- Email: [email protected]
Pulsed microwave plasma production in a conducting tube with a radius below cutoff
Vacuum 58 (2000) 222}232
Pulsed microwave plasma production in a conducting tube with a radius below cuto! 夽 Sudeep Bhattacharjee*, Hiroshi Amemiya The Institute of Physical and Chemical Research (RIKEN), Hirosawa 2-1, Wako-shi, Saitama 351-0198, Japan
Abstract High-power (60}100 kW), short-pulse (0.05}1.0 ls) microwaves of 3 GHz with a repetition frequency of 10}500 Hz are used to produce a plasma in a pressure range of 10\}10 Torr in a circular conducting tube with a cross section below the cuto! value for the fundamental waveguide mode (TE ). The waves are launched perpendicular to the cusped magnetic "eld, created by permanent magnets surrounding the tube. Results indicate that, the plasma density is higher at the tube entrance and at a location inside the tube near the exit. From regions of higher density, plasma di!uses towards the tube center with the radial di!usion suppressed by the magnetic bottle. The density uniformity is better below 0.1 Torr. The repetition frequency has only a small in#uence on the discharge properties, although the peak current and the decay time constant increase with pulse duration. The electron temperature is 6}10 eV even in the power-o! phase and the current build-up is delayed to a few to tens of microseconds from the end of the pulse. These "ndings indicate distinct di!erences from conventional afterglows. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Waveguide cuto!; Density cuto!; Perpendicular launch; Narrow cross-sectional plasma; High power shortpulse microwaves; Plasma build-up; Plasma dispersion; Ponderomotive force; Pulse duration; Repetition frequency
1. Introduction Microwave plasma production in a narrow tube is of interest because a high-density narrow cross-sectional plasma with a high electron temperature is required in multicharged ion sources [1], laser guiding through plasma in narrow tubes for particle acceleration [2] and inner surface processing of small diameter tubes [3], etc. 夽
Paper presented at the 11th International School on Vacuum, Electron and Ion Technologies, 20}25 September 1999, Varna, Bulgaria. * Corresponding author. E-mail address: [email protected] (S. Bhattacharjee). 0042-207X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 0 ) 0 0 1 7 2 - X
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When the cross section is reduced, microwave power density in the tube increases. This helps in the production of a plasma with a density even higher than the cuto! density [4] (overdense plasma). Despite the problems of wave propagation through a waveguide below cuto! size and wave re#ection from an overdense plasma, compact microwave plasmas with densities above the cuto! density of ordinary mode have been produced and maintained over an axial length of &40 cm in 10\ Torr range of pressure [5,6]. Physical mechanisms have been presented to explain the plasma production and maintenance through the peripheral plasma [6] where electron cyclotron resonance heating (ECR) was expected and the electron temperature could be made rather high (10}14 eV). The above experiments [4}6] are concerned with the use of microwaves in the continuous (cw) mode at a low-pressure (10\}10\ Torr) regime. Meanwhile, pulsed plasmas by high-power short-pulse microwaves have been investigated for several applications [7,8]. Pulsed microwaves are useful to obtain discharges at a higher pressure. Recently, the plasma state between the pulses (interpulse plasma) has been found to produce metastables, radicals and negative ions [9]. Unlike conventional afterglows, the electron temperature is high in the power-o! phase of the discharge. Although the work was performed in a waveguide of large diameter, it is of interest to produce and maintain such a plasma in a narrow tube from the viewpoint of new applications. With high-power microwaves, e!ects such as particles driven by potential and ponderomotive forces, non-linear dispersion, additionally, the anisotropic di!usion of the plasma brought about by the arrangement of the magnets are expected. 2. Experimental set-up and procedures Fig. 1 shows a schematic of the experimental apparatus. The pulsed microwaves produced by a magnetron oscillator OSC have a frequency of 3 GHz, output peak power 60}100 kW and a pulse duration t 0.05}1.0 ls in full-width at half-maximum (FWHM). The pulse repetition U frequency f is varied in the range 10}500 Hz. The waves are guided through an isolator ISO, an attenuator ATT, a coaxial cable Cx, a power monitor PM, a matching element M, a rectangular
Fig. 1. A schematic of the experimental apparatus; Magnetron oscillator (OSC), Isolator (ISO), Coaxial cable (Cx), Attenuator (ATT), Power monitor (PM), Matching element (M), Rectangular bend (H), Window (W), Chamber (C), Multicusp (MC), Waveguide (WG), Langmuir Probe (P), Computer (PC), Digital oscilloscope (DSO), Trigger signal (Trig), Probe voltage (< ), Boxcar integrator (BX), X}Y recorder (XY), Resistor (R).
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bend H, a quartz window W and launched into a circular conducting tube WG (37 cm in length, 5.74 cm i.d.) located inside a vacuum chamber C. A trigger signal Trig is used for pulse initiation and as a reference signal for diagnostics. PC is a computer for storing data obtained through a 4 channel digital oscilloscope DSO. The cuto! radius of the TE mode is given by R "o j /2p, where o "1.841, is the "rst M root of the derivative of the Bessel function J , and j is the vacuum wavelength of microwaves. M For microwaves of 3 GHz, j "10 cm giving R "2.93 cm. The inner diameter of WG is therefore M smaller than the cuto! value. WG is inserted into a multipolar magnet structure (MC) from henceforth referred to as a `multicuspa, constructed with permanent magnets (10 poles) to provide a minimum-B "eld for particle con"nement. The con"guration results in a "eld which is mainly transverse to the axis (z) of the tube. The waves are launched perpendicular to the transverse "eld. The design of the multicusp and the "eld distribution have been described earlier [5]. The temporally varying pro"les of ion (I ) and electron currents (I ) and probe characteristics > were measured by a Langmuir probe (plane, 5 mm diameter) denoted by P in Fig. 1, using the DSO with time averaging (64 shots) and a Boxcar integrator BX, respectively. The probe was inserted through an axial port and could be moved along WG. For measuring I and I the probe was > biased at "xed negative and positive voltages against ground, respectively. Whereas, the voltage was swept for obtaining the probe characteristics. The gate aperture of BX was set at 0.1 ls and the probe characteristics were measured to a delay of 30}50 ls from the end of the microwave pulse in steps of &1.0 ls, by a slow scanning of the probe voltage. From the probe characteristics the temporal variation of the electron temperature ¹ and the plasma (electron) density N were deduced. During the probe measurements the probe surface was set parallel to the wave vector. WG together with MC served as the reference electrode which was connected with the grounded chamber. The ratio of the inner surface of WG where the plasma was con"ned to the probe area was &1700, which may be considered as adequate for obtaining reliable probe characteristics. Measurements were mostly made along the axis of the tube (cf. Fig. 1) where the magnetic "eld is almost zero. In this position, the ion and electron currents to the probe are very little in#uenced by the "eld. The ion current I was measured at a deep negative bias so that its dependence on the probe > voltage < was small and I is proportional to N . On the other hand, the electron current I was > > measured in the retarding potential region, i.e.,
i¹ !e(< !< ) exp . (1) I "N eS > 2pm i¹ From the ratio of I and I the space potential < can be estimated from the following equation: > I i¹ < " ln > #m, (2) I e where m is a constant to be determined by considering the boundary condition that < P0 at Q tPR. The microwave electric "eld EI inside the tube was measured using a needle-type probe with a 1.5 mm length aligned parallel to the central electric "eld in the circular mode. The electric "eld
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impulse was recti"ed by a crystal diode responsive to the GHz range microwave "eld. The axial variations of I and E were measured in DSO by moving the respective probes along the > waveguide and recording the peak current and the "eld signal, respectively. The axial variation of N was also measured for checking reproducibility. > 3. Experimental results Fig. 2 shows a typical temporal pro"le of the ion current I at pressure p"0.7 Torr measured at > an axial distance z"22 cm inside the tube. Unless otherwise stated the peak power, the pulse repetition frequency and the pulse duration was set at 60 kW, 246 Hz and 1.2 ls, respectively. Distance z"0 corresponds to the entrance of the waveguide at the microwave input side. Time t"0 corresponds to the beginning of the pulse. It is noted that the plasma is produced inside the narrow tube and the build up is delayed from the end of the microwave pulse marked as `End of pulsea: the plasma build-up time is about 2.0 ls. From the time delay of build-up q at z, the ion drive velocity v was determined by v"z/q. Fig. 3 shows the dependence of the drive velocity v on the pressure p. v was determined by shifting the probe along z near the tube entrance and recording the temporal shift of the peak ion I and electron I currents. It is seen that v is of the order of &10 cm/s and slightly increases
>
with pressure. A comparison of v with the ion accoustic velocity C ("0.3 } 0.5;10 cm/s) shows Q that they are of the same order.
Fig. 2. The temporal variation of the ion current at a pressure p"0.7 Torr and axial position z"22 cm.
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Fig. 3. The dependence of the drive velocity v with pressure p. v is found to be comparable to the ion accoustic velocity.
Fig. 4 shows the temporal variation of the space potential < as determined from Eq. (2) at some pressures measured at z"2 cm. It is noted that < has a higher value during the initial stages and gradually decreases with time. At lower pressures (eg. 0.06 and 0.1 Torr), the slope d< /dt is larger and the plasma seems to reach the potential equilibrium more quickly. The temporal variation of the electron temperature ¹ determined from the probe characteristics shows a value of about 6}10 eV for at least few tens of microseconds after the end of the microwave pulse. At a time close to the end of the pulse, ¹ was higher. At a higher p, ¹ decays faster temporally and with increase in time the dependence on p becomes small. The electron density N showed a peak value over 10 cm\. In evaluating the plasma density, an assumption of a Maxwellian plasma was made, which will introduce a certain error in the density if the electron energy distribution is non-Maxwellian. The error was estimated to be in the range 5}9%. Fig. 5(a) shows the axial variation of the plasma (ion) density N with p measured at t"10 ls > after the end of the pulse. Measurements at a time close to the end of the pulse was di$cult because the ion current had a disturbance. The maximum value of N is'10 cm\. It may be noted that > N is peaked near z&0 and a second peak appears at z"z &20}30 cm and "nally falls beyond >
30 cm. The value of N in the intermediate region lies in the range of 10 cm\. Thus, two regions > with higher plasma density have been identi"ed, the peak current of the latter being usually 50% of the "rst. Fig. 5(b) shows the axial variation of the microwave electric "eld EI for some pressures p. The axial variation of EI shows a maximum near the tube entrance and another maximum around z"20}30 cm near the exit. Between the two maxima a few crests and troughs are seen at an interval of &5 cm. As p is lowered (0.06 Torr) the peaks become di!used and broader. However,
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Fig. 4. The temporal variation of the space potential < measured at an axial position z"2 cm for some pressures p.
the presence of higher "elds near the entrance and exit of the waveguide are still noticeable. Measurements under vacuum showed that the "eld is higher near the entrance and decreases exponentially along the tube. The "eld pattern is distinctly di!erent than that during the presence of the plasma, depending upon the plasma density and its gradient at the entrance of the tube. The axial variations of EI and N have a spatial correlation. > Fig. 6 shows the e!ect of varying the pulse repetition frequency f (10}500 Hz) on the axial pro"le of the peak ion current I at pressure p"1.0 Torr. Two prominent current peaks are
> observed which is consistent with Fig. 5(a) but the magnitude of the current and the spatial pro"le only weakly depends on f . At p)0.1 Torr the axial current gradually decreases along the tube and the second peak is not observed, indicating that the plasma uniformity is better at lower pressures. Fig. 7 shows the e!ect of varying the pulse duration t on the peak electron current I at
pressures p"0.1, 0.5 and 1.0 Torr, respectively, measured at z"20 cm. An increase in t leads to an increase in I for pressures above 1 Torr.
4. Discussion The results indicate that higher density plasmas are produced at the tube entrance (z&0) and at z"z &20}30 cm near the tube exit. A high electron temperature helps plasma production and K maintenance in the interpulse regime. From regions of higher density, the plasma can di!use axially
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Fig. 5. The axial variation of (a) plasma (ion) density N measured at a time t"10 ls from the end of the microwave > pulse and (b) the microwave electric "eld EI , at pressures p"5.0 Torr, 1.0 and 0.06 Torr, respectively.
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Fig. 6. The e!ect of varying the pulse repetition frequency f on the axial pro"le of the peak ion current I at a pressure
> p"1.0 Torr.
Fig. 7. The e!ect of varying the pulse duration t on the peak electron current I .
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toward the tube centre where the density is lower. Additionally, a shift in the axial position of the peak current indicates that the charged particles are driven through the tube inlet. With regard to this, the e!ect of the electrostatic and ponderomotive forces may be considered. 4.1. Electric xeld penetration Although the radius of the tube is smaller than the cuto! value, experimental results indicate that even under vacuum conditions the "eld can penetrate into the tube. This is considered to be due to an e!ect of the evanescent high-power wave, the "nite length e!ect of the tube and power loss e!ect due to a "nite conductivity of the wall. These e!ects will cause discrepancies from an in"nitely long conducting wall tube. The strong "eld near the tube entrance (cf. Fig. 5(b)) will help in the production of a dense plasma at that location. After the plasma is created at the entrance, the refractive index g is modi"ed from that of vacuum. Calculations using the cold plasma dispersion, including collisions, for waves launched perpendicular to B show that g(r) is constant (0.875) from the tube centre until r"1.4 cm, but increases sharply toward unity near the wall. The pro"le of g(r) suggests that the plasma at the "rst maximum N behaves similar to a concave lens. > As a possible mechanism of the second peak in the microwave electric "eld, it is considered that the waves are refracted by the plasma lens and diverge towards the inner wall of the tube. After they are re#ected by the wall, phase mixing will occur and a second point of maximum amplitude will occur. This corresponds to the region z as found experimentally.
4.2. Plasma build-up The high power in the pulse generates strong electric "elds of short interval which can accelerate electrons to high energies. The high-energy (hot) electrons gradually lose energy by collision with neutrals, in the event of which the ionization increases due to convolution of collision cross section with electron energy distribution function (peak &50 eV for singly charged Ar ions), before eventually decreasing at lower energies. This slowing down process could be a reason for the observed delay in the plasma build-up. The higher plasma densities at z&0 and z can be explained by the higher ionization e$ciency
since the electric "eld was stronger at these positions. The correlation between the axial variations of N and EI supports this view. > Fig. 4 shows that at the entrance of the tube (z"2 cm) the space potential < drops rapidly in about 1 ls. Such a potential drop would repel electrons and force them to move in the axial direction. Ions would eventually follow electrons by the space charge "eld. We de"ne here v as an Q electrostatic drive velocity caused by this potential e!ect. Besides this, high-power microwaves during the pulse can exert a ponderomotive force on the electrons. The force is expressed as F "!(u/u) (o EI /2), where o and EI are the dielectric M M constant in vacuum and the microwave electric "eld, respectively [10,11]. F can be written as F "! (P/2cA), where P, c and A are the power, the light velocity and the cross section of the wave. If we assume that u u and the wave cross section is equal to that of the waveguide N (A"pd/4"25.9;10\ m), we have o EI /2"(3}4);10\ (J m\) for P"60 kW. On the M other hand, the force F due to the pressure gradient is given by F " (N i¹ ). For typical
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experimental conditions of N "10}10 m and ¹ 10 eV, N i¹ "(2}16);10\ (J m\). Therefore, under the present experimental situation, F and F become of the same order. We de"ne v as a drive velocity due to the ponderomotive force. The measured drive velocity v shown in Fig. 3 is considered to be the sum of two kinds of driven velocity, v"v #v which drives the particles through the tube inlet. The minimum-B structure of the multicusp magnetic "eld suppresses radial di!usion. At p"1 Torr and ¹ "6 eV, the electron gyroradius at a position near the wall (B"1000 G) is &0.01 cm. Therefore, the plasma would be transported mostly by the axial di!usion. The delayed build-up, high electron temperature and particle transport in the power-o! phase are new properties as compared to the conventionally known afterglows. 4.3. Pulse repetition frequency and pulse duration It was seen that the pulse repetition frequency f does not signi"cantly change the ion current and the spatial pro"le. This suggests that any charge accumulation by pulse repetition is small. The phenomena at each pulse can be therefore considered as independent. However, an increase in the pulse duration increases the energy input to the plasma. This leads to higher values of peak current and decay time constant, thereby allowing additional control of the plasma in the tube.
5. Conclusions A pulsed microwave plasma has been produced in a circular conducting tube with a radius smaller than the cuto! value. The principal mechanisms of plasma production and maintenance are gaseous breakdown by electric "eld penetration and wave propagation by non-linear dispersion. Charged particles are axially driven into the tube by plasma electrostatic and ponderomotive force of the high-power wave. The anisotropic di!usion of the charged particles is favorable for axial plasma uniformity in the tube. The interpulse plasma, characterized by a high electron temperature and a delayed build-up are new features of a plasma without an energy source.
Acknowledgements One of the authors (S.B.) gratefully acknowledges the support from a special postdoctoral fellowship of the basic science program (RIKEN).
References [1] Biri S, Nakagawa T, Kidera M, Miyazawa Y, Hemmi M, Chiba T, Inabe N, Kase M, Kageyama T, Kamigaito O, Goto A, Yano Y. Nucl Instr and Meth 1999;152:386. [2] Dorchies F, Marques JR, Cros B, Matthieussent G, Courtois C, Velikoroussov T, Audebert P, Geindre JP, Rebibo S, Hamoniaux G, Amirano! F. Phys Rev Lett 1999;82:4655.
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[3] Fujiyama H, Tokitu Y, Uchikawa Y, Kuwahara K, Miyake K, Kuwahara K, Doi A. Surf Coatings Technol 1998;98:1467. [4] Amemiya H, Maeda M. Rev Sci Instrum 1996;67:769. [5] Bhattacharjee S, Amemiya H. Jpn J Appl Phys 1998;37(1):5742. [6] Bhattacharjee S, Amemiya H. Rev Sci Instrum 1999;70:3332. [7] Askaryan GA, Batanov GM, Barkhudarov AE, Gritsinin SI, Korchagina EG, Kossyi IA, Silakov VP, Tarasova NM. J Phys D 1994;27:1311. [8] Gurevich AV, Borisov ND, Lukina NA, Sergeichev KF, Sychov IA, Kozlov SI, Smirnova NV. Phys Lett 1995;A 201:234. [9] Bhattacharjee S, Amemiya H. J Appl Phys 1998;84:115. [10] Chen FF. In: Introduction to plasma physics and controlled fusion, Vol 2. New York: Plenum Press, 1984. p. 305 (Chapter 8). [11] Ito H, Nishida Y, Yugami N. Phys Rev Lett 1996;76:4540.
Pulsed microwave plasma production in a conducting tube with a radius below cuto! 夽 Sudeep Bhattacharjee*, Hiroshi Amemiya The Institute of Physical and Chemical Research (RIKEN), Hirosawa 2-1, Wako-shi, Saitama 351-0198, Japan
Abstract High-power (60}100 kW), short-pulse (0.05}1.0 ls) microwaves of 3 GHz with a repetition frequency of 10}500 Hz are used to produce a plasma in a pressure range of 10\}10 Torr in a circular conducting tube with a cross section below the cuto! value for the fundamental waveguide mode (TE ). The waves are launched perpendicular to the cusped magnetic "eld, created by permanent magnets surrounding the tube. Results indicate that, the plasma density is higher at the tube entrance and at a location inside the tube near the exit. From regions of higher density, plasma di!uses towards the tube center with the radial di!usion suppressed by the magnetic bottle. The density uniformity is better below 0.1 Torr. The repetition frequency has only a small in#uence on the discharge properties, although the peak current and the decay time constant increase with pulse duration. The electron temperature is 6}10 eV even in the power-o! phase and the current build-up is delayed to a few to tens of microseconds from the end of the pulse. These "ndings indicate distinct di!erences from conventional afterglows. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Waveguide cuto!; Density cuto!; Perpendicular launch; Narrow cross-sectional plasma; High power shortpulse microwaves; Plasma build-up; Plasma dispersion; Ponderomotive force; Pulse duration; Repetition frequency
1. Introduction Microwave plasma production in a narrow tube is of interest because a high-density narrow cross-sectional plasma with a high electron temperature is required in multicharged ion sources [1], laser guiding through plasma in narrow tubes for particle acceleration [2] and inner surface processing of small diameter tubes [3], etc. 夽
Paper presented at the 11th International School on Vacuum, Electron and Ion Technologies, 20}25 September 1999, Varna, Bulgaria. * Corresponding author. E-mail address: [email protected] (S. Bhattacharjee). 0042-207X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 0 ) 0 0 1 7 2 - X
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When the cross section is reduced, microwave power density in the tube increases. This helps in the production of a plasma with a density even higher than the cuto! density [4] (overdense plasma). Despite the problems of wave propagation through a waveguide below cuto! size and wave re#ection from an overdense plasma, compact microwave plasmas with densities above the cuto! density of ordinary mode have been produced and maintained over an axial length of &40 cm in 10\ Torr range of pressure [5,6]. Physical mechanisms have been presented to explain the plasma production and maintenance through the peripheral plasma [6] where electron cyclotron resonance heating (ECR) was expected and the electron temperature could be made rather high (10}14 eV). The above experiments [4}6] are concerned with the use of microwaves in the continuous (cw) mode at a low-pressure (10\}10\ Torr) regime. Meanwhile, pulsed plasmas by high-power short-pulse microwaves have been investigated for several applications [7,8]. Pulsed microwaves are useful to obtain discharges at a higher pressure. Recently, the plasma state between the pulses (interpulse plasma) has been found to produce metastables, radicals and negative ions [9]. Unlike conventional afterglows, the electron temperature is high in the power-o! phase of the discharge. Although the work was performed in a waveguide of large diameter, it is of interest to produce and maintain such a plasma in a narrow tube from the viewpoint of new applications. With high-power microwaves, e!ects such as particles driven by potential and ponderomotive forces, non-linear dispersion, additionally, the anisotropic di!usion of the plasma brought about by the arrangement of the magnets are expected. 2. Experimental set-up and procedures Fig. 1 shows a schematic of the experimental apparatus. The pulsed microwaves produced by a magnetron oscillator OSC have a frequency of 3 GHz, output peak power 60}100 kW and a pulse duration t 0.05}1.0 ls in full-width at half-maximum (FWHM). The pulse repetition U frequency f is varied in the range 10}500 Hz. The waves are guided through an isolator ISO, an attenuator ATT, a coaxial cable Cx, a power monitor PM, a matching element M, a rectangular
Fig. 1. A schematic of the experimental apparatus; Magnetron oscillator (OSC), Isolator (ISO), Coaxial cable (Cx), Attenuator (ATT), Power monitor (PM), Matching element (M), Rectangular bend (H), Window (W), Chamber (C), Multicusp (MC), Waveguide (WG), Langmuir Probe (P), Computer (PC), Digital oscilloscope (DSO), Trigger signal (Trig), Probe voltage (< ), Boxcar integrator (BX), X}Y recorder (XY), Resistor (R).
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bend H, a quartz window W and launched into a circular conducting tube WG (37 cm in length, 5.74 cm i.d.) located inside a vacuum chamber C. A trigger signal Trig is used for pulse initiation and as a reference signal for diagnostics. PC is a computer for storing data obtained through a 4 channel digital oscilloscope DSO. The cuto! radius of the TE mode is given by R "o j /2p, where o "1.841, is the "rst M root of the derivative of the Bessel function J , and j is the vacuum wavelength of microwaves. M For microwaves of 3 GHz, j "10 cm giving R "2.93 cm. The inner diameter of WG is therefore M smaller than the cuto! value. WG is inserted into a multipolar magnet structure (MC) from henceforth referred to as a `multicuspa, constructed with permanent magnets (10 poles) to provide a minimum-B "eld for particle con"nement. The con"guration results in a "eld which is mainly transverse to the axis (z) of the tube. The waves are launched perpendicular to the transverse "eld. The design of the multicusp and the "eld distribution have been described earlier [5]. The temporally varying pro"les of ion (I ) and electron currents (I ) and probe characteristics > were measured by a Langmuir probe (plane, 5 mm diameter) denoted by P in Fig. 1, using the DSO with time averaging (64 shots) and a Boxcar integrator BX, respectively. The probe was inserted through an axial port and could be moved along WG. For measuring I and I the probe was > biased at "xed negative and positive voltages against ground, respectively. Whereas, the voltage was swept for obtaining the probe characteristics. The gate aperture of BX was set at 0.1 ls and the probe characteristics were measured to a delay of 30}50 ls from the end of the microwave pulse in steps of &1.0 ls, by a slow scanning of the probe voltage. From the probe characteristics the temporal variation of the electron temperature ¹ and the plasma (electron) density N were deduced. During the probe measurements the probe surface was set parallel to the wave vector. WG together with MC served as the reference electrode which was connected with the grounded chamber. The ratio of the inner surface of WG where the plasma was con"ned to the probe area was &1700, which may be considered as adequate for obtaining reliable probe characteristics. Measurements were mostly made along the axis of the tube (cf. Fig. 1) where the magnetic "eld is almost zero. In this position, the ion and electron currents to the probe are very little in#uenced by the "eld. The ion current I was measured at a deep negative bias so that its dependence on the probe > voltage < was small and I is proportional to N . On the other hand, the electron current I was > > measured in the retarding potential region, i.e.,
i¹ !e(< !< ) exp . (1) I "N eS > 2pm i¹ From the ratio of I and I the space potential < can be estimated from the following equation: > I i¹ < " ln > #m, (2) I e where m is a constant to be determined by considering the boundary condition that < P0 at Q tPR. The microwave electric "eld EI inside the tube was measured using a needle-type probe with a 1.5 mm length aligned parallel to the central electric "eld in the circular mode. The electric "eld
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impulse was recti"ed by a crystal diode responsive to the GHz range microwave "eld. The axial variations of I and E were measured in DSO by moving the respective probes along the > waveguide and recording the peak current and the "eld signal, respectively. The axial variation of N was also measured for checking reproducibility. > 3. Experimental results Fig. 2 shows a typical temporal pro"le of the ion current I at pressure p"0.7 Torr measured at > an axial distance z"22 cm inside the tube. Unless otherwise stated the peak power, the pulse repetition frequency and the pulse duration was set at 60 kW, 246 Hz and 1.2 ls, respectively. Distance z"0 corresponds to the entrance of the waveguide at the microwave input side. Time t"0 corresponds to the beginning of the pulse. It is noted that the plasma is produced inside the narrow tube and the build up is delayed from the end of the microwave pulse marked as `End of pulsea: the plasma build-up time is about 2.0 ls. From the time delay of build-up q at z, the ion drive velocity v was determined by v"z/q. Fig. 3 shows the dependence of the drive velocity v on the pressure p. v was determined by shifting the probe along z near the tube entrance and recording the temporal shift of the peak ion I and electron I currents. It is seen that v is of the order of &10 cm/s and slightly increases
>
with pressure. A comparison of v with the ion accoustic velocity C ("0.3 } 0.5;10 cm/s) shows Q that they are of the same order.
Fig. 2. The temporal variation of the ion current at a pressure p"0.7 Torr and axial position z"22 cm.
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Fig. 3. The dependence of the drive velocity v with pressure p. v is found to be comparable to the ion accoustic velocity.
Fig. 4 shows the temporal variation of the space potential < as determined from Eq. (2) at some pressures measured at z"2 cm. It is noted that < has a higher value during the initial stages and gradually decreases with time. At lower pressures (eg. 0.06 and 0.1 Torr), the slope d< /dt is larger and the plasma seems to reach the potential equilibrium more quickly. The temporal variation of the electron temperature ¹ determined from the probe characteristics shows a value of about 6}10 eV for at least few tens of microseconds after the end of the microwave pulse. At a time close to the end of the pulse, ¹ was higher. At a higher p, ¹ decays faster temporally and with increase in time the dependence on p becomes small. The electron density N showed a peak value over 10 cm\. In evaluating the plasma density, an assumption of a Maxwellian plasma was made, which will introduce a certain error in the density if the electron energy distribution is non-Maxwellian. The error was estimated to be in the range 5}9%. Fig. 5(a) shows the axial variation of the plasma (ion) density N with p measured at t"10 ls > after the end of the pulse. Measurements at a time close to the end of the pulse was di$cult because the ion current had a disturbance. The maximum value of N is'10 cm\. It may be noted that > N is peaked near z&0 and a second peak appears at z"z &20}30 cm and "nally falls beyond >
30 cm. The value of N in the intermediate region lies in the range of 10 cm\. Thus, two regions > with higher plasma density have been identi"ed, the peak current of the latter being usually 50% of the "rst. Fig. 5(b) shows the axial variation of the microwave electric "eld EI for some pressures p. The axial variation of EI shows a maximum near the tube entrance and another maximum around z"20}30 cm near the exit. Between the two maxima a few crests and troughs are seen at an interval of &5 cm. As p is lowered (0.06 Torr) the peaks become di!used and broader. However,
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Fig. 4. The temporal variation of the space potential < measured at an axial position z"2 cm for some pressures p.
the presence of higher "elds near the entrance and exit of the waveguide are still noticeable. Measurements under vacuum showed that the "eld is higher near the entrance and decreases exponentially along the tube. The "eld pattern is distinctly di!erent than that during the presence of the plasma, depending upon the plasma density and its gradient at the entrance of the tube. The axial variations of EI and N have a spatial correlation. > Fig. 6 shows the e!ect of varying the pulse repetition frequency f (10}500 Hz) on the axial pro"le of the peak ion current I at pressure p"1.0 Torr. Two prominent current peaks are
> observed which is consistent with Fig. 5(a) but the magnitude of the current and the spatial pro"le only weakly depends on f . At p)0.1 Torr the axial current gradually decreases along the tube and the second peak is not observed, indicating that the plasma uniformity is better at lower pressures. Fig. 7 shows the e!ect of varying the pulse duration t on the peak electron current I at
pressures p"0.1, 0.5 and 1.0 Torr, respectively, measured at z"20 cm. An increase in t leads to an increase in I for pressures above 1 Torr.
4. Discussion The results indicate that higher density plasmas are produced at the tube entrance (z&0) and at z"z &20}30 cm near the tube exit. A high electron temperature helps plasma production and K maintenance in the interpulse regime. From regions of higher density, the plasma can di!use axially
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Fig. 5. The axial variation of (a) plasma (ion) density N measured at a time t"10 ls from the end of the microwave > pulse and (b) the microwave electric "eld EI , at pressures p"5.0 Torr, 1.0 and 0.06 Torr, respectively.
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Fig. 6. The e!ect of varying the pulse repetition frequency f on the axial pro"le of the peak ion current I at a pressure
> p"1.0 Torr.
Fig. 7. The e!ect of varying the pulse duration t on the peak electron current I .
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toward the tube centre where the density is lower. Additionally, a shift in the axial position of the peak current indicates that the charged particles are driven through the tube inlet. With regard to this, the e!ect of the electrostatic and ponderomotive forces may be considered. 4.1. Electric xeld penetration Although the radius of the tube is smaller than the cuto! value, experimental results indicate that even under vacuum conditions the "eld can penetrate into the tube. This is considered to be due to an e!ect of the evanescent high-power wave, the "nite length e!ect of the tube and power loss e!ect due to a "nite conductivity of the wall. These e!ects will cause discrepancies from an in"nitely long conducting wall tube. The strong "eld near the tube entrance (cf. Fig. 5(b)) will help in the production of a dense plasma at that location. After the plasma is created at the entrance, the refractive index g is modi"ed from that of vacuum. Calculations using the cold plasma dispersion, including collisions, for waves launched perpendicular to B show that g(r) is constant (0.875) from the tube centre until r"1.4 cm, but increases sharply toward unity near the wall. The pro"le of g(r) suggests that the plasma at the "rst maximum N behaves similar to a concave lens. > As a possible mechanism of the second peak in the microwave electric "eld, it is considered that the waves are refracted by the plasma lens and diverge towards the inner wall of the tube. After they are re#ected by the wall, phase mixing will occur and a second point of maximum amplitude will occur. This corresponds to the region z as found experimentally.
4.2. Plasma build-up The high power in the pulse generates strong electric "elds of short interval which can accelerate electrons to high energies. The high-energy (hot) electrons gradually lose energy by collision with neutrals, in the event of which the ionization increases due to convolution of collision cross section with electron energy distribution function (peak &50 eV for singly charged Ar ions), before eventually decreasing at lower energies. This slowing down process could be a reason for the observed delay in the plasma build-up. The higher plasma densities at z&0 and z can be explained by the higher ionization e$ciency
since the electric "eld was stronger at these positions. The correlation between the axial variations of N and EI supports this view. > Fig. 4 shows that at the entrance of the tube (z"2 cm) the space potential < drops rapidly in about 1 ls. Such a potential drop would repel electrons and force them to move in the axial direction. Ions would eventually follow electrons by the space charge "eld. We de"ne here v as an Q electrostatic drive velocity caused by this potential e!ect. Besides this, high-power microwaves during the pulse can exert a ponderomotive force on the electrons. The force is expressed as F "!(u/u) (o EI /2), where o and EI are the dielectric M M constant in vacuum and the microwave electric "eld, respectively [10,11]. F can be written as F "! (P/2cA), where P, c and A are the power, the light velocity and the cross section of the wave. If we assume that u u and the wave cross section is equal to that of the waveguide N (A"pd/4"25.9;10\ m), we have o EI /2"(3}4);10\ (J m\) for P"60 kW. On the M other hand, the force F due to the pressure gradient is given by F " (N i¹ ). For typical
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experimental conditions of N "10}10 m and ¹ 10 eV, N i¹ "(2}16);10\ (J m\). Therefore, under the present experimental situation, F and F become of the same order. We de"ne v as a drive velocity due to the ponderomotive force. The measured drive velocity v shown in Fig. 3 is considered to be the sum of two kinds of driven velocity, v"v #v which drives the particles through the tube inlet. The minimum-B structure of the multicusp magnetic "eld suppresses radial di!usion. At p"1 Torr and ¹ "6 eV, the electron gyroradius at a position near the wall (B"1000 G) is &0.01 cm. Therefore, the plasma would be transported mostly by the axial di!usion. The delayed build-up, high electron temperature and particle transport in the power-o! phase are new properties as compared to the conventionally known afterglows. 4.3. Pulse repetition frequency and pulse duration It was seen that the pulse repetition frequency f does not signi"cantly change the ion current and the spatial pro"le. This suggests that any charge accumulation by pulse repetition is small. The phenomena at each pulse can be therefore considered as independent. However, an increase in the pulse duration increases the energy input to the plasma. This leads to higher values of peak current and decay time constant, thereby allowing additional control of the plasma in the tube.
5. Conclusions A pulsed microwave plasma has been produced in a circular conducting tube with a radius smaller than the cuto! value. The principal mechanisms of plasma production and maintenance are gaseous breakdown by electric "eld penetration and wave propagation by non-linear dispersion. Charged particles are axially driven into the tube by plasma electrostatic and ponderomotive force of the high-power wave. The anisotropic di!usion of the charged particles is favorable for axial plasma uniformity in the tube. The interpulse plasma, characterized by a high electron temperature and a delayed build-up are new features of a plasma without an energy source.
Acknowledgements One of the authors (S.B.) gratefully acknowledges the support from a special postdoctoral fellowship of the basic science program (RIKEN).
References [1] Biri S, Nakagawa T, Kidera M, Miyazawa Y, Hemmi M, Chiba T, Inabe N, Kase M, Kageyama T, Kamigaito O, Goto A, Yano Y. Nucl Instr and Meth 1999;152:386. [2] Dorchies F, Marques JR, Cros B, Matthieussent G, Courtois C, Velikoroussov T, Audebert P, Geindre JP, Rebibo S, Hamoniaux G, Amirano! F. Phys Rev Lett 1999;82:4655.
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[3] Fujiyama H, Tokitu Y, Uchikawa Y, Kuwahara K, Miyake K, Kuwahara K, Doi A. Surf Coatings Technol 1998;98:1467. [4] Amemiya H, Maeda M. Rev Sci Instrum 1996;67:769. [5] Bhattacharjee S, Amemiya H. Jpn J Appl Phys 1998;37(1):5742. [6] Bhattacharjee S, Amemiya H. Rev Sci Instrum 1999;70:3332. [7] Askaryan GA, Batanov GM, Barkhudarov AE, Gritsinin SI, Korchagina EG, Kossyi IA, Silakov VP, Tarasova NM. J Phys D 1994;27:1311. [8] Gurevich AV, Borisov ND, Lukina NA, Sergeichev KF, Sychov IA, Kozlov SI, Smirnova NV. Phys Lett 1995;A 201:234. [9] Bhattacharjee S, Amemiya H. J Appl Phys 1998;84:115. [10] Chen FF. In: Introduction to plasma physics and controlled fusion, Vol 2. New York: Plenum Press, 1984. p. 305 (Chapter 8). [11] Ito H, Nishida Y, Yugami N. Phys Rev Lett 1996;76:4540.