rate); in these conditions V, z V , (see Fig. 39c) and one obtains V , = 10-12 V. This is called “minimum cathode fall” and its value is similar to the cathode fall of a classical cathode arc discharge, using the same combination of tantalum metal and argon gas. This value is confirmed by the following experiment. Let us vary the gas-flow rate Q so that different values of I are observed, while recording the total discharge voltage. If the vessel pressure and the discharge current are meanwhile kept constant, it is expected that the changes of the discharge voltage are not due to the external plasma or the anode region, but only to the cathode region. A plot of V ( / )yields the rate of increase of the cathode voltage drop as the IPC becomes longer. The result of such an experiment is presented in Fig. 40. From this plot it would be rather crude to infer that the IPC presents a uniform axial electric field along its length; it is more exact to consider the slope of V / l as the average value of the electric field X , along the IPC. Table I11 presents the values of X , for constant discharge current ( I = 15 A ) and various cathode channel radii. All values are fairly high (several volts per centimeter), decreasing with increasing diameter, as would be expected from a crude comparison with an ordinary positive column.

!.

(cm)

6

4

2

-

60

-

20

0

FIG.40. Discharge voltage vs. coordinate of the maximum wall temperature, obtained

by varying the gas-flow rate at constant vessel pressure and discharge current, V / / - 8 V cm-’ ( R 1.45 mm, I - 20 A, B = 0). From Trindade ( 2 1 , p. 23). -

152

JEAN-LOUP DELCROlX A N D A R M A N D 0 ROCHA TRINDADE

TABLE 111 AVERAGE AXIAL ELECTRIC FIELDI N THE IPC“

R(mm) X,(V/cm)

1.05 10

1.3 8

1.45 7.8

1.8 4.3

2.3 3.7

2.8 3.3

a Measured by the growth-rate of the discharge voltage with the IPC length, for I = 15 A. From Minoo (31, p. 100)

The presence of a longer IPC is associated with an increase of the (radial) sheath potential near the tip of the cathode, where it is maximum (see Fig. 39); as a conclusion, we may state that the hollow geometry, allowing for a plasma column to form inside the cathode channel, provides a high sheath potential which is responsible for the large ionization activity of the wall-emitted electrons. Based on these results, we shall use for a simplified description of the potential along the axis of the IPC the expression

4. Pressure Drop Along the Cathode Channel The local values of the pressure along the cathode channel are important quantities to evaluate, since the direct ionization rate is a linear function of the neutral gas density. The latter is dependent on the gas temperature (another quantity to evaluate) and, through its relation with the gas pressure, on the gas-flow rate and vessel pressure. Direct measurement of the pressure along the cathode channel is not easy to perform, due to the high cathode temperatures; so, either this quantity is calculated for the gas-flow situation of the experiment or an “overall cathode pressure drop is directly measured, between an upstream cold region (where a pressure gauge can be inserted), and the discharge vessel. The calculation of the neutral gas density along the terminal length of the cathode channel (including the IPC) was done by Trindade (21) with the following assumptions: the reference pressure is taken at the exit hole, (x = 0) and p ( x = 0)= p E (vessel pressure); the neutral gas is everywhere in thermal equilibrium with the cathode wall (this is approximately true in most cases unless the gas-flow rate is too high);? the gas-flow regime inside the cylindrical tube of radius R is laminar (cf. Section IV, B) and is intermediate between a viscous and a molecular flow. ”

t Numerically, the length Llhthat the gas has to travel in contact with the wall to reach the local value of the wall temperature within 10% maximum error is given (for argon gas) (22). by Llh(cm)= Q(atm-~rn~-sec-~)/3

153

HOLLOW CATHODE ARCS

Under these assumptions one obtains the relation between the pressure at the points A and B (corresponding t o distances . y A , xBfrom the end) in a tube of average temperature T , with

R4 ( \ ? A ~- , O B ~ ) / ( X A- X,)

B

= 6.3kTm/a

+ 2BR3

and

- P B ) / ( ~A XB) -

(/-’A

CQ =0

C = 16qp0 Tn,lnTo,

where 0 is the elastic cross section between atoms; q is the dynamic viscosity of the gas; p o , To are the standard pressure and temperature; and Q is the STP gas-flow rate. Considering the theoretical dependencies of o and q on the temperature (84) one obtains, putting x B = o and p R = pE

where a(Tn,)and b(Tm)are the functions presented in Fig. 41A for argon gas. When the vessel pressure is low enough so that PE

the equation above reduces t o

G ( b / R )kTm

3

+

p(x)=(kT,b/R) {[a(xQ/R’)

- I}.

In Fig. 41 B we present the curves relating the neutral gas (argon) density n, = p / k T , to the flow parameters for three different values of the average temperature T,. Obviously, these curves apply only t o the regions where the cathode wall temperature is fairly constant; specifically, t o the hot zone of the cathode (say, T 2 0.7 T,,,), excluding the vicinity of the cathode support. Direct measurement of the overall pressure drop in the cathode channel has been performed by some authors, with interesting results. Minoo (80, 81) measured the pressure inside a large diameter cathode support at the entrance of the cathode channel (10 cm long, 2.6 mm i.d.), with the results shown in Fig. 42A. The vessel pressure was lower than lo-’ Torr and was thus negligible as compared with the measured values (of the order of tens of Torr). Measurements by Lorente-Arcas ( 4 2 )and Brunet (39) in similar conditions yielded comparable results, and are shown on the same figure (it must be noticed that the cathode dimensions are not the same and so, quantitative comparisons are not directly possible). In Fig. 428 the ordinate concerns the absolute pressure p I at one point inside the cathode channel; however, Lorente-Arcas (42) considers the pressure drop between this point and the region upstreams t o be negligible and, as the vessel pressure is also comparatively small, p , z Ap. As t o Fig. 42C, the right-hand side of the curves should

154

JEAN-LOUP DELCROIX A N D ARMANDO ROCHA TRINDADE

0.6

0.4

0.2

0

I

1000

0

-

1

100

I

80

2000

I

60

3000

LO00

I

L

40

20

T,PK)

-

0

(b)

FIG.41. Data for calculation of the neutral gas density (argon) inside the cathode channel. (a) Functions a ( T , ) ,b(T,); (b) no R vs. x Q / R 2 for different values of the average temperature T,,,. From Trindade (21, pp. 44,45).

be disregarded for the purpose of this comparison, since the vessel pressure in this regime becomes high enough to affect significantly the pressure in the cathode channel. In the discussion of these results, it should be kept in mind that the cathode wall temperature along the channel is dependent on the current density across the cathode section (see Fig. 36); and one can show that a thermal equilibrium is established between the flowing gas and the surrounding wall (unless flow rates that are too high are used (21)).Therefore, considering that

I55

HOLLOW CATHODE ARCS

A D (Torr)

t

50 25

0

p

=

1

2

3

crn3sei')

~p (Torr)

100

0.1 27 a t m c m 3 s e i '

a:i

23

75

(bl

50

25

*

I

I

I

0

10

20

30

j(Amm

3

0.0.6

0 0.01

I

1

0.1

1

lo

p (Torr)

-2

)

p, (Torr)

12

0

E

FIG.42. Pressure measurements upstream the cathode channel. (a) Overall cathode pressuredrop(R = 1 . 8 m m , B = O , p , - IO-'Torr)(BO, p.21).(b)Overallcathode pressure drop vs. current density ([is)(42, p. 183). (c) Upstream pressure p , vs. vessel pressure p , (39, P 22).

I56

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

for a constant mass flow through the channel the pressure drop for a given length is approximately proportional to T I , it is expected that the pressure 2500°K) gradient downstream is much higher when the arc is operating (T,,, than in the situation I = 0 ( T 300°K). In general terms, the pressure drop along the cathode channel must be an increasing function of the current density across the cathode section. However, while this temperature effect explains fairly well the difference between the curves for f = 0 and for f = 10 A, for instance (Fig. 42A), it fails to account for the separation between curves for 10, 20, 30, and 40 A (in the same figure), as the variation in cathode temperatures is a small effect for low and moderate currents. This causes a discrepancy to exist between measured and calculated values of the overall pressure drop, which are consistently lower. The following explanations for this " overpressure effect " are proposed. (i) Lorente-Arcas (42) and Minoo (81) consider the electron pressure at the active zone of the cathode channel to be responsible for an important increase of the total pressure at this level; this would cause a higher pressure to be measured upstream, where the gas is not ionized. Minoo (81)calculates the electron density which it is necessary to postulate in order to make the agreement, between experimental measurements and theoretical predictions, of the pressure drop along the channel; the resulting value of the plasma density, in excess of lo'* cm-3 seems a bit too high$ but cannot beexcluded. (ii) An additional effect can be ascribed, possibly, to neutral gas pumping due t o the charged particle drift, which may occur in the vicinity of the cathode and inside it. This effect is unfortunately rather tricky to analyze ( 8 3 , and the gross result is known t o depend on the precise experimental conditions, for it can operate in either sense (pumping into o r from the cathode channel). (iii) It is possible that, with very high flow rates, a sonic throat may occur at the channel exit (39);this would cause, again, an upstream overpressure not accountable by a straightforward Poiseuille-law calculation. However, this effect should not occur in most experiments, as there is no point in increasing the gas-flow rate more than is strictly necessary for N regime operation. (iv) Finally, we remark that all three experiments were made with rather high flow rates, which caused the IPC length to be very small (a few millimeters) and the T ( x )curves in those conditions to decrease steeply for x > 1. It is possible that in these conditions thermal equilibrium with the wall will not be reached; this is known to influence the radial velocity profile of

-

N

t This applies, for argon gas, to the range 1500 < T < 3000'K; for lower temperatures, the dependence is a slower function of T ( 2 1 ) . 2 The only measurement of the electron density inside the cathode channel, thoroughly reported, was done by laser interferometry along the channel ( 6 ) .It yielded 17. < 5 Y I O l 4 Another (briefly) reported result, without mention of the measuring method and no further confirmation, reached as high as 10Ih (82).

HOLLOW CATHODE ARCS

157

the gas stream, and the pressure drop calculations must be made carefully to account for this complicating factor. It would be very interesting to know if an “overpressure effect is noticed for lower values of the gas-flow rate. ”

vr. THEORY OF THE HCA I N THE N REGIME A . General Comments A complete, self-consistent theory for the HCA in the N regime should be able to explain qualitatively the various phenomena occurring in these discharges and, more specifically, should permit calculations of the discharge parameters when the values of the independent variables (materials, geometry, vessel pressure, gas-flow rate, discharge current or voltage, and external magnetic field) are specified. The most directly available experimental, dependent quantities are the discharge voltage (if the current is imposed, or conversely), the cathode voltage drop, and (most important in these discharges) the T ( x ) wall temperature distribution. It is possible to obtain full knowledge of the external plasma through appropriate diagnostic techniques; as to the plasma in the IPC, those techniques must be more elaborate and, so far, the reported data are extremely scarce. We think that an effort should be made on this subject, as any direct measurement pertaining to the plasma in the IPC could be very valuable indeed in assessing the peculiar mechanisms of the HCA. The difficulties of a self-consistent theory are mostly due to the longitudinal dependence of the parameters pertaining to the cathode channel. The ionization rate in the IPC depends on the local values of the neutral gas density, on the density of the primary (wall-emitted) electrons, and of their energy (sheath potential.) All those quantities may vary strongly over a length of a few centimeters. The density gradients and the separation of the charged particles determine the shape of the electric field inside the IPC and the ion current distribution upon the metal wall. Finally, the heat balance on the cathode surface, depending on the above quantities, should yield the T(x) curve, if enough accuracy was possible in the previous calculations. At the present time, to build such a theory would probably be too ambitious an aim, as the T ( x )function is the solution of a heat-transfer differential equation of the second order in T. To write and solve this equation, one would need a perfect quantitative knowledge of all the processes of heat gain and loss on the cathode wall, even if only a modest degree of accuracy was sought. Since it is easy to measure, it seems more reasonable to consider the temperature distribution T ( x )as a given datum and try to deduce all other unknown quantities on the basis of a specified theoretical model.

158

JEAN-LOUP DELCROIX A N D A R M A N D 0 ROCHA TRINDADE

B. TJie Nature of the Actiae Zone” “

The most characteristic feature of the N regime is the longitudinal T ( x ) profile of the cathode wall temperature, which presents a maximum at some distance x = 1. This distance is a decreasing function of the gas-flow rate and (in a less pronounced way) of the absolute value of the cathode maximum temperature. This hottest region of the cathode has often been called the actioe zorie as it is associated with the highest current density of thermionic origin ; however, there is not full agreement on its nature, as viewed by the various authors. It is tempting to compare this active zone to the localized hot spot of a plain, conventional cathode. Its spatial extension in an HCA. and the absence of a definite boundary, could be explained in terms of a hypothetical azimuthal motion of a localized spot on the metal surface, with a slight fluctuation of the distance. However, there is no experimental evidence to support this hypothesis, up to this time. Before presenting our views on this subject we shall review three different points of view reported in the literature, ascribing some particular properties to the active zone. (i) The active zone occurs at a distance where a definite condition is satisfied by the neutral gas pressure. This point was first raised by Lidsky er al. (If), pointing out that “the arc runs from the cathode interior. deep enough that p o x d = I cm Torr” ( p o is the local value of the gas pressure and d the channel diameter). Delcroix et al. ( 4 ) working with a larger range of experimental conditions, have established a general rule for the location of the active zone: at this level (x = I) the gas pressure, as calculated by gas-flow conditions, is approximately constant ( p l z = 2 Torr). Further work by one of his co-workers (31)detected a small increase of the product p 1 x R with the gas-flow rate QCO. I < p , R < 0.8 Torr-cm in the range lo-’ < Q < 2atmcm3 sec- ‘), irrespective ofthechannel radius. It must be pointed out that this result refers to a constant discharge current ( I = 15 A) with no magnetic field applied. Even if these rules are only empirical and approximate, they are rather useful to predict the IPC length (at low and moderate currents) for given flow rates and channel radii ; they account also for the IPC length-reduction effect when separating the gas flow into several channels (see Section VII, A). (ii) Another point of view by Minoo (22) suggests that the active zone is established at a level of the channel where the neutral gas density is the most suitable for the production of metastable atoms. The following assumptions have been made to reach this conclusion: the fast electrons (emitted by the cathode wall) possess an energy of 12 eV, for the Ar-Ta combination; the

I59

HOLLOW CATHODE ARCS

balance of production and destruction of metastable atoms in a unit length of cathode channel is written as 0 = dn,/dt

=P

+

1

D,

where P is the metastable production term (by electron collisions upon neutral atoms) and D,the destruction terms, by radial diffusion and subsequent annihilation upon the cathode wall; ionization by electron impact ; two- or three-body deexcitation upon unexcited atoms; inelastic collisions between metastable atoms. Comparing only the two terms concerning the metastable production and destruction, both by electron impact (cross sections respectively CJ* and a‘) the author writes that ”0

o* > I?, oi

as the whole production mechanism must outweight one of the destruction processes. This yields for 12 eV electrons and, according to that author?, nm/nO< 8.3 x as a maximum value of the “degree of excitation of metastables in the IPC. On the other hand, as all the appropriate cross sections are fairly well known for argon, the author solves numerically the metastable balance equation and, for given values of the neutral gas density, obtains the corresponding metastable density 11,. From this point of view, the maximum metastable density was found to correspond to a neutral density of 2 x 10l6 ~ m - which ~ , is (roughly) the estimated density at the active zone level. Commenting on these results, we think this method of approach is slightly oversimplified, as it amounts to calculating a balance equation over a volume where homogeneous conditiotis preiwil (without a n axial diffusion term); this condition does not apply to the hollow cathode in the N regime, as a density gradient is present along the channel. Also, we must keep in mind that the sheath voltage may vary significantly even within a length of 1 cm; this opens the possibility of a very different balance of the metastable atoms when the emitted electrons possess kinetic energies higher than 12 eV. However, the proposed model is not so crude as might be inferred from the preceding remarks: it should apply to short internal columns (up to several millimeters long) where the sheath voltage does not reach much higher than 12 V at any point. The fact that in those conditions the profile of the wall temperature falls steeply for x > / insures that the electron emission is limited t o the distances x < I ; furthermore, the electrons which fail to perform inelastic collisions within this distance are effectively lost as far as ”

t We think that a more accurate value for 0*(12 eV) in argon is cr* (85), instead of 8.5 x as was used in those calculations.

=

3

i,

cm2

160

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

metastable production is concerned. So, the basic assumptions of this model are satisfied in this case. On the contrary, the conclusions now discussed do not apply at all for long IPC; as the emitted electrons can now acquire an energy of a few tens of electron volts, they can perform several successive inelastic collisions of different kinds, before complete thermalization. It should further be noted that, in the range of 20 eV energy, the cross sections for metastable production and ionization by electron impact are of the same order of magnitude (85), and the limit for the “degree of excitation of metastables” in the IPC can be considerably higher than the value stated before. (iii) According to Lorente-Arcas (20),the active zone has a quite different character. It is a limited region, centered at the region of the maximum wall temperature where all the emitted electrons are coming from. The plasma density in this region is determined by the balance between the ionization of the neutral gas and the volume recombination between electrons and ions. The ionization process goes through previous creation of metastables (twostep ionization) ; the only ionizing particles are those thermalized electrons of the plasma (Maxwellian distribution function) which possess an energy higher than eVim( V i m= Vi - V , = 4.2 V for argon). The upstream limit of the active zone is a sheath determined by ambipolar diffusion and volume recombination of the charged particles. The downstream limit is not explicitly given. Since we do not agree with some of the postulates of this theory we shall comment (briefly) on the most controversial points. First of all, we question the generality of the proposed theory. Stating that “the electron emission occurs in the active zone is accurate enough in the situations where a high gas flow is present, for the hot zone is then limited to the vicinity of the cathode tip. This is true in the case studied experimentally by Lorente-Arcas (20), where 1 = 3 mm (I is the distance where the wall temperature is maximum). On the contrary, for low gas-flow rates, I can attain several centimeters and the limits of the so-called “ active zone ” need precise definition. This is not a minor point; we know that long IPC are associated with larger cathode falls. The presence of an axial electric field in the IPC and a radial field in the vicinity of the wall, have not been taken into account in the theory discussed here. The hypothesis of a Maxwellian distribution for the electrons in the active zone is a dangerous oversimplification. Again, this is a very important point; in a Maxwellian distribution with T, of the order of a very few electron volts, only the high-energy tail is able to produce ionization; then, to satisfy the requirements of the discharge current, a very high electron density must be postulated which in turn causes a very high recombination rate. This may account for the very high values of n, (of the order of 10l6cm-3) calculated in that paper. ”

161

HOLLOW CATHODE ARCS

Assuming that the electron distribution function is not Maxwellian, having instead an extended high-energy tail due t o electrons injected through the sheath, the balance between creation and destruction of charged particles is satisfied with much lower plasma densities. In that case, even the hypothesisof volume recombination must be reexamined and usually surface recombination upon the wall will be the dominating annihilation process. We think that the two objections above are serious enough t o question the validity of the conclusions of Lorente-Arcas (20). (iv) As t o our own views on the nature of the active zone, we d o not consider it as a limited region with discontinuous properties; the existence of a maximum in the wall temperature profile is only the result of a heat-transfer process which is essentially continuous along the cathode wall. With this point of view, the hollow geometry and the fact that the cathode wall is made of conducting, emissive material, favor the deformation of the equipotential surfaces so that they penetrate inside the channel. This is simultaneously the cause and effect of the existence of a plasma inside the hollow cavity. The plasma heats the metal wall up t o thermionic temperatures; becoming emissive, the cathode surface is the source of the primary electrons. Those which are produced by the inner surface ionize the streaming gas if the pressure conditions in the channel are adequate. The resulting secondary electrons, guided by the reflecting sheath potential, reach the discharge vessel, while the ions are absorbed by that sheath and impinge upon the cathode wall, delivering their kinetic and potential energy. All those phenomena influence the cathode wall temperature, as they contribute to the wall heating or cooling. An independent cooling process is imposed by the heat sink at the cathode support. Considering an elementary slice of the cathode wall cylinder at a distance x (length d x , wall thickness e << Ri,,, R e x , ) .the heat balance at this metal volume is given by (see Fig. 43) N

[G,(x) -

D,(x)]2nR dx - [d FL(x)/dx] 2nRe dx

= 0,

where G,(x)is the radial heat flux incoming to the cathode wall; D , ( x ) is the radial heat flux dissipated by the wall; and FL(x)is the longitudinal heat flux along the cathode wall through the unit area of metal cross section. Introducing the thermal conduction equation

FL (x)=

-2

dT/d~

into the balance equation, we obtain G,

-

D,= - e d/dx(AdT/dx).

or, neglecting the A( T ) dependence at first approximation G , - D,= -eA d2TJdx2.

162

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

I I I I

I

I

IG, c D,

I

-

I

I

I

I I

I I

I

I

I

I

I

I

1

x (cm)

0 ,D,.(x)

G, (x)

-ANODE

-============: FIG. 43. Heat balance at the metal wall. A and B are the inflection points of the T(x) curve; for higher gas-flow rates B does not occur.

This equation gives the answer to the particular profile observed in the normal regime (see Fig. 43). The region of the T ( x ) curve presenting a downward concavity corresponds to the heating processes outweighing the radial dissipation. The inflection points of T(x) correspond to abscissas [at least one (A) at x > I ] , where the radial loss balances the heat input upon the wall. Let us examine now the principal radial heating and cooling processes of the cathode wall, i.e., heating processes: ion, metastable and photon bombardment, Joule effect, gas-metal conduction; and cooling processes: thermal radiation, electron emission, metal evaporation, metal-gas conduction. The corresponding quantities are given by the following expressions : a. i o n bombardment. where,ji,(x) is the radial ion current density upon the metal wall; V is the local value of the sheath potential; Vi is the ionization potential of the gas,

HOLLOW CATHODE ARCS

163

and cp is the work function of the cathode material. This expression assumes that all ions impinging upon the wall recombine with an electron from the metal, yielding a neutral atom with negligible energy?. T o calculate this term it is necessary to make a hypothesis about the sheath voltage distribution (see Section V, D, 3) and t o calculate the radial ion current density (Section VI, C ) . h. Metastable bombardment. If the working gas possesses metastable levels (as in the case of argon 4s3Py.,, V , = 11.55; 11.72 eV), their contribution to the wall heating may be important. Due to the long lifetime of these particles, they may reach the cathode wall in the course of their thermal motion and suffer deexcitation, releasing their potential energy. The corresponding energy flux upon the metal wall is given by G,,(X) = 17, ( X . 4 ~ , , , c I eV”,/4

in the hypothesis of a Maxwellian metastable distribution function (average velocity F,,,); 17, (x,].) is the metastable density near the wall, within one mean free path distance A ; q, is the electronic charge. c. Photon bonibardment. This term is not easy to calculate, as we are dealing with a complicated system consisting of a plasma not in thermodynamic equilibrium ( T , # Ti ,To) surrounded by a metal wall. The plasma radiation, due to radiative deexcitation, recombination, and bremsstrahlung due to electron-ion and electron-neutral interactions, may contribute to wall heating, enhance the electron production by photoemission, or be reflected back to the plasma. Only the electron-ion bremsstrahlung power density is easy t o evaluate; for a plasma (n,,Te)not absorbing this radiation, the power density on the surrounding cylindrical wall (radius R ) is given by Gb(x)= 7.6 x

17,’

Te‘’2R[W/cm’; ( ~ m - ~ )(eV)’”; *; cm].

d. Joule heating. The Joule power produced per unit area of the cathode wall is given by

p being the metal resistivity ( p = IW4 R cm for Ta at 2500°K) and e the wall thickness; ji,is the radial ion current density collected by the cathode wall andj,, is the electron current density emitted by the cathode surface.

t Ecker (66) who has analyzed thoroughly the cnergy balance on the cathode of arc discharges, suggests that this term should be divided into two separate effects, concerning the energy transfer of kinetic and potential energy, with different acconimodation coefficients.

I64

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

e. Thermal conduction from the hoi gas in the IPC to the wall. Considering the cathode channel from the support to the tip, there is an initial length t o consider, full of neutral gas; and the remaining length where a plasma exists. The latter is the only region where the gas can be at a higher temperature than the wall, due t o the collisions of its atoms with faster particles (mostly electrons, either primary or secondary). Let us assume that the gas attains thermal equilibrium with the cathode wall before reaching the IPC; it is then overheated in the IPC by various collisional mechanisms. The power delivered t o the gas through these processes is an upper limit t o the gas-metal conduction heat transfer. f. Thermal radiation of the cafhode wall. The power radiated per unit area of the outer cathode surface is given by

D, ( T )= &(T)(rT4, and E ( T )the where D is the Stefan constant [o= 5.67 x lo-' W,Jcm' emissivity of the cathode metal: for tantalum, this is approximately a linear function of the temperature between 300 and 3000°K.

+

E(T)= &(TO) a ( T - To),

(OK)-' with To = 300"K, &(TO) = 0.05, and CI = 1.05 x g . Thermionic emission. Consideration of the Richardson-Dushmann equation for electron emission, yields, for the power loss per unit area of the emissive surface (inner and outer wall surfaces)? D t h ( T )=2 A (PT' C b o i T

for tantalum, A = 55 A (cm"K)-', b, h. Metal evaporation.

= 4.86 x

D,, ( T ) = Q, C T -

J2

lo4 ( O K ) , and cp = 4.12 V

e - DJT,

where Q,is the sublimation heat; C and D are constants depending on the cathode metal (for tantalum, Q, = 4.17 x lo3 J gm'; C = 8.1 x gm/cm' sec-'("K)"'; D = 9.2 x 10-4(0K) i . Metal-to-gas heat conduction. This effect occurs in the cathode channel in the zone preceding the IPC. It is obviously dependent on the gas-flow rate; when this is not too high, thermal equilibrium is achieved within a short length and the power transferred t o the gas flow (mass flow rate: qm)is given by AW=q,C,,(T-T,)

t We suppose that thermal emission is not field enhanced. Other emission mechanisms were neglected, which may be reasonable for low and moderate discharge currents.

165

HOLLOW CATHODE ARCS

-

where C , is the specific heat of the gas and T , the temperature of the gas entering the channel ( T , 300°K if no preheating is used). For argon gas at 2500°K C , = 0.52 J/gm"K and the average power flux from the length of the wall preceding the IPC is

Dm-g,( T )= A WI2xR(L,

-

I)

L, being the cathode length. For a given experimental situation the cathode wall temperature is known at each distance x ; so. the radial dissipation terms are therefore easy t o calculate, as they are known functions of T . As to the radial heat input upon the wall, the corresponding terms depend on quantities not directly available through experiment, which must be calculated on the basis of some theoretical model. For instance, the ion bombardment term, which is probably the most important contribution to G , ( x ) , depends on the local values of the sheath potential and on the ionization rate inside the IPC, both depending on the theoretical model used for their computation. Thus, rather than using the heat balance equation as a way to obtain the curve T ( x ) ,it is more sensible t o use this equation to verify the compatibility of a theoretical model with the experimental evidence. From this point of view. any theory of the HCA in the N regime may be checked in two independent ways: the discharge current requirements must be met, so that the various mechanisms of charged-particle production, acceleration and annihilation, justify the magnitude of the discharge current; the power balance equation for the cathode wall must be verified, so that the calculated radial heat input term (resulting from the choice of a given model), exceeds the radial heat dissipation (as calculated from the experimental T(x) curve), in the region where d2T/dx2 < 0. This method was used (21) to verify the validity of the model for the HCA that we have been presenting throughout the present section. By calculating the ionization rate along the IPC, (using a method described in detail in Sections VI C, D), we were able to evaluate the various terms of the heat balance equation. for a given experimental situation. These calculations concerned an HCA discharge with the following parameters: argon gas; vessel pressurep, = 5 x l o w 3Torr; Q = 6 x atm cm3 sec-'; cylindrical tabular, tantalum cathode: R = 0.145 cm: c = 0.2 mm; L, = 8 cm; I = 20 A ; B = 0; V = 77.5 V ; Vc = 45 V , I = 4.5 cm; A', = 8 V/cm. We obtained the following results ( 2 / ) :(i) The most important radial dissipation term concerns the black-body emission of the cathode wall ; the electron emission cooling was about seven times lower at T = T,,,(x = !),

166

JEAN-LOUP DELCROIX A N D ARMANDO ROCHA TRINDADE

and the remaining mechanisms were negligible for those conditions. (ii) The most important radial heat flux to the cathode wall was due to the ion bombardment; among the remaining terms calculated, only the one due to metastable bombardment was significant (even so, about 15 times lower than the former). (iii) The calculated discharge current presented a defect of about 30% in relation to the experimental value: (iv) The maximum heat gain to the wall was about 50 % lower than the maximum radial heat dissipation at x = I, while it should be higher. Both defects are compatible with an underestimation of the radial ion current t o the cathode wall; and a possible underestimation of the photon bombardment term, as the resonant photons were neglected. However, these difficulties raise more questions about the quantitative exactitude of the calculations than the validity of the proposed model, which we shall discuss in the next sections.

C . Balance of the Current in the Cathode Region Let us consider a length dx of the IPC, located at abscissa x (see Fig. 44). The conservation of charged particles in the volume Sdx ( S being the IPC cross section) yields the following equations, for the ion and electron current densities : Zon current (Fig. 4 4 a ) :

Sdji, + j i , dS‘ = 4i (9- 9 ) S d ~ , whereji,(x) is the net radial ion current density leaving the IPC across the cylindrical boundary (area d S ’ ) ;ji,(x) is the longitudinal ion current density across the transverse section S (the positive direction of the axial ion flow is indicated on the figure);Y(x) and B(x) are the ionization and recombination rates (number of pairs of electron-ions created and annihilated at abscissa x, in the volume of the IPC, per unit time and volume). Taking S = nR12, dS‘ = 2nR’ dx one obtains ( d j i ~ / d x+ ) (2/R’)jir= 4i (9- 9) Electron current (Fig. 44b) : Considering the corresponding quantities for the electron current density, with the positive directions of the radial and axial electron flows, taken as indicated in Fig. 44b [j,,(x) = q e y e r ( x )jeL ; = 4,yrL; ye, is the net electron flow entering the IPC across the cylindrical boundary], one obtains:

(djeJdx)

+ (2/R’)jer= 4e (4- 9).

Accepting now the simplified model for the potential in the IPC, as outlined in Section V, D, 3, we postulate that: (i) The electric field is purely axial over

167

HOLLOW CATHODE ARCS

*

I

+

x+dx

I 1--

Y

1 0

(b)

FIG.44. Conservation of charged particles in the 1PC. (a) Ion flux y , ( j , = y , q , ) ; (b) electron flux yc ( j , = 9. ye).

the greater part of the channel cross section ( r < R ‘ ) ,with the exception of a thin sheath in the vicinity of the cathode wall ( R > r > R’)where the field is purely radial. ( i i ) The axial field will be taken a s constant along the IPC ( I > x > 0) and its value equals the average axial field determined experimentally as in Section V. D, 3. I n these conditions, the sheath potential is a linear function of the abscissa, and is maximum at x = 0 (channel exit hole); (iii) The ions of the IPC which attain the sheath boundary ( r = R’)in consequence of their thermal motion, are accelerated by the local sheath voltage and finally recombine upon the cathode wall; ( i v ) The electrons emitted by the wall (by thermionic emission, photoemission and secondary emissionl.) are accelerated by the radial field and enter the 1PC volume, where their kinetic energy is partly lost through successive inelastic and elastic collisions. These electrons cannot again cross the sheath boundary in the opposite sense, as they are repelled by the sheath potential; ( v ) As to the actual direction of the longitudinal ion flow, it is necessary to evaluate in the first place the Also by field eniission or T-F emission, if the local current density is high enough

(j c r

> lo5 A/cniZ)(66); unless very high currents are drawn from the cathode, as in the case

of the pulsed regime. this condition is not likely to occur, due to the absence of in the N regime.

it

hot spot

I68

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

relative importance of the gas streaming effect and the electric mobility processes, under the specific experimental conditions. The longitudinal ion velocity is the sum of the electric drift and of the macroscopic velocity imposed independently by the gas flow toward the channel exit hole. The average gas-flow velocity is given by uo = ( Q / S ) ( n ~ / n o )

where no is the (distance-dependent) neutral gas density and nL the Loschmidt ) . resulting axial ion current density is number (nL = 2.687 x l O I 9 ~ m - ~ The given by . i i L = Ei q i (pi X , - i d == ~ i q i ( n L / ~ o ) [ p i o - (Q/S)l, Ei being the radially averaged value of the ion density at a given abscissa and p i 0 the reduced ionic mobility;jiL, referred to the OX axis, can be positive or

negative. Analysis of the magnitude of the parameters under actual experimental may reverse its direction when Q varies within the conditions shows that jiL range where the N regime occurs. Calculations of the values of Peril(argon gas) for whichjiL= 0, with the aid of data from Table I11 [ W , ( R ) ]and from TABLE I V GAS-FLOWRATE CORRESPOND~NG 1PC LENGTHS"

CRITICAL VALUES OF THE

R (cm)

Qcri,(atmcm3 sec-')

0.105 0.13 0.145 0.18 0.23 0.28

0. I98 0.240 0.291 0.248 0.348 0.459

AND

lcrit(cm) 1.1

I .48 1.8 3.36 4.94 4.6

Fig. 5 [ / ( Q ,R)],show that in long TPC, the ions flow against the neutral gas stream, penetrating deeper inside the channel; while for higher values of Q (shorter columns), the ions follow the direction of the neutral gas flow. Table 1V shows the result of these calculations (pie = 1.6 cm2 V-' sec-' at STP).?

t pio(T)= plo(To)x (To/T)"2;in the present case we took T - 2500 K , so p l o= 0.57 cm2 V - l sec-l.

HOLLOW CATHODE ARCS

169

Introducing the expression for the radial ion current density, in agreement with the previous hypothesis (radial motion as a consequence of the ion thermal agitation), and assuming that the ions have a Maxwellian velocity distribution. with average value Fi j i ,= ni ( R ’ )qiEi/4,

where ni ( R ’ ) is the ion density in the IPC near the sheath boundary ( r = R’). I n the case of the lPC, the ionization is produced by the primary electrons emitted by the wall; it can also be shown that ionization occurs mainly in a peripheral region of the IPC (annular ionization). Both facts (ionization created by “external” agents and within a short distance from the wall) contribute to flatten the radial profile of the electron density(21). It is then a reasonable approximation to neglect the t i i dependence on the radial coordinate in the TPC (x < R’). In those conditions n i ( R ’ ) N iii and one obtains the following relation betweenjiLa n d j i , :

Introduction of this relation in the ion current equation yields tC+iL/dJ

+ An0

jiL

=41(

4 - A?,

where the quantity A (independent of the distance if one takes the ion temperature as constant along the IPC) is given by

Two different situations arise, depending on the magnitude ofthe gas-flow rate: ( I ) Q > QCri,( A < 0 ) . In this case the ion current flows from the channel toward the vessel; this current is produced by internal ionization and the externally produced ions d o not contribute at all-they are kept from reaching the channel by the gas flow. The radial current is also provided by the internal ionization but the maximum ion bombardment upon the wall occurs nearer and nearer to the exit hole ( x --* 0) as the flow increases. (2) Q < Qcri,( A > 0). In these conditions the ion current flows into the channel, against the gas flow; the externally produced ions may contribute to the ion current inside the cathode channel. This case has been studied by Trindade (21), performing a numerical integration of the differential equation of the axial ion current. Formal integration of this equation yields

170

JEAN-LOUP DELCROIX A N D A R M A N D 0 ROCHA TRINDADE

wherejiL(0)is the ion current entering into the cathode through the section x = 0 (external ion current). This equation was solved with the following simplifications (21): the ion velocity was taken as determined by mobility alone [we considered the case of a long IPC ( Q 6 Qcri,)];the ion current ,jiL(0)coming from the external plasma was neglected as compared with the one generated in the IPC (this is justified when the cathode is working at high temperature and the vessel pressure is low); the volume recombination was neglected, as compared with the radial ion loss (surface recombination).? In these conditions ( A > 0)

For this current t o be an increasing function of the abscissa in the range

(0, I) it is sufficient that the ionization rate 4 ( x ) is itself an increasing function of x in this length range. This is likely to occur in the N regime, where the electron emission increases in the range I > x > 0; as t o the pressure gradient

along the channel, the mfp. for ionization has a tendency to decrease for increasing distance. So, the fact that the axial ion current (and consequently, the radial component as well) increases with the distance between 0 and I, complies with the requirements of the heat balance equation for the cathode wall (see the preceding section), ensuring that a strong ion bombardment exists in the same region where the radial heat dissipation is the highest (x I ) . Further we notice that, when the internal ionization term is not high enough to overcome the externally produced ion current (which may happen due to the existence of pressure conditions adverse to internal ionization in the LQ or HP regimes; or due to insufficient cathode heating in the LI regime), we obtain

-

showing that the T ( x )curve must be decreasing from the cathode tip toward the holder, which agrees with the experimental evidence. We next study the method for calculating the ionization term inside the IPC. D. The Ionization Term in the IPC

The calculation of the inelastic collisions in the IPC and the corresponding charged-particle yield, is complicated by the dependency of the intervening parameters on the axial distance: the current density of the primary electrons depends on the local wall temperature; their energy when entering the IPC is a function of the local value of the positive sheath voltage; the

-

f Recombination is negligible in respect to radial diffusion loss when (33, p.156) n. G 1020/rroh2a. Taking the recombination coefficient c( lo-” cm3 sec-’ (86); tio 1OI6 cm-3, and A of the order of magnitude of the cathode radius R 1 mm, one obtains G lo’* which certainly applies in the IPC. N

N

HOLLOW CATHODE ARCS

171

densityof the neutral particles varies along the column as a result of the gas flow. An approach to this problem has been made by Trindade (21), using a simplified description where the IPC is decomposed in homogeneous slices of finite length Ax along the longitudinal axis. Thus, the neutral gas density, as calculated from gas-flow conditions, the electron emission current density (assumed purely thermionic) corresponding to the local values of the wall temperature, the sheath potential, calculated at each point from the overall cathode drop and the hypothesis of a uniform axial field, were taken as constant quantities within each slice, in a stepwise description. Their value in a slice is then the local average of the highest and lowest values calculated therein (see Fig. 45). The criterion for the definition of the appropriate length Ax was based on the following assumptions: the primary (wall-emitted) electrons acquire, from crossing the cathode sheath, quantized amounts of kinetic energy (in accordance with the stepwise description of the sheath potential profile); this energy depends directly on the abscissa of the emission point; a simplified three-level model for the rare gas atom reduces the number of different kinds of heavy particles to ground-state and metastable neutral atoms, and ground-state singly charged ions. In these conditions. a primary electron can only lose energy by inelastic collisions by amounts equal to: e V i ; e V , ; e( Vi - V , ) (where V i and V , are the first ionization and the metastable excitation potentials, the third quantity being the energy required to ionize a metastable atom): We took, for the argon gas ( Vi = 15.7 V; V , = 11.6 V), e( Vi - V,) h~ 4 e V as one writ of energy loss by inelastic collision, corresponding to ionizing a metastable atom. Thus, direct ionization (from ground state) amounts to 4 units of energy loss, and 3 units correspond to metastable excitation. Depending on the energy of the primary electron (after crossing the sheath), one or several successive inelastic collisions of the preceding kind can be performed until this electron reaches thermalization. The probability for a collision of a given type to occur is proportional to the product of the corresponding cross section and the local density of the target particle (no or 4,). The energy loss by elastic collision of the primary electrons upon the heavy particles was considered negligible ; however, those collisions were taken into account when calculating the axial drift along the IPC. On the basis of the preceding assumptions, an adequate length x of the slices composing the IPC is given by the condition:

X , A x = I unit of energy loss

( X , is the axial gradient of the sheath potential). In these conditions, the electrons emitted at adjoining slices differ by 4 eV in initial energy; those of

172

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE I I

Q Q

-

I I I I I I

ANODE

I I

I

e

1 UNIT

ENERGY LOSS

- 2.4 -

*

x

e

12

- 0 0

“0 (arb. units)

I

4

X

e

FIG.45. Stepwise approximation of the cathode sheath potential ( V ) and the neutral gas density ( n o ) for the computation of the ionization yield in the IPC.

higher energy can perform one more inelastic collision than their neighbors which is the reason they should be regarded as separate populations. Now, a balance equation must be written for each slice, and for each discrete energy level of the electrons in that slice; the rates of production, annihilation and transit of heavy particles and electrons of definite energy are the raw material for these calculations. This rather tedious computation was performed for a given experimental situation (21) (argon gas; R = 1.45 mm; Q = 0.06 atm cm3 sec-’; I = 20 A ; B = 0). The principal quantitative results are shown in Fig. 46.

173

HOLLOW CATHODE ARCS

1-

0.1

-

( 0 )

x(crn) 7

6

5

*(c)l

xkm) 8

L

3

2

1

0

I

I

,

7

6

5

.14

n,(d

3

2

1

0

3

FIG.46. Theoretical results for a HCA in the N regime ( R = 1.45 mm, Q = 0.06 atm cm3 sec-', I = 20 A, B = 0). (a) Cathode wall temperature (measured), thermionic current density; (b) radial ion current density, electron production by ionization in the IPC; (c) unexcited and metastable atoms deosity. From Trindade (21, pp. 106-1 14).

174

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

The following conclusions have been obtained : The internal ionization efficiency (secondary electron yield for one primary electron) calculated by this method, was of the order of 50%. This rather modest value is due to the fact that the higher values of the ionization cross sections occur for the electrons emitted at the lower values of the abscissa, where the neutral gas density is lower. Metastable atoms are of extreme importance in the ionization process, chiefly at the higher abscissas (x /) where the sheath potential is too low for one-step ionization to occur. However, the calculated value of the metastable density in the IPC (of the order of magnitude of n, loi4~ m - is~probably ) too high. As a matter of fact the only metastable destruction mechanisms considered by Trindade (21) were the volume ionization and the surface deexcitation upon the metal wall ; the possibility of their deexcitation by collision upon slow electrons, unexcited, or other metastable atoms, would yield a lower metastable density. Nevertheless, it is possible that the metastable density is high enough in a HCA to make it an interesting source of that kind of particles. This point has been raised by Delcroix, who suggested the use of HCA in chemical reactors (87). Experiments are being done to assess the metastable density in HCA by optical absorption: preliminary results (9) have shown that the metastable yields can be some two orders of magnitude larger in HCA than in the best glow discharge. As we have pointed out (Section VI, B), only qualitative agreement between theoretical and measured discharge current was obtained, indicating the necessity for improving the HCA theory.

-

-

E . Prospects of Improving the Theoretical Approach As compared to the method of calculation of the internal ionization outlined in the previous section, Allis (88) proposes a finer approach, to obtain simultaneously the electron distribution function in the IPC. It is based on his “gain-function” method, which takes into account the influence of both elastic and inelastic electron collisions upon neutral particles (89). The gain function is defined as the flux (in velocity space) of the electrons crossing the surface of a sphere of given radius w (electron velocity). Changes of this velocity can occur through: elastic collisions upon neutral particles (or Coulomb collisions, depending on the ionization degree); acceleration by an electric field ; inelastic collisions upon heavy particles. The balance of charged particles in velocity space appears as a differential equation of the gain function the steady-state solution yields, through appropriate relations, the electron distribution function.

HOLLOW CATHODE ARCS

175

The adaptation of this method to the IPC requires that the energy of the primary electrons is a continuous (linear?) function of the abscissa. The resulting analytical complexity (it must be kept in mind that the appropriate cross sections must be introduced to integrate the balance equation in velocity space) probably requires extensive computation ; the first preliminary results of these calculations are still unpublished (90). F . Coriclrrsioii Obviously, the theory of the HCA is not a closed subject. Even if we may consider that, in the moderate current range, qualitative agreement was found between theory and experiment, several points need closer scrutiny, i.e., the possibility of photoemission of primary electrons; the possibility of field emission, at least in the higher current range and in the pulsed regime; the possibility of secondary emission by ion bombardment, mostly when doublecharged ions are present (higher current range); the exact shape of the positive sheath inside the cathode must be assessed (this is closely related t o the problem of determining experimentally the exact depth of the plasma penetration in the IPC). The metastable production by the HCA is a n important matter as to its possibilities of application, and needs further research. A better experimental knowledge of the plasma inside the IPC (density, temperature, electron distribution function) is badly needed to guide and support the theoretical research on the internal mechanisms of the HCA.

VII. APPLICATIONS

OF

HCA

A . Multichannel HCA

As we pointed out in Section IV, B, single channel hollow cathodes are not suitable for working with an extended current range. To support the highest current, a larger diameter channel must be used to guarantee a reasonable lifetime; this causes difficulties during ignition and may impair the lowcurrent performances. Moreover, a strong gas flow is necessary to insure the N regime in a large diameter cathode; this may be undesirable from the point of view of the pumping capacity of the vacuum system. As to the problem of the discharge efficiency, the IPC should not be too long, as this is associated with a high cathode voltage drop, which increases the discharge voltage. A problem arises, therefore, when a high discharge current (imposing a large diameter cathode) and a low gas consumption are simultaneously required. Multichannel cathodes were conceived and developed for these purposes by Delcroix ef al. (6, 7, 91). The idea was to divide the gas flow among

176

JEAN-LOUP DELCROlX AND ARMAND0 ROCHA TRINDADE

parallel, cylindrical channels which compose the cathode device. Such a structure can be made in several ways; we describe here the most interesting one, a multitube assembly named by its authors the “ macaroni packet.” Figure 2(B3) (Section 1) shows this device, made by introducing a great number of slender tubes inside a large diameter cylinder. No special clamping is necessary to hold the tubes, if the packet is reasonably tight, because the metal evaporation occurring during arc ignition is enough to weld the structure firmly together. The outer cylinder is fixed to the holder as with a single channel cathode. In these conditions, the gas flows inside the internal tubes as well as in the spaces left among them. Comparison of the gas-flow conditions between a single channel and a multichannel cathode with equal area of the hollow cross section shows that the latter presents a steeper gradient of the neutral gas pressure for the same total gas-flow rate. So, considering the empirical rule stating that the active zone in the cathode channel occurs for a fixed value of the neutral gas pressure (Section ID, A), it becomes possible to assess the IPC length in a multichannel cathode. The relation between this value (1” )for a cathode having n elementary equal channels, and the IPC length I, for the equivalent (same hollow cross section) single channel cathode, is given approximately by (7, p. 1557)

I2!=

4

[

l/n

+ (I0.9/Jn(A0/d,) 1 + 10.9(A()/dI)

I,

where A, is the mean free path of the neutral atoms at average temperature and pressure in the channel, and dl is the internal diameter of the single channel cathode. Table V shows the result of the calculations for argon gas at 2500”K, TABLE V

I P c LENGTHREDUCTION EFFECTOF MULTICHANNEL CATHODES

9

I,

= 11/36

I,

= 11/14

1,

= 1,/1.8

1 Torr for a different number of channels, and two diameters of the equivalent single channel cathode. Knowing that the discharge voltage is strongly dependent on the IPC length (due to the high values of the axial electric field inside the cathode channel), multichannel cathodes are expected to need lower discharge

HOLLOW CATHODE ARCS

177

voltages (for given values of the current and the gas-flow rate) than single channel cathodes. However, for this effect to occur in agreement with the theoretical predictions it is necessary to postulate that the gas flow is parted equally among the n elementary channels; this is not always the case, as we shall see now. It has been stated in Section 111, C that hollow cathodes do not ignite when the discharge current density is lower than a certain threshold value; in the case of multichannel cathodes of large diameter this phenomenon is particularly obvious. In a low-current operation only a few channels are ignited, their number increasing as the discharge current is augmented ; only at high enough current does the whole cathode section participate in the discharge. This can be considered as an autoniatic adaptation of the cathode cross section to the variable current requirements. Thus, a cathode can be designed to support very high discharge currents (large overall diameter cross section) while insuring a good low-current performance by using very slender elementary channels, of which only few are ignited. It is obvious that the gas flow does not divide evenly among all elementary channels when the cathode cross section is only partly lit; this is due to the unequal gas temperatures inside the active channels and the remaining ones. Analysis of this effect (7) shows that the gas flows preferentially through the inactive channels; the IPC length reducing factor given before ( A = /J/,) is now affected by a corrective term: /in//,

+(I -4(~7~np*],

= A[@

where CL is the fraction of the cathode cross section corresponding to the active channels and T' and T" are the gas temperatures inside the lit channels and the inactive ones (T'> T"),respectively. As the factor between brackets is bigger than unity, the IPC length reducing effect in the case of partly lit cathodes is seriously impaired. Figure 47 shows the comparison between multichannel and single channel cathodes, from the point of view of the IPC length and the discharge voltage, the latter for steady-state and pulsed operation. The advantages of these cathodes, namely their higher efficiency and wider current range, make them very useful for operation under stringent conditions. I n the next sections we present some selected applications of HCA reported in the literature.

B. HC Ion Luser Large laser continuous radiation power in the ziisible region (up to 100 W) witha fair efficiency( z IOP3)canbe obtained with argon ionlasers; moreover, the fact that their light is in the blue-green region of the spectrum, corresponding to the highest sensitivity of the receivers, makes them very interesting

I78

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

60

60

x(rnrn)

20

60

I

0

I

10

0 (C)

20

-

\

$>6.?/------

-

I

1

I

0

20

40

60

I

I(A)

80

I

2o

I(kA)

FIG.47. Performances of multichannel HCA (dimensions on drawing). (a) IPC lengthreducing effect; (b) V-I characteristics in steady state; (c) V-I characteristics in pulsed regime. From Delcroix ef al. (7, pp. 1559, 1560).

devices for a great number of applications. On the other hand, it seems that the most promising way to increase the output power and efficiencyof the Ar' laser is to use large diameter discharge tubes and very high discharge currents (92). The high power Art laser presents two serious technological difficulties : the huge power dissipation at the column, and the capacity for the cathode to deliver the required current without serious damage to itself, and for the

HOLLOW CATHODE ARCS

179

necessary purity of the rest of the laser. We shall examine briefly the electrode problems of the Ar’ laser and discuss the use of hollow cathodes as a possible solution. The first attempts to use an HCA as the excited medium in cw ion laser operation, have been reported to meet no success (93, 94). In these experiments the arc ran between tantalum hollow electrodes and a gas flow was injected through the cathode into the interelectrode space. The reasons for this device’s failure to show laser action were concerned more with the external column conditions (which were not adequate) than with the cathode itself; the plasma was magnetically confined inside a discharge tube of excessive diameter. This was shown later by Huchital and Rigden (24, 95) who first obtained laser action with an HCA external column as the active medium. ln order to obtain the necessary current density, they used, either small diameter discharge tubes (a few millimeters i.d.) o r another type of wall confinement, consisting of several radiation-cooled disks placed along the discharge axis, with a small central aperture to limit the radial diffusion of the plasma. In these devices, the hollow cathodes appear as a possible alternative against the thermionic cathodes. Other authors followed this trend, using HC more because of its ruggedness and current delivering capacity, than for a definite idea about their possible influence on the excitation mechanisms of the ion laser (25, 27, 96, 97). Nevertheless, there is at least one point of difference between hollow cathodes and conventional ones, which may affect the excitation mechanisms in the laser column. The distribution function of the electrons leaving the cathode region is obviously not the same in the two cases because of the different shape and magnitude of the cathode sheath, and the occurrence of internal ionization in the hollow cathode (97). I n order to analyze this problem, Jennings et d . (26) made a careful comparison of the performances of these two types of cathodes, using the same geometry for the active length of the laser (external column), with the following results: the total output (radiation) power was the same for the two systems for given values of the discharge current and of the vessel pressure (an optimized value of the axial magnetic field was imposed for each case); the same applies for the threshold currents needed, at different pressures, to start the laser action; finally, the total input power (including the heating power for the “ h o t ” cathode) was found to agree within 2 for the two systems operating in similar conditions. The authors concluded that, for the moderate pressure range necessary for ion laser operation, any differences in the composition of the electron current just outside the cathode region, for the two cathode systems, were destroyed by collision interaction within a very short length. This makes the HC and the thermionic hot cathode fairly equivalent as far as laser performance goes; however, a few remarks are felt to be necessary about this conclusion.

180

JEAN-LOUP DELCROIX A N D A R M A N D 0 ROCHA TRINDADE

As a matter of fact, no mention is made in this reference t o the opfinzizcifion of the HCA for one o f t w o possible aims, either to obtain the maximum output power for a given geometry, or t o secure the maximum efficiency in the light generation process. Compared with the thermionic hot cathode, the hollow cathode has one more degree of freedom when a given current is required : the gas-flow rate through the cathode channel, which has a strong effect on the cathode sheath potential. Obviously, for this optimization research t o be meaningful it is necessary that the cathode gas-flow rate could be varied without influencing the vessel pressure. Another word o f caution about the comparison between hollow cathodes and conventional ones for laser devices: even if their performances are found to be nearly equal for the moderate current range, it is obvious that in the high-power ion laser, the HC is the more adequate, for its current-delivering capacity is much higher than the known systems of thermionic hot cathodes (98); and the conventional cathode working in the hot spot arc mode is not suitable for laser operation. C. Ion Sources for Electric Propitlsion Systenis Among the various systems useful for orbital maneuvering of spacecraft, electric thrusters based on ion acceleration have been most extensively studied. In those devices, the highly ionized plasma from which the ions are extracted may be created by different methods; one of them incorporates a cathode producing a copious supply of electrons, with energy adequate for ionization of the neutral propellant atoms (electron bombardment ion engines) (28, 29, 99-105). For the production of the electron current, different cathode materials and geometries have been tested; froni the point of view of cathode durability and current-delivering capacity, hollow cathodes were found to be the most adequate (29, 100). As to the global efficiency of the thruster, it is not clear whether hollow cathodes are the best cathodes for this purpose (104) as it is generally assumed. We first describe a hollow cathode geometry which has been extensively used in ion thrusters, formerly developed by Rawlin and Pawlick (102). A hollow tantalum tube is supplied with a gaseous mercury feed from a suitable vaporizer; a pierced disk of thoriated tungsten ( - I mm thick) is welded to the cathode tip to restrict the gaseous flow (orifice diameter: 0.1 t o 1 mm). The cathode wall is electrically heated by a wire wound around i t , and embedded in an alumina coating. The hollow cavity may be coated with low workfunction materials; or an insert of tantalum foil coated with the same materials may be placed inside the tantalum tube. The pressure inside the cathode channel is determined by the mercury feed, and is much higher (several Torr up to several tens of Torr) than the pressure in the discharge vessel (below Torr).

181

HOLLOW CATHODE ARCS

Experimental results showed that this discharge worked in two different cathode modes: “plume” mode, with a bright discharge between cathode and anode, corresponding t o low vapor feed rates through the cathode, low discharge currents (some 100 mA), and a voltage of about 15 V (100, 101); and a “spot” mode where only the cathode orifice is specially bright, corresponding t o currents of a few amperes and lower discharge voltages (10 V). It is remarked by Csiky (101) that self-heating of the cathode is possible even at moderate currents, due to the ion bombardment of the cathode wall. We identify the “ s p o t ” mode described above with the N regime of a gasfed HCA which we have discussed in the present review. In fact, the presence of a small diameter orifice at the end of the cathode causes most of the pressure drop in the cathode channel to occur at about this level; the active zone sets in at the very end of the channel and the TPC is virtually absent in this regime. However, due t o the small thickness of the aperturing disk, some plasma penetration may occur into the cathode channel due t o incoming ions and ionization by the electrons emitted at the orifice level. The fact that a minimum current density is found t o be needed for the spot” mode t o set in is in accordance with our results for the LI -,N regime transition; the threshold current corresponds t o the minimum ion bombardment required for self-heating of the emitting region. An additional point in favor of this assimilation is given by the results of a very interesting experiment described by Fearn et a/. (103):introducinga probe inside the cathode channel, the authors were able t o measure the plasma density at a point -2 mm upstream from the cathode orifice. This density was found t o be lower there than at the interelectrode space and, moreover, density was a decreasing function of the mercury vapor feed rate. Viewed under the light of the known characteristics of the N regime, these results are easy to understand; the probe was probably placed at a transition region, upstream in respect t o the active zone, where the plasma density is much lower. The increase of the gas flow, “pushing” the plasma farther downstream causes the density measured at a fixed point t o be a decreasing function of the gas-flow rate. Pawlik et al. (28) studied more thoroughly this “orifice” cathode, analyzing the output and input heat flux on the cathode wall, and comparing the theoretical predictions with experimental temperature measurements on the various regions of the cathode. Their conclusions agree with our expectations for the HCA N regime, as the electron emission from the metal was ascribed entirely to the orifice region, while the power input by ion bombardment was found t o occur either at the cathode inner surface o r at the orifice but no? at the cathode face (the end disk)-thus excluding the contribution of an externally created ion current. A most interesting point made by Pawlik et a/. (28) concerns the comparison, for the same “ orifice ” cathode, between their performances with and “

182

JEAN-LOUP DELCROIX A N D A R M A N D 0 ROCHA TRINDADE

without external wall heating. It was concluded that: running the cathode at a higher temperature while in the self-heating regime (by reducing the cathode heat losses by radiation or thermal conduction) decreased the power extracted from the plasma to heat the cathode wall, and increased thedischarge efficiency; the external heating of the cathode consumed more power than self-heating by the discharge current; finally, it was found that coating the cavity with low workfunction material causes the cathode temperature to lower (for the same discharge current) and the discharge voltage is smaller in these conditions. However, running the discharge for several hours (even at moderate currents) causes depletion of the coating material inside the cathode. Then, the discharge efficiency is found to decrease accordingly, after some 50 hr of operation. In conclusion we suggest that using multichannel hollow cathodes, either “orifice” or tubular shaped, might contribute to increase the efficiency of these thrusters. Other hollow cathode configurations which are not of the axial HCA type we are most interested in have been used in ion sources for propulsion puposes; only brief descriptions will be given of these devices. Zeyfang (106) describes two different hollow cathode ion sources, working in the high-current glow regime. The first has an axial geometry (the anode opposing a hollow cylinder as a cathode); the external column is wallconstricted (bore diameter I .5 t o 6 mm). The gas is fed through the anode and the ions are extracted from the back of the cathode channel. The second type of ion source mentioned in the same article has a transverse geometry, in the form of two ring-shaped electrodes: the annular anode faces two concentric rings constituting a circular slotted cathode. Thus the discharge is also circular in shape, running from the anode (in which vicinity the gas is injected), into the slot between the two ring cathodes; the ions are extracted past the latter region. Another transverse geometry is described by Ibadov (107),concerning an ion source with coaxial electrodes. The anode is a rod placed at the axis of a cylindrical hollow cathode which also serves as a discharge chamber; the ions are extracted from an opening in the cathode wall. In the interelectrode space the pressure is uniform (no gas flows between the electrodes): the cathode is heated only by the ion bombardment, up to a temperature of the order of 2500°K. This discharge may even be made to run on the vapors of the cathode material.

-

D. HC MPD

Thrusters

Magnetoplasmadynamic (MPD) arc thrusters have been proposed for spacecraft missions ranging from auxiliary propulsion systems (satellite station keeping, altitude control) t o the high-power, primary propulsion

HOLLOW CATHODE ARCS

183

system for deep-space exploration (30, 108). Usually the device consists of an annular anode and a cathode centered at the anode axis; a magnetic field diverging in the downstream direction provides the MPD acceleration for the charged particles. The article by Fradkin et a/. (f08)concerns a high-power (25 kW) thruster working with Li vapor fuel; comparison is made between its performances when using a conventional arc (plain cathode) and a HCA. The latter was found to be superior in many respects, i.e.. higher thermal efficiency (ratio of the total power in the plasma beam to the total input power); smaller current and voltage fluctuations; the hollow cathode was not damaged by operation in the “high voltage mode” (occurring when the vapor feed was smaller than a given threshold value), nor when extinguishing and restarting the arc at the pressure and flow rate running conditions. In both situations, the conventional cathode suffered serious damage; the hollow cathode (and the remaining parts of the system) were not damaged while running without the magnetic field. We further remark that the high voltage mode” occurring at low vapor feed rates may possibly be identified with the LQ regime we have studied for noble-gas HCA (even if in our conditions the current range was much lower, which may weaken the validity of the comparison). Burkhart (30) reports using an Xe-fed HCA in a low power (up to 1 kW) MPD thruster. The most interesting point in his experiment is the downstream position of the cathode, at the exhaust side of the thruster. The author finds that this arrangement improves the system efficiency in the whole range of specific impulses (Z5p < 2000 sec), as compared with the more usual position of the electrodes (anode downstream). He further remarks that the best performances occur at zero cathode flow, all the gas injection being made at anode level. This is quite understandable, as the cathode flow would be running opposite to the exhaust direction. “

E. ac Operatioti of HCA Two interesting applications were reported in this domain of HCA operation : electrodes for low pressure discharge lamps and high-power rectifiers. An electrode design for a gas discharge lamp as described by Bouwknegt and van der Kooi ( f 0 9 ) ,consists of a hollow cylinder with one closed end. The inside surface is of the nickel matrix type, where an emitting material is embedded. The two identical electrodes whose open ends face each other. are positioned at opposite sides of the discharge tube; the gas filling is 3 Torr Ar plus saturated Hg vapor (standard filling for fluorescent lamps). Measurements of the temperature distribution along each electrode show that the discharge penetrates a little distance into the electrodes. This mode of

184

JEAN-LOUP DELCROIX AND A R M A N D 0 ROCHA TRINDADE

operation is not exactly comparable to the dc regimes in HCA operation; if any, it shows some similarities with the H P (moderate pressure) regime. When a rectifying effect is sought in the ac operation of a n HCA, we must take a n approach just opposite to the one in the preceding reference (symmetrical electrodes). Now the electrode design must emphasize the difference between cathode and anode, so that the current passes preferentially in one direction. Articles by Koltypin et a l . ( / / U - / 1 2 ) describe such a device. A cylindrical box-shaped metal chamber serves as the hollow cathode, enclosing a flat circular anode ; a n axially symmetrical, nonuniform magnetic field is created by a solenoid placed under the base of the chamber. Using this geometry with a chamber pressure p E 10-’-10-2Torr, a n arc ignites between the electrodes when the anode potential is several hundred volts positive with respect t o the cathode; when the polarity is reversed, the arc does not start up to voltages of several kilovolts between the electrodes. This performance is due to the proper choice of the interelectrode distance and the chamber pressure. When the “hollow cathode effect” is not present (during the cycle when the box is positive with respect to the disk) the ignition voltage is very high and no current flows; when the situation is reversed, the ignition voltage drops strongly and glow-to-arc transition occurs. The shape of the magnetic field helps to enhance this asymmetrical behavior. This device was found to be suitable for high-power rectification (discharge currents up to 100 kA).

-

F . Other Applications of H C A

We will only mention several other reported applications for HCA: plasma jets and torches (113). high current thyratrons 1/14}, thermionic converters (115, 1/61, electron sources ( / / 7 ) , metastable sources (9, l o ) , plasma accelerators (118). We finally report their use in plasma machines for research work, which we have mentioned before (18, 37, 78).

VIII. CONCLUSION We have studied hollow cathodes in the arc regime operation (HCA), where their advantages with regard to ruggedness, construction simplicity, and current-delivering capacity are the most interesting. A gas feed through the cathode channel allows a plasma to exist inside the hollow cavity; diffuse, extensive heating of the cathode wall by this plasma, causes a high electron emission yield, without damage t o the cathode itself, o r to the purity of the external plasma. As the cathode sheath voltage can be varied by adjusting the gas-flow rate, optimal conditions can be obtained for efficient ionization of the streaming gas; on the other hand, as no contribution of the external plasma is required for proper cathode operation, a n HCA can work in near vacuum conditions. So, the ionization degree of the external plasma is mostly limited by the pumping capacity o f the vacuum system.

HOLLOW CATHODE ARCS

185

One of the most interesting features of HCA is the possibility of working in a very extended current range; when using multichannel hollow cathodes, the hollow cross section adapts automatically to the current requirements. However, the high-current performances of HC. either single o r multichannel, have not received much attention up t o now and extensive lifetime tests have not been performed. Another point deserving further research is the pulsed, high-current operation of these cathodes, which has scarcely been studied (6, 119). This regime presents many complicating phenomena (generation of shock waves, high field emission processes, thermal fluctuations) which are interesting to examine, and the experimental setup is quite easy to assemble due t o the low (average) power requirement. Finally, we must state that the theory of HCA operation still needs improving; a most decisive contribution would be given by better experimental knowledge of the internal plasma column parameters.

ACKNOWLEDGMENT The authors wish to thank Professor W. P. Allis, of the Massachusetts Institute of Technology and Dr. H. Minoo of the Laboratoire de Physique des Plasmas, Universite de Paris Sud for many discussions and helpful comments and Mr. F. Ronieiras of the lnstituto Superior Tecnico, University of Lisbon for his help in the bibliographic research work. The authors are also indebted to the Editors of the following publications: Applied Physics Letters, Coniptes Rendiis de I’Academic rles Sciences (Paris), Journal of Applied Physics, Journal of Quaiifum Spectroscopj, and Radiatiae Tramfer, Phjwks of Fluids. Pla.rma Physics, Proceedings of the 1st Interna~ioiialConference on Holloiv Cathode Discharges and Their Application.s, Quarterlv Progrrw Report (Research Laboratory of Electronics, Massachussets Institute of Technology), rapport.^ dii Cbmmissariar d I‘Energic. Atomiqiie (France), Rapportx Interno.\ c/u Laboratoiri. de PIiy.sicliie des Plasmas (Orsay), Revue Roumaine cle Plij~sique,Reoiew of Scientific In.w/tments,who graciously granted permission for us to use material previously published in these sources.

REFERENCES *1. A. Guntherschultze, Z . Phys., 19, 313 (1923). 2. J. S. Luce, lntense gaseous discharges. Proc. h i t . Cot$ Peaceful Uses A t . Energy, 2rrd, 1958, p. 31 (1958). 3. H. Minoo and A. R. Trindade, Low pressure hollow cathode arc discharge behaviour in a magnetic field, Proc. 1111.Corr. fhenoniena Ionized Gases, 8th, 1967, p. 97 (1967). 4. J. L. Delcroix, H. Minoo. and A. R. Trindade, Etablissement d’une rkgle generale pour une decharge d’arc a cathode creuse. J . P1iy.s. ( f a r i s )29, 605 (1968). 5 . J. L. Delcroix, H. Minoo, and A. R. Trindade, Nouveau mode de fonctionnement d‘une decharge d’arc a cathode creuse. C . R . Acacl. Sci., Ser. B 266, 76 (1968). 6. J . L. Delcroix, H . Minoo, and A. R. Trindade, Etude de decharges B cathode creuse en regime d’arc. Rec. Roiun. Phys. 13(5), 401 ( 1968). 7. J. L. Delcroix, H . Minoo, and A. R. Trindade, Gas-fed multichannel hollow cathode arcs. Rei’. Sci. Znstri~m.40, 1555 (1969). 8. J. L. Delcroix, H. Minoo, and C. Popovici, Fonctionnemcnt a haute pression des decharges d’arc a cathode creuse (cathotrons). J . Phys. (Poric.), tcoltoq. &an) p. I71 (1971).

186

JEAN-LOUP DELCROIX A N D A R M A N D 0 ROCHA TRINDADE

9 . A. Richard, M. Touzeau, and J. L. Delcroix, Production of metastable atoms in a hollow cathode arc discharge-comparison with a glow discharge. Proc. Itlr. Cot$ Gus Dkclrarges, 2 4 1972 p. 376 (1972). 10. A. R. Trindade and J . L. Delcroix, Theoretical evaluation of metastable production in a gas-fed hollowcathode arc. Proc. h i t . Cot$ Gas Discharges, 2nd, 1972 p. 105 (1972). I I . L. M. Lidsky, S. D. Rothleder, D. J. Rose, S. Yoshikawa, C. Michelson, and R. J. Mackin, Highly ionized hollow cathode discharge. J . Appl. Phys. 33, 2490 (1962). 12. G . J . Ahsmann, and W. Van Benthem, A hollow cathode discharge yielding a highly ionized, hot plasma beam. Nut. Lab. Philips Rep. 4112 (1966). 13. J. C. Boiilassier, M. Clement, J . Cuvellier, M. Dagai, and C. Manus, RCsistivite anorniale d’un plasma. Proc. Int. ConJ Phenomena Ionized Gases, 6th, 1963, Vol. I , p. 359 (1963). 14. R. Cano, M. Mattioli, and B. Zanfagna, Study of the plasma column in hollow electrode arc. Rap. C.E.A. R.2935 (1968). 15. M . Hudis, K . Chung, and D. J. Rose, Ion teniperature charge exchange and Coulomb collisions in an argon plasma column. J . Appl. Phys. 39(7), 3297 (1968). 16. D . L. Morse, Plasma rotation in a hollow cathode discharge. Phys. Fluids 8(3), 516 (1965). 17. C . B . Kretschmer, F. Boeschoten, and L. J. Demeter, Plasma waves and rotation in the gas-fed hollow cathode arc. Phys. Fluids 11(5), I050 (1968). 18. J. C. Woo, and D. J . Rose, Generation of a quiescent, variable parameter arc plasma. Phys. F1uid.s 10, 893 (1967). 19. B. E. Keen, and R. V. Aldridge, Low frequency wave mixing in a magnetoplasma. Phys. Lert. A 29(5), 225 (1969). 20. A. Lorente-Arcas, A model for the hollow cathode discharge. Plasmu Phys. 14, 651 ( I 972). 21. A. R. Trindade, Etude des m6chanisnies de fonctionnernent de cathodes cremes en rkgime d‘arc. Port. Phys. 6(1-2), 160 (1970). 22. H . Minoo, Gas-fed hollow cathode arc mechanisms. Proc. Int. Conf. Hollow Cuthode Discharges Appl. I s t , 1971 p.15 (1971). 23. A. Morosov, and A. V. Trofimov, Theory of physical processes in plasma hollow cathode. Presented at Int. Corrf. Hollow Cathode Dischtrrges Appl. Ist, I971 (1971). 24. D. A. Huchital, and J. D. Rigden, Functional ion laser based upon a therniionic hollow cathode discharge. Rev. Sci. /n.s/runi. 39, 1472 (1968). 25. J. L. Delcroix. H. Minoo, 2. Szili, and A. R. Trindade, Retard entre I’inipulsion du courant de la decharge et celle de la puissance d’un laser 6 argon ionise. C . R . Acad. Sci. Ser. B 210, 173 (1970). 26. W. C. Jennings, J . H . Noon, and E. H. Holt, Comparison of hollow cathode and conventional argon ion lasers. Rev. Sci. Instrum. 41(3), 322 (1970). 27. J . Jolly, Argon ion laser using hollow cathode and graphite confining structure. Proc. Int. Conf. Hollow Cathode Discharges Appl. h i , 1970, p. 20 (1971). 28. R.Goldstein, E. Pawlick, and L. C. Wen, Preliminary investigations of ion thruster cathodes. Jet. Prop. Lab. (Pnsudenu) Tech. Rep. 32 1536 (1971). 29. B. P. Day, D. G . Fearn, and G. F. Burton, Ion engine development at the Royal Aircraft Establishment, Farnborough. RAE Tech. Rep. 71102 (1971). 30. J . A. Burkhart, Exploratory tests on a downstream cathode MPD thruster, J . Spacecr. 8(3), 240 (1971). 31. H . Minoo, Etude des dkharges 6 cathode creuse flux de gaz en regime d’arc. These d’ktat, Rapp. Orsay LP 94 (1969). 32. A. R. Trindade, Etude de la colonne positive interieure d’une decharge d’arc 6 cathode creuse en regime d’arc. These de 3eme Cycle, Orsay (1968).

HOLLOW CATHODE ARCS

187

*33. J . L. Dclcroix, ’‘ Physique des Plasmas,” Vol 11, p. 92. Dunod, Paris, 1966. 34. J . 1.Dclcroix, H. Minoo, and C . Popovici. High pressure operation of hollow cathode arc discharges (cathotrons). Proc. III!. CiwJ Hollow Critlrork Di.\clirirp.s Appl. Is/, lY71, p. 18 (1971). 35. J. L. Dclcroiu. H . Minoo. and C. Popovici, Patent A N V A R (France) No. 7045793 ( 1970). 36. H . hlinoa, Noise and low frequency oscillations in the gas-fed hollow cathode arc discharges. Proc. l i i t . Corrf: Hoftobi, Crirliotfc. /li\c/rtrrgcJ,s .4ppl. /,st? 1971. p. 3 I (1971). 37. E, T. Gcrry, and 0. J . Rose, Combined anode-cathode feed of a hollow cathode discharge. J . .4ppl. Plmys. 37(7), 2725 (1966). 38. .I. Jolly, Etude experimentale de lasers ioniques dc grandes puissances dans I’argon, en rCginie continu et pulse. Thkse de 3eme Cycle. Orsay (1971 1. 3Y. A . Brunet, Flow conditions into the cathode i n the ‘internal positive column’ regime. Proc. l i l t . CoiiJ Ho//ow Ctrr/rocli~Di.sclinrge\ .4pp/. /.\/, IY71 p. 22 11971). 40. T. J. Gritzmacher, E. L . Boyer. and J. F. Holt, A plasma scanner and data-processing system for current-voltage curves. Rer. Sci. lt/.vtrimr,40, 721 ( 1969). 41. K . Chung, Oscillations in the hollow cathode discharge arc. Qnnrt. Progr. Rep. ( M I T )84, I59 (I967). 4-7. A . Lorente-Arcas. Mise en Cvidcnce d‘une pression elevde dans la zone active d’une cathode creuse. C. K. Actrrl. Sci.Ser 5 271, 180 (1970). 43. R . Bleckrode, and W. Van Benthem, Spectroscopic investigations of high-current hollow cathode discharges i n flowing nitrogene at low pressures. J . Appl. P/i.y.y. 40(13), 5274 (1969). 44. R. A . Gibbons. and R. J. Mackin, Development and study of a highly ionized steadystale dctrterium plasma. frnc. Int. Con/: fhPnornenrr Ionized Gas~s,5th 1961 1769 (1961). 45. R . L. Gunshor, J. H. Noon, and E. H. Holt, Correlation measurements of i o n acoustic waves in a highly ionized plasma. P/ry.r. Niri0.r 2, 1763 (1968). 460. B. Van der Sijde, Excitation mechanisms i n the argon-ion spectrum at near laser conditions and temperatures and densities i n ;i hollow cathode argon-arc discharge. J . Q i i m t . Specfrosc. Raditrf. Trtrns/+r. 12, I S 1 7 (1972). 46h. B. Van der Sijde, Temperature and density profiles of electrons i n a hollow cathode argon-arc discharge. J . Q i w r r . Spcc/ro.\c. Rtmdior. Trcrtrsfer 12, 1497 (1972). 46c. R . Van der Sijde, Configuration temperatures in a hollow cathode argon arc and transition probabilities o f A r I I spectrum. J . Quoirt. Spectrarc. Rtrdirrt. Trtm.sfir 12, 703 ( 1 772). *47. 1,S. Hall, and A . L. Gardner, Highly ionized steady state plasma system. PIIS.\. Nrrit1.c 3 7 ) . 788 ( I962). 48. J . N. Haniawi. and L. M. Lidsky. Argon excited-stale densities in a hollow cathode discharge. Qmuirr. Progr. Rep. (MZT)76, I33 ( I965). *4Y. D. J. Rose, and M. Clark “Plasmas and Controlled Fusion.”p.169. MIT Press, Cambridge. Massachusetts, 1961. 50. E. I . Gerry, and D . J. Rose, Plasma diagnostics by Thonison scattering of a laser beam. J . Appl. Plryc. 37.(7) 2715 (1966). 5 1 . R. V. Aldridge. and B. E. Keen. Rotationally-convected drift wave instability in an inhoniogeneous plasma column. P/r.snia. P l i w 12. I (1970). 5-7. D. L. Flannery, and S. C. Brown, Alternating current diagnostic study of diffusion in a highly ionized plasma in a magnetic field. Phys. %ids 13(4), 1066 (1970). 53. S. L. Leonard, Electron and ion teniperatures i n steady-state H e and Ar plasmas i n a lotrized Guses, 9/11, 1969 p. 170 (1969). magnetic field. Proc. I n / . ConJ Pl~enoi~ieno

188

JEAN-LOUP DELCROIX A N D ARMAND0 ROCHA TRINDADE

54. G . K. McCormick, and L. M. Lidsky, Thomson scattering from a hollow cathode discharge plasma. Quarf.Progr. Rep. ( M I T ) 101, 72 (1971). 55. J . H. Noon, H. A . Schmidt, and E. H. Holt, Connection between self exicted low frequency oscillations and anomalous plasma diffusion. Plasma. Phys. 12,477 (1970). 56. A. S. Roberts, Jr. and W. H. Benett, Plasma temperature measurements for the hollow cathode discharge. J . Appl. Phys. 35(12) 3434 (1964). 57. J. K. Silk, ion temperature measurement in the hollow cathode arc plasma. Qrinrt. Progr. Rep. ( M I T ) 88, 149 (1968). *58. A. M. Cravath, The rate at which the ions loose energy in elastic collisions. Phys. Rev. 36, 248 (1930). *59. L. Spitzer, and R. Harm, Transfer phenomena in a completely ionized gas. Phys. Rev. 89, 977 (1953). ‘60. P. Mahadevan, and G . D. Magnuson, Low energy (1-100 eV) charge transfer cross section measurement for noble gas in collisions with gases. Phys. Reu. 171, 103 (1968). 61. F. Boeschoten, and L. J. Demeter, Measurements of plasma rotation in a hollow cathode discharge. Plasma Phys. 10, 391 (1968). 62. M. Hudis, D. J. Rose, J. Small, and K. Chung, Experimental study of hollow cathode arc plasma. Qunrf. Progr. Rep. ( M I T )85, 193 (1967). 63. M. Hudis, and L. M . Lidsky, Observation of a centrifugally driven E x B flute in a hollow cathode discharge. Bull. Amer. Phys. Soc. (1969). 64. K . Chung, and D. J . Rose, Correlation study of a drift wave instability. Appl. Phys. Left. 11(8), 247 (1967). *65. R. W. Montgomery, and C. M. H. Sharp, The effect of the cathode geometry in the stability of the arcs. Brif. J . Appl. Phys. 2, 1345 (1969). *66. G . Ecker, Electrode components of the arc discharge. Ergeb. Exukt. Nafur. 33,9 ( I 961). *67. B. B. Kadomtsev, “Plasma Turbulence.” p. 99. Academic Press, New York, 1965. 68. N. M. Ceglio, and L. M. Lidsky, Ion acoustic wave propagation near the ion cyclotron frequency. Phys. Fluids 13, 1 108 (1970). 69. B. E. Keen, and R. V. Aldridge, Experimental dispersion curves for low frequency drift waves in an inhomogeneous magneto-plasma. Plustiin Phys. 12, 839 (1970). 70. B. E. Keen, and R. V. Aldridge, Suppression of a drift type instability in a magnetoplasnia by a feedback technique. Phys. Rev. Left. 22(25), 1358 (1969). 71. B. E. Keen, and R. V. Aldridge, Apparent parametric enhancement of a “drift type” instability. Phys. Letf. A 29(l I ) , 690 (1969). 7-1. B. E. Keen, Interpretation of experiments on feedback control of a “drift type” instability. Phys. Rev. Lerf. 24(6), 259 (1970). *72a. A. Guthrie, and R. K. Wakerling, “The characteristics of Electrical Discharges in Magnetic Fields” Chapter 11. McGraw-Hill, New York, 1949. 73. S. Yoshikawa, and D. J. Rose, Anomalous diffusion of a plasma across a magnetic field. Pliys. Fluids 5(3), 334 (1962). 74. D. L. Flannery, Diffusion waves in hollow cathode arc. Qimrt. Progr. Rep. ( M I T ) 82, 97 ( 1966). 75. M. Hudis, and L. M . Lidsky, Particle flux measurements in a hollow cathode arc. Quart. Progr. Rep. ( M I T ) 91, 141 (1968). 76. R. Cano, and M. Mattioli, Diffusion transversable dans une colone de plasma fortement ionise. Rep. C.E.A. (1968). 77. K . Chung, and K. Huang, Quiescent and weakly turbulant plasma column, produced by a hollow cathode arc discharge. Proc. I t i f . ConJ Hollow Cathode Di.celiiirge.r Appl. I s t , 1971 p. 35 (1971).

HOLLOW CATHODE ARCS

189

78. J. C . Woo, L. M. Lidsky. and D. J. Rose, Hollow cathode discharge III experiment. Quart. Progr. Rep. ( M I T ) 76, 130 (1965). 79. D. J . Rose, and J. C . Woo, Physical model of a plasma column universal instability. Bull. Amer. Phys. SOC.p. 802 (1967). 80. H. Minoo, Discharge-induced pressure inside the gas-fed hollow cathodes in arc regime. Proc. Int. Conf. Hollow Cathode Discharges Appl. Is/, 1971 p. 20 (1971). 81. H. Minoo, La pression de gaz et la densite des electrons au niveau de la zone active des dkharges d’arc a cathode creuse. Rapp. Orsay LP 119 (1970). 82. M. 0. Lubin, and D. G . Rose, Internal gaseous electronics and emission mechanism of the HCD. Bull. Amer. Phys. SOC.p. 694 (1967). *83. A. N. Chester, Gas pumping in discharges. Phys. Rev. 169, 172 (1968). *84. J. Hirschfelder, C . F. Curtiss, and R. B. Bird, “Molecular Theory of Gases and Liquids.” Wiley, New York, 1954. *85.L. Vriens, Calculations of absolute cross-sections of He...Hg. Phys. Lett. 8, 4 (1963). *86. D. Wanless, Electron-ion recombination in argon. Proc. Phys. Soc. London ( A t . Mot. Phys.) 4, 522 (1971). 87. J. L. Delcroix, Gaseous Electronics Conf., Hartford, Connecticut (1970). 88. W. P. Allis, personal communication (1972). 89. W. P. Allis, “Les fonctions de distribution.” Internal Rep. LP, Orsay (1972). 90. C. M. Ferreira, personal communication. (1972). 91. J. L. Delcroix, H. Minoo, and A. R. Trindade, Plasma source using gas-fed multichannel HCA. Proc. I n / . Conf. Phenomena Ionized Gases, 9th, 1968 (1969). ‘92. V . F. Kiteava, A. N. Odintsov, and N. N. Sobolev, Continuously operating ion laser. Sou. Phys. Usp. 99(3,4), 699 (1970). 93. P. H. Edmonds, E. T. Gerry, and L. M. Lidsky, The hollow cathode discharge as a laser. Quart. Progr. Rep. (MIT)76, 129 (1965). 94. M. D. Lubin, Measurement of the optical gain of the hollow-cathode discharge. Quart. Progr. Rep. ( M f T )79, 133 (1966). 95. D. A. Huchital, and J. D. Rigden, Argon laser action in a thermionic hollow cathode discharge. IEEE J . Quantum Electron. 3(9), 378 ( 1 967). 96. V. F. Kitaeva, Yu. 1. Osipov, P. L. Rubin, and N. N . Sabolev, On oscillation mechanism in cw-ion argon laser. ZEEE J . Qunnrutn Electron. 5(2), 72 (1969). 97. A. R. Trindade, 0 laser de argon ionizado: mecanisnios fundamentais. Mem. Acad. Cienc. Lisbon 14, 327 (1970). *98. D. MacNair, Study of electron emitters for use in gas lasers. I€€€ J. Quantum Electron. 5(9), 460 (1969). 99. B. P. Day, and S. R. Hastings, The RAE 10 cm hollow cathode mercury thruster. DGLR Symp. Elec. Space Proprilsion Syst., 1971 p. 71-028 (1971). 100. C. M. Philip, The design and operation of a hollow cathode for electron bombardment ion thrusters. RAE Tech. Rep. 69 213 (1969). 101. G. A. Csiky. Investigation of a hollow cathode discharge plasma. AIAA J . 69, 258 ( 1969). 102. V. K. Rawlin, and E. V. Pawlick, A mercury plasma bridge neutralizer. A f A A J . 67, 670 ( I 967). 103. D. G . Fearn, C. M. Philip, and J. W. Pye, The development of hollow cathodes, vaporizers and isolators for use in mercury ion thrusters. DGLR Symp. Elec. Space Propulsion Sysr., 1971 p. 71-044 (1971). 104. B. P. Day and R. Hastings, Experiments with the first RAE electron bombardment ion engine. RAE Tech. Rep. 71 023 (1971).

190

JEAN-LOUP DELCROIX AND ARMAND0 ROCHA TRINDADE

105. W. Knauer, and R. L. Poeschel, Investiagtion of hot cathode reflex discharges. Proc. Znt. Conf. Phenomena Zonked Gases, 9tl1,1 9 6 9 ~219 . (1969). 106. E. Zeyfang, High current hollow cathode ion sources. Pror. Znt. ConJ Gas Discharges, Is,, 1971 251 (1971). 207. S. Ibadov, Optimization and properties of ion plasma source based on hollow cathode. Radio Eng. Electron. Phys. (USSR) 15(5), 836 (1970). 108. D. B. Fradkin, A. W. Blackstock, D. J. Roehling, T. F. Stratton, M. Williams, and

K . W. Liewer, Experiments using a 25-kW hollow cathode lithium vapor MPD arcjet. AIAA J . 8(5), 886 (1969). 109. A. Bouwknegt, and A. G. van der Kooi, An electrode design for low pressure gas discharge lamps. Proc. Int. Conf: Gas Dbcharges, Ist, 1971 p. 217 (1971). 110. A. E. Koltypin, A. I . Nastyakha, and P. A. Smirnov, A valve effect in the low pressure arc discharge in the system of electrodes with a hollow cold cathode. Proc. Z.C.P.Z.G., 9th, I969 p.164 (1969). 111. A. E. Koltypin, A. I. Nastyakha, and P. A. Smirnov, Rectification in a low-pressure arc with a hollow cold cathode. Sou. Phys. Tech. Phys. 15(10), 1703 (1971). 112. A. E. Koltypin, A. I. Nastyakha, and P. A. Smirnov, Arc dynamics in a high current . 1710 (1971). hollow cathode rectifier. Sou. Phys.-Tech. P h y ~ 15(10), 113. A. S . An'shakov, V. V. Koslov, and M. I. Sazonov, Study of the free plasma jet. Proc. Z.C.P.I.G., Yth, 1969 p. 247 (1969). 114. B. 0. Baker, and J. Gowar, Hot hollow cathode phenomena. Pvor. Znt. ConJ Hollow Cathode Discharges Appl., Is?, 1971 p. 48 (1971). 115. E. G. Busygin, V. G. Grigor'yants, and 1. P. Yavor, Hollow cathode thermionic converter operating with a low-voltage cesium arc. Sou. Phys.-Tech. Phys. 2(1 l), 1593 (1970). 116. H. L. Witting, Hollow cathode discharge with thermionic cathodes. J . Appl. Phys. 42(13), 5478 (1971). 117. A. S. Roberts, J. L. Cox, and W. H. Bennett, Electron beams from a Duoplasmatron using a hollow cathode arc as an electron source. J . Appl. Phys. 37(8), 3231 (1966). 118. H. C. Cole, and A. J. Travis, The hollow cathode as a means of triggering and sustaining a plasma accelerator. Proc. Int. ConJ Hollow Cathode Discharges Appl., Is!, 1971 p. 46 (1971). 119. W. S . Bickel, Acoustical plasma wave in a hollow cathode discharge. J . Appl. Phs. 37(11), 4300 (1966).

* General references, not dealing specifically with HCA.