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Study of the velocity distribution in an intense pulsed hydrogen beam
Nuclear Instruments and Methods in Physics Research A239 (1985) 443-454 North-Holland, Amsterdam
STUDY OF THE VELOCITY A.S. B E L O V , S.A. K U B A L O V ,
DISTRIBUTION V.E. K U Z I K
IN AN INTENSE
443
PULSED
HYDROGEN
BEAM
a n d V.P. Y A K U S H E V
Institute for Nuclear Research of the Academy of Sciences of the USSR, 60th October Anniversary prospect 7a, Moscow 117312, USSR Rrceived 24 October 1983 and in revised form 6 March 1985
We present the results of measurements of the velocity distributions of particles in a pulsed hydrogen beam obtained from a dissociator with a radio frequency discharge (duration 1.0 ms, repetition rate 1 Hz). It is shown that the hydrogen inside the dissociator is heated up to - 2800 K, so the thermal dissociation of hydrogen molecules is essential. In order to cool the atoms, the gas was let through a pyrex channel 5 mm in diameter. The cooling channel walls being at room temperature and the channel having a length of 50 ram, we have obtained a supersonic beam of hydrogen atoms with a Mach number n i l = 2.7 +0.25. When the channel walls were cooled by the flowing liquid nitrogen and the channel was 70 mm long we obtained a beam of cooled atoms with a Mach number MII = 4.14 + 0.35. The velocity distribution of atoms depends on the power of the rf discharge inside the dissociator and on the gas consumption per pulse, and varies during the discharge pulse. For a temperature of the cooling channel walls Tch = 77 K, a gas consumption N = 3.3 × 1017 molecules per pulse and a discharge power of 0.23 kWcm -3, we have obtained an atomic beam with intensity I(0)= (2.8 + 0.8);,< 1020 atoms sr-1 s-1 and a most probable velocity oMp = (1.97 + 0.07)× 105 cm s-1.
1. Introduction The constant improvement of the atomic beam-type polarized proton sources (PPS) has resulted in the development of sources with a beam current greater than 100 /~A [1,21. At present, the acceleration of polarized protons in high energy accelerators [3-8] makes the development of pulsed PPS a very important problem. Earlier, Parker et al. [9] have shown that for a pulsed source with a low repetition frequency it is possible to obtain an improvement in the beam intensity of a factor of - 3 by operating the dissociator in the pulsed mode. Since the acceptance angle of the separating magnet in the atomic beam-type PPS is inversely proportional to the energy of the atoms [10], the current of the polarized ion beam increases as the hydrogen temperature falls, so in a number of PPS the dissociator was cooled by liquid nitrogen [2,11-14]. For a pulsed source the cooling of the dissociator nozzle to 28 K has led to an increase in the current of the polarized proton beam by a factor of 2.5 [15]. One more way to increase the beam current in the PPS is to obtain a supersonic flow of atoms from the dissociator. The nozzle sources of supersonic molecular beams proposed by Kantrowitz and Grey [16] give beams with intensity as high as 10 21 particles sr -1 s -1 [17], i.e. nearly two orders of magnitude higher than the intensity of beams in effusion sources. As far back as 1960, Keller et al. [18] have proposed to use supersonic beams in the PPS. At an adequate selection of the 0168-9002/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
nozzle and skimmer geometry the improvement in the intensity of an ideal supersonic beam in comparison with effusion beams is proportional to the Mach number squared [19]. The better monochromaticity of the supersonic beam [16] must lead to an additional increase of the atom density behind the separating magnet due to the smaller chromatic aberration during the focusing of atoms. U p to now the advantages of supersonic flows have not been fully used in PPS. Partially, this is due to the low hydrogen pressure ( - 1 Torr) in the PPS dissociator. For a beam of hydrogen atoms obtained from a microwave pulsed dissociator cooled to 77 K, the measured Mach number was about 1.5 [13]. As was discussed in ref. [19], the experimental investigation of conditions necessary for the formation of a supersonic flow at low gas pressures is an imperative necessity. A high intensity beam of hydrogen atoms was obtained from the pulsed dissociator designed for the PPS of the Moscow Institute for Nuclear Research [20]. In the present paper we present the results of the time-offlight measurements of the velocity distributions in supersonic flows of atomic hydrogen obtained from this dissociator. The aim of our work was to study experimentally the effect of such factors as the rf discharge power, gas consumption and atom cooling on the atom velocity distribution and on the density of a pulsed atomic beam. The time-of-flight measurements of the atom velocity are also a direct method to obtain information necessary for designing the optimal polarization system of the atomic beam in PPS.
444
A.S. Belov et aL / Velocity distribution in a pulsed hydrogen beam
2.1. General description o f the set
_y..The scheme of the set is shown in fig. 1. The electromagnetic valve injected molecular hydrogen into the dissociator tube, where the H 2 molecules were dissociated in pulsed rf discharge, excited inside the tube. The rf generator was pulsed by modulation of the anode voltage. The atomic beam was formed by the skimmer and the collimator. The dissociator tube and the rf coil of the generator were installed in a vacuum chamber, evacuated by a titanium sublimation pump with a pumping speed of ~ 4000 1 s -1 (H2). The apparatus for measuring the beam parameters was installed in the second vacuum chamber, evacuated by the same pump. The pulsed pressure in the chambers and the gas consumption in the dissociator were measured by a fast ionization-type pressure gauge. The beam density was measured by the time-of-flight mass spectrometer. For measuring the velocity distribution the beam was chopped into short segments by a mechanical chopper. The segments were detected by an ionization gauge whose signals were amplified and recorded by a storage-type oscilloscope. In the measurements of the particle density by the mass spectrometer the chopper was moved out of the beam. The zero-time signal for the time-of-flight velocity measurements produced by the light emitting diode-photodiode pair was also used to trigger the set. 2.2. Dissociator
In its main features the dissociator was similar to the one described in ref. [20]. The measurements were performed for three different dissociator tubes shown in fig. 2. The tubes were made of pyrex glass and, before installation into the vacuum chamber, were treated by hydrofluoric acid and after that by distilled water in order to lessen the surface recombination of atoms.
ELECT::~A~E NET]O ]~ANJ6Z~ETION/~oILM~I~;O~SDEC~NSETER
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DISS0CIAT0O tIagr EMITTIN6
ASSEMBLY
DIOI~E
OOLLINATOP
4 9. 3 4 5 er~ 9ISS0OlATOQ TUEE I-I. O. /
2. Experimental apparatus
SEAM
OIAOPPEQ
Fig. 1. Scheme of the experimental set.
c~
IONI::ATION GAUBEP-
~',-
%
.
000LING N= t~ OI-IANNEL
j J
80NII] NOZZLE
Fig. 2. Scaled drawing of the dissociator tube and of the system forming the atomic beam.
The geometry of the tube in fig. 2a was selected in view of measuring the gas temperature inside the tube. In the dissociator shown in fig. 2b the atoms were cooled as the beam was let through a channel with a length of 50 mm, an inner diameter of 5 mm and a wall temperature of 300 K. In the dissociator shown in fig. 2c the walls of a 70 mm long channel were cooled, by the flowing liquid nitrogen to 77 K. In all three cases the orifice diameter of the nozzle was 2.3 mm. The beam was formed by a skimmer made of stainless steel - a truncated hollow cone with an inlet diameter of 4 mm and internal and external angles of 45 ° and 50 ° respectively. A collimator ( ~ 6 ram) was installed for lowering the pulsed pressure in the apparatus chamber. For short, we will call the beams obtained from the dissociators shown in figs. 2a, 2b and 2c the hot, the warm and the cooled beams, respectively. The rf power was fed to the dissociator by a coil (5 turns, ~ 15 mm) inductively coupled with the rf discharge and supplied by the rf voltage with a frequency of 70 MHz from the rf generator. The modulator of the anode voltage of the rf generator produced voltage pulses with a height up to 6 kV and a duration varying from 0.05 to 3 ms. In the present work the measurements were done for a pulse duration of 1 ms and a repetition frequency of 1 Hz. The rf discharge was supplied by a power up to 0.8 kW cm -3 (the volume of the dissociator tube was 8 cm3). The highest rate of hydrogen dissociation was observed when the rf discharge was turned on simultaneously with the gas injection into the dissociator tube [20]. The fast electromagnetic valve used for injecting hydrogen into the dissociator was similar to the one designed by Dudnikov et al. [21]. The usual pressure of hydrogen inside the valve was about 2 atm. The amount of gas injected into the dissociator tube could be varied
445
A.S. Belov et al. / Velocity distribution in a pulsed hydrogen beam
from 1017 to 5 × 10 's molecules per pulse by changing the height of the current pulses fed to the winding of the valve electromagnet. The duration of these pulses at half-height was 140 #s. The gas was injected into the tube in - 600/Ls after the corresponding current pulse was fed to the winding, which is due to the mechanical inertia of the valve. The time during which the tube was filled with hydrogen was determined by the rise time of the molecular beam density and was about 100 #s. The gas consumption per pulse N was determined from the following formula
(1 - r,/r2) N = An,/I1 [exp( - Atm/,2) -- exp( - a tin/z,) ] '
[LEOTItON AOOEL[PATING OOLLEOTOROF 6UN
..i
-300V
/
where a t m is the time interval between the moment the gas is injected into the tube and the moment the pressure in the dissociator chamber reaches its maximum, An, is the change in the density of the gas in the dissociator chamber during the time at=, r~ is the characteristic time of the gas escaping from the dissociator tube, % is the characteristic time of the hydrogen evacuation from the dissociator chamber by the pump, and V, is the volume of the vacuum chamber containing the dissociator. For the values of parameters typical for our set, i.e. % - 1.5 ms, r= = 60 ms and atm - 5 ms, the gas consumption is N = 1.1 x An I V~ with a few percent accuracy. The gas consumption was measured with the rf discharge turned off (in units of H 2 molecules per pulse), since, when the rf discharge is on, the gas in the dissociator chamber consists of a mixture of atoms and molecules, and the recombination of atoms in the chamber makes the interpretation of the measurement results difficult. The pulsed pressure in the vacuum chambers was measured by the ionization gauges with sensitivity 1.1 X 10 4 #A T o r r - ' for an emission current of 1 mA. The systematic measurement error of about 30% was due to the accuracy of gauges guaranteed by the manufacturers. For the typical gas consumption N---10 ,8 molecules per pulse the amplitude of the pulsed pressure in the dissociator chamber was about 1.5 × 10 -4 Tort. Due to the differential pumping of the apparatus chamber the amplitude of the pressure in this chamber was about 130 times smaller than in the dissociator chamber. This ratio changed slightly as the nozzleskimmer distance was varied. The dissociator was mounted on a movable flange which made it possible to vary the nozzle-skimmer distance and to adjust the dissociator to the axis of the skimmer and the measuring apparatus. 2.3. M a s s spectrometer
The time-of-flight mass spectrometer was designed specially for measuring the density and the composition of a pulsed hydrogen beam [22]. The scheme of the mass
/
-50 V
/ MOnULATOg
/
J
\ \HOLEOULAP
ELEOTI~OgE t
BEAM
OOLLIHATOI~
II j
(1)
ELECTPONBEIP1
ELEffI'I~OI]E
IO, 1 I 1
,
OOLLEOTOli ,
l_.L.-0nms
Fig. 3. Scheme of the time-of-flightmass spectrometer.
spectrometer is presented in fig. 3. The axis of the molecular beam is perpendicular to the plane of the drawing as well as to the direction of the electron beam and to the direction of the ion flow from the ionization region. At the input of the mass spectrometer the molecular beam was collimated by a ~ 1 2 mm diaphragm. The electron beam with an energy of 250 eV and a current of 0.6 mA was produced by an electron gun with an indirectly heated flat cathode and was modulated by the voltage supplied to the modulator electrode. The duration of the electron current pulses could be varied from 2 to 14 #s; the repetition time was 100 #s. Before intersecting the molecular beam, the electron beam was collimated by a 6 × 17 mmz diaphragm. During the pulse of the electron beam, H + and H~ions and the ions of the residual gas are formed in the ionization region and are retained in this region by the electric field of the space charge of electrons. After the end of the electron pulse a short voltage pulse with a height of 110 V and half-height duration - 0.1/~s is fed to the accelerating electrode, and the ions accumulated in the ionization region are accelerated towards the collector by the electric field between the accelerating electrode and the grounded grid. During the acceleration the ions have no time to leave the region between the accelerating electrode and the grid, which ensures the monochromaticity of the ions with the same charge-mass ratio. During the drift (L d = 17 cm) from the ionization region to the collector the ions in the bunches are separated with respect I t the mass according to their time of flight. The collector of ions was shielded from the electrons scattered in the ionization region by a grid with a potential of - 3 0 0 V. The amplitude and duration of the accelerating voltage pulse
446
A.S. Belov et al. / Velocity distribution in a pulsed hydrogen beam
hydrogen atoms [23] o i H = 3 . 9 × 10 -17 cm2), C is a coefficient accounting for the transparency of the mass spectrometer grids. The ion charge
Qk=-~Ff_?ukout dt,
Fig. 4. Characteristic oscillogram of the mass spectrometer pulses; rf discharge turned on; N =1 x10 TM molecules per puls; Pre = 3.6 kW, Tch= 300 K. From left to right: electron beam current pulse (0.2 mA/div.), accelerating voltage pulse, and ion current pulses of the atomic and molecular hydrogen (50 mV/div.). Horizontal scale: 0.5 ~s/div.
as well as the dimensions of the ion collector (40 × 60 mm 2) were selected on the grounds of experimental tests to minimize the ion losses during the path from the ionization region to the collector; this is important for the absolute density measurements in the molecular beam. The transparency of the mass spectrometer in the direction of the molecular beam (inside O 12 mm) is 100%. From the collector the ion current pulses were fed to the amplifier (pass band 10 MHz, sensitivity 200 mV /~A -1) and were recorded by a storage-type oscilloscope. A typical oscillogram of recorded signals is shown in fig. 4 (the signal of the electron current and the pulse of the accelerating voltage were fed to an inverting input of the oscilloscope). Since the current of the electron beam is measured in the mass spectrometer and the dimensions of the beams are known, we can determine the density of the molecular beam from the values of parameters of the recorded ion current pulses. One can easily derive the following expression for the density of particles n k of the kth kind: N k = Ok//CIetaecZioik,
(2)
where Qk is the charge of the bunch of ions of the kth kind exhausted out of the ionization region during a pulse of the accelerating voltage, I e is the electron beam current, ta,~ is the time during which the ions are accumulated in the ionization region, which is equal to the duration of the electron beam pulse, 7.i is the average length of the intersection region of the electron and the molecular beams along the electron beam axis, eik is the ionization cross-section for particles of the kth kind by electrons with an energy of 250 eV (for
where R F is the feedback resistance of the current amplifier and uokut is the voltage of the pulse for particles of the k th kind at the output of the amplifier. The relative error of our measurements was determined by the accuracy with which the quantities in formula (2) were measured and amounted to about _ 27%. In addition, the mass spectrometer was calibrated by filling the vacuum chamber with hydrogen and taking account of the difference in the effective ionization volumes (a factor of 3.2) for particles of the molecular beam and for molecules of the residual gas. The mass spectrometer was also calibrated by the ionization gauge 2 (see fig. 1), by which the density of the molecular hydrogen beam was measured independently. The resuits of these calibrations differ from the values given by formula (2) by no more than 20% in the region of gas consumptions N - 2 × 1017 to 2 × 1018 molecules per pulse.
2.4. Apparatus for measuring the velocity distribution of particles The velocity distribution of particles in the beam was measured by the usual time-of-flight method (see fig. 1). The chopper disk with a diameter of 13 cm and rotational speed up to 24000 r.p.m, had two diametrically opposite slits each 3 mm wide. The beam was collimated by a 3 x 15 mm2 diaphragm installed before the chopper disk. The time-of-flight signal was detected by an ionization gauge placed at a distance of 79.5 cm downstream from the disk. The electron emitting filament of the gauge was parallel to the beam axis. The cylindrical ion collector had a diameter of 27 mm and a length of 26 mm. The optical transparency of the gauge in the direction of the beam was about 94%, its sensitivity being 4.4 × 104 /~A Torr -~ for an emission current of 4 mA. The current signal from the collector gauge was amplified by a wide-band amplifier and recorded by a storage-type oscilloscope. The zero-time signal was produced by the light emitting diode-photodiode pair placed near the chopper disk, diametrically opposite to the point where the disk intersects the molecular beam. When the rf discharge in the dissociator was turned on a current signal appeared in the gauge collector simultaneously with the signal from the photodiode. This signal was apparently due to the photoemission of electrons in the gauge caused by the ultraviolet emission produced
A.S. Beloo et al. / Velocitydistribution in a pulsed hydrogen beam 3. Processing of the time-of-flight signals
I ~,+"p"
O"
£8 ,
,o
I !
A typical oscillogram of the time-of-flight signal for warm hydrogen atoms is shown in fig. 6. In processing the signals it was assumed that the chopper function is of triangular form with pulse duration at the base At = d/~rfR, where d is the width of the slits in the chopper disk and in the collimato r, f is the rotation frequency of the chopper disk, and R is the distance between the axes of the beam and the disk (R = 5.4
i
:i
I
+
0.6
/
o'
,+
!,
I
+-
3.3.4047
cm).
The time-of-flight signal ~ ( t ) is related to the distribution function of particles in the beam f ( v ) by the well-known equations
mot W2 per ptttse
0.~
i
~ _ o - 6.~.40 ~' -- 4 7"404~
l,
x -
4
~
447
3
4
4.O'f .01~ •
5
t
6
7
~(t)
=f~ c(r)F(t-r)
dr,
f ( v ) = f ( L / t ) cx F ( t ) t 2. Fig. 5. Relative fraction of atoms in the beam vs the rf discharge power.
by the rf discharge; it was used as a zero-time signal in the measurements with the rf discharge turned on. The signal from the chopper photodiode, the repetition frequency of which (400 Hz) was reduced to 1 Hz by the frequency devider, triggered the feeding system of the dissociator, synchronizing the latter with the chopper. By varying the time delay of triggering of dissociator units with respect to the photodiode signal it was possible to "shift" the moment of turning on the dissociator with respect to the moment the disk slit intersected the molecular beam, and, thus, to study the variations of parameters of the atom velocity distributions during the pulse of the discharge. The employed ionization gauge was not mass-sensitive. This was not essential when the rf discharge was turned off, since in this case the b e a m consists of only the H 2 molecules. However, in the atom velocity measurements with the rf discharge turned on the relative fraction of atoms in the beam had to be large, since the time-of-flight separation in bunches of hydrogen atoms and molecules is not sufficiently good for a supersonic beam with a small Mach number. Fig. 5 shows the relative fraction of atoms x in the beam for the studied dissociator versus the rf discharge power for different N. x is determined as x = n H / ( n H + nil2 ), where n H and nil2 are the densities of atoms and molecules in the beam respectively. The density of the beam was measured by the mass spectrometer. The dotted lines in fig. 5 and in other figures below are plotted for clarity. In order to avoid errors in the measurements of the atom velocity distribution the latter were done for such an rf discharge power that x was not less than 0.8.
(3a) (3b)
Here c(r) is the chopper function, F(t) is the signal for a delta-shaped chopper function, and L is the distance between the chopper disk and the center of the ionization gauge. The pass bands of both the ionization gauge amplifier (A f = 0-100 kHz) and the oscilloscope (A f = 0 - 1 MHz) were sufficiently wide and were not taken into account when the signals were processed, as well as the effect of the finite dimensions of the ionization gauge on the form of the signal. The distribution function of the longitudinal velocities of particles in the beam was approximated by the function usually used for a supersonic particle flow (see, e.g., [13]) f ( v ) = Bv 2 exp[ - m ( v - u ) 2 / 2 k T 1],
(4)
where B is the normalization constant, m and v are the mass and the velocity of particles, respectively, u is the mass velocity of the flow, T1 is the temperature corre-
Fig. 6. Oscillogram of the time-of-flight signal; rf discharge turned on; N = I ×10 TM molecules per pulse, Prr = 3.2 kW, Tch = 300 K. Vertical scale: 2 mV/div., horizontal scale: 50 #s/div.
448
A.S. Belov et aL / Velocity distribution in a pulsed hydrogen beam distribution (4) are related by the expression
tO
u
~ o.8
VMp = ~- +
~ 0.6
The errors in the measurements of VMe, M and To presented below consist of the error connected with the accuracy with which parameters u and T a were determined from the apparatus Signal by a computer, and the error connected with the accuracy of the calibration of the oscilloscope time scale. The relative error A u / u was about _+3.5%, and A T 1 / T a - _+7%.
\
N 0.~
0.9
2
5
5
""~.1..... 6 z t,t0-~
Fig. 7. Comparison of the apparatus signal with the signal corresponding to the approximating velocity distribution function (4). Solid fine: apparatus signal (Tch = 77 K, N = 4 X 1017 molecules per pulse) normalized to unity; circles: signal corresponding to the approximating velocity distribution function for u =1.93×10 S cm s -t, T~ =18.3 K; rf discharge is on.
sponding to the longitudinal movement of particles in the center-of-mass frame of reference, and k is the Boltzmann constant. Function (4) is normalized to the density of the particle beam n; the intensity of the beam is expressed through f ( v ) as
= fo~Of(o)do. When processing the apparatus signal on a computer the parameters of the distribution function (4) - T 1 and u - were selected in such a way that the mean-square deviation of the signal corresponding to the approximating function from the apparatus signal would be minimal with account of relations (3a) and (3b). Fig. 7 shows the signal corresponding to the velocity distribution function found in this way; the apparatus signal is normalized to unity. F r o m fig. 7 one can see that distribution (4) is in good agreement with the experimental time-offlight signal everywhere except in the region of large. times of flight i.e., the experimental spectrum has a deficit of slow atoms. The processing has shown that the greater the Mach number, the better distribution (4) agrees with experimental results. Using the known values of parameters T 1 and u we calculated the Mach number 3,/11 and the temperature To of the gas in the dissociator [16]: MII = u /
~ykr m
'
To= T , ( I + ~ - ~ J - M , ~ ) ,
(5) (6)
where "y is the specific heat ratio. VeLocity u and the most probable velocity vMp for
+ -
(7)
m
4. Results and discussion
4.1. Velocity distribution of particles in a molecular hydrogen beam The measurments were performed first for a molecular hydrogen beam with the rf discharge turned off. In this case the dissociator is similar to the usual source of supersonic molecular beams. The aim of our measurements was to determine the parameters of velocity distributions in the molecular beam for relatively low pressures in the tube, typical for a dissociator in which it is still possible to obtain a beam with a large fraction. of hydrogen atoms. Fig. 8 shows the parameters of velocity distributions for warm molecules versus the gas consumption per pulse N for a fixed nozzle-skimmer distance. The maxim u m Mach number M = 3.5 + 0.3 was obtained at N =
T,I~
M
V,,~OSern..s-'
IJ.44~""/4f
I ,yl
.I ]," I
r'Ll t!il, !
,rhli¢
,.o
,oo
[,,
80
:
t'J IIIII (o
9
.'[I
t
5
/*
-~.+_o .~'[ tO~
9
5
I
t0 ~s
N, mot H,per pu~se Fig. 8. Parameters of the velocity distributions of molecules vs the gas consumption per pulse. Tch = 293 K.
449
A.S. Belov et al. / Velocity distribution in a pulsed hydrogen beam 4 x 1018 molecules per pulse. As the gas consumption was increased further, the Mach number decreased, while temperature Tz grew. Apparently, the decrease of M is due to the so-called beam-skimmer interference. This effect was also observed in the usual nozzle sources of supersonic beams at high gas pressures in the source (see e.g. ref. [24]). However, we must note that in our experiments we did not observe the pronounced sharp dependence of the beam density on the nozzle-skimmer distance XNs, typical for the supersonic beam sources in which the stagnation gas pressure P0 > 100 Torr. The density of the molecular hydrogen beam depended weakly on XNs and reached its maximum at XNS = 15 mm. It is for this optimal distance that the measurements of the velocity distributions of molecules and atoms were performed. The cooling of the channel walls to 77 K has led to an increase of the Mach number in the molecular beam. For a gas consumption of 2 × 1018 molecules per pulse we have obtained a beam of cooled molecules with a Mach number MII = 6.8 _ 0.6, velocity VMa = (1.30 _+ 0.05) X 105 cm s -1 and temperature T1 = (5.9 _ 0.4) K. The measurements of the temperature TO showed that it coincides with the temperature of the cooling channel walls (77 K) within the error of the measurements for a gas consumption up to N = 2 x 1018 molecules per pulse. For higher gas consumptions TO grows due to the incomplete cooling of molecules at high gas densities in the cooling channel. One of the factors leading to an increase in the Mach number when the gas is cooled, is the increase of the density of the gas in the cooling channel in comparison with a warm flow for the same gas consumption per pulse. This assertion was tested by measuring the hydrogen flow rate from the dissociator (see sect. 2.2 and ref. [20]). The characteristic time of the gas escaping from the tube can be presented as
Td/ ro. This "compression" effect plays an even greater role in the dissociator with the rf discharge turned on, since, as will be shown in the next section, the gas in the rf discharge is heated to a considerably high temperature. 4.2. Temperatuie of hydrogen in the dissociator with the rf discharge turned on As was established in ref. [20] (see also fig. 5), in order to obtain a high dissociation degree of hydrogen molecules at a gas consumption up to 4 x 1018 molecules per pulse, one must feed the rf discharge with a power up to 0.8 kW cm -3. For determining the gas temperature in the tube under such conditions the measurements of the atom velocity distributions were done for the tube without the cooling channel (fig. 2a). The results of the measurements are presented in fig. 9. The measurements were made at the moment corresponding to the middle of the discharge pulse (tm~ s = 0.5 ms). According to the results presented in fig. 9, temperature TO strongly depends on the power of the rf discharge and reaches - 2800 K, so the pulsed pressure of the gas in the volume occupied by the rf discharge is about 30 Tort (for N = 6.6 X 1017 molecules per pulse).
T~
7+1
vo ~ a o A n / ~ no]
hydrogen in the channel is cooled, the increase in the gas density is greater than the decrease of the speed of sound. Obviously, the increase of the density in the cooled gas is due to a gas temperature gradient in the cooling channel. According to our measurements, the degree of compression of hydrogen also depends on the diameter of the nozzle orifice. For a sufficiently small nozzle orifice area, and, consequently, for a small gas flow through the channel, the pressure gradient in the channel must also be small and we must have n o/n a -
...4h •
(8)
where a 0 is the speed of sound at gas temperature TO in the cooling channel, n d and n o are the gas densities in the dissociator and in the cooling channel respectively, Vd is the volume of the dissociator tube, and A , is the area of the nozzle orifice. At a temperature of the cooling channel walls Tch = 293 K the factor n d / n o is close to unity and the experimentally measured value of zI is in agreement with formula (8) within a 10% error. At Tch = 77 K our measurements give ~.77= 0.8~.293, where the upper indices indicate the temperature of the cooling channel walls. Since a o tx I"ol/2, from this result it follows that n o / n d > (Td/TO) 1/2, where T~ and TO are the temperatures of the gas in the dissociator tube and the cooling channel respectively. This means that as the molecular
,9500
1¢/
~"1!'
I!
1500
;/
~000
o~ +
L,
e
P~,~W
Fig. 9. Atom temperature in the dissociator tube vs the rf discharge power, tm~s = 0.5 ms. O: 3.3x1017 molecules per pulse, + : 6.6 x 101-/ molecules per pulse, e: 1.7 × 1018 molecules per pulse.
A.S. Belou et al. / Velocity distribution in a pulsed hydrogen beam
450
It is worth noting that the temperature of the dissociator tube walls ( - 3 0 0 K) differs greatly from the temperature of the gas, and there is no thermal equilibrium in the tube. Obviously, the temperature distribution of the gas in the tube must be inhomogeneous, and the temperature in the center of the dissociator tube must be higher than in the outlying areas of the discharge, including the vicinity of the nozzle where the gas temperature was measured. As is known, the degree of hydrogen dissociation depends on the temperature. For a gas density n = 3 × 1017 cm -3 and a temperature of 2800 K, the dissociation degree exceeds 80% [25]: F r o m fig. 9 it follows that in the considered dissociator the thermal mechanism of hydrogen dissociation is essential. This is confirmed by the observed dependence of the relative fraction x of atoms in the beam on the power of the rf discharge (see fig. 5). Comparing figs. 5 and 9 one can see that x increases in the same range of the rf discharge power where the gas temperature grows. Because of this, the considered dissociator can be called a dissociator of the combined type, since it is also a thermal dissociator. The dynamics of heating and cooling of atoms are shown in fig. 10, from which one can see that the temperature of the atoms increases during the rf discharge, and after the latter is turned off, the atoms are cooled during - 2 0 0 Vs. A beam of hot atoms is an effusion-type beam; after the discharge is turned off, the Mach number increases as atoms are cooled. The time variation of the atomic beam density for this dissociator geometry was described in ref. [20]. In particular, a sharp increase of the beam density after the rf discharge is turned off is explained by the results of the present work concerning the changing of the Mach number after the rf discharge is turned off.
T~
t
g F dLseborge
4.3. Velocity distribution in beams o f warm and cooled H atoms
In the measurements for beams of warm and cooled atoms it was found that the velocity distributions of atoms depend on gas consumption and on the rf discharge power and vary during the discharge pulse. The fact that the velocity distributions of atoms depend on the named parameters is explained by the heating of the gas in the rf discharge of the dissociator which was described in the previous section. This effect modifies the typical dependence of the particle velocity distribution parameters on the pressure in comparison with a source which has a constant stagnation gas temperature. Fig. 11 shows the velocity distribution parameters versus the gas consumption for warm atoms. F r o m the results presented in fig. 11 it follows that, at N < 1018 molecules per pulse, the atoms are cooled practically to room temperature. The value of TO calculated from (6) at N ~< 1018 molecules per pulse, is systematically smaller than the temperature of the cooling channel walls (T~h = 300 K). The reason for this discrepancy is not clear to US.
For gas consumption N = 1 × 1018 molecules per pulse the Mach number of the atom flow reaches MII = 2.7 + 0.25, while the most probable atom velocity is Vup = (3.05 ___0.12) × 105 cm s -a and the atom temperature in the beam is T 1 = (71 + 5) K. For gas consumptions higher than 1018 molecules per pulse the cooling of atoms is not sufficiently effective. As N grows, temperature TO rises and reaches 423 K at N = 5 × 1018 molecules per pulse. Temperature T 1
M
T, I~
V,~OScm.s"' &8
i
3.4
9000
3
i
4500
/
I! :1|
0
/
4000 500 --
3
;¢
,
"" °
e
~00
5.0
590 ~
2.6
240
1
9
1
6
0
~
%.
4.o t9 4.~ t.6 t~ ~
t, ms
Fig. 10. Changes in the atom temperature TO (1) and in the Mach number (2) of the beam during the rf discharge pulse for a tube without the cooling channel. N = 2.5 × 1018 molecules per pul.se, P,f = 6 kW.
2
5
t0 ~
~
5
tO~g
N, tool W=por p={s0 Fig. ] l . Parameters o f the atom v e l o c i t y distributions vs the gas
consumption per pulse. ~h = 300 K, tmeas = 0.5 ms, x = 0.85.
451
A.S. Belov et aL / Velocity distribution in a pulsed hydrogen beam
also rises, while the Mach number decreases to M = 2.1. The length of the cooling channel Lch was selected using the following estimation [20] Lc h -- 0.4R2/-•,
(9)
where R , is the radius of the nozzle orifice and ~ is the mean free path length of atoms in the channel, which was calculated from the value o f the atom density averaged over the length of the cooling channel. As N increases, the density of atoms in the channel grows and ~, decreases. Consequently, the time of diffusion of atoms towards the cooling channel wall increases and the efficiency of cooling falls. This is in qualitative agreement with the obtained experimental results. A more complete cooling of atoms at large N can be achieved by either increasing the channel length L~h or, as it follows from formula (9), by reducing the radius of the nozzle orifice R . . In both cases the time during which the atoms pass through the channel increases, but unfortunately, this leads to a decrease of the relative fraction of atoms in the beam due to the recombination of atoms in the channel. Fig. 12 shows the dependence of x on N for different radii of the dissociator nozzle orifice R , . For each value of N, the power of the rf discharge is the same for different R , . F r o m fig. 12 it follows that the possibility of achieving a more complete cooling of atoms by modifying the channel and nozzle geometry is limited by the recombination of atoms. The incomplete cooling of atoms at large N is also due to the increase in the rf discharge power necessary
,I.0 ~ o.g
'--
0.8
•
liH',, , l
0.6
2
5
lOm
~
5
I0m
N, mot I-l~pgr ptdsg Fig. 12. Relative fraction of atoms in the beam vs the gas consumption per pulse for dissociator tubes with different nozzle orifice radii R n" T~h = 300 K, tm¢as= 0.5 ms.
M
T.~4
l'0 11( ~ )/
L~O0
2.fi
300
_
t
2.~
200
"
2.0
T4 -'('~ 0..-- - 0
400
O" " 0
3
~-
4
"~/
5
6
7
8
P,~, kW Fig. 13. Parameters of the atom velocity distributions vs the rf discharge power at fixed N = 2.5 × 10 Is molecules per pulse, Tch = 300 K, trneas 0.5 ms. =
for obtaining a high degree of hydrogen dissociation. This is illustrated in fig. 13, which shows the parameters of the atom velocity distribution versus the rf discharge power for a fixed value of N = 2.5 × 1018 molecules per pulse. As the rf discharge power grows, one observes a nearly linear increase of temperatures TO and T 1, and a weak decrease of the Mach number. The temperature TO of warm H atoms increase during the rf discharge by 10-20%, depending on the gas consumption, and the Mach number slightly decreases, but the variations of these parameters are considerably weaker than in the case of a beam of hot atoms. The rf discharge power in the dissociator tube becomes the main factor determining the parameters of the velocity distribution for cooled atoms, since the relative variations of these parameters versus the rf discharge power for a beam of cooled atoms are a few times greater than in the beam of warm atoms. For this reason in fig. 14 parameters VMp, M and TO for a beam of cooled atoms are presented as functions of the rf discharge power. A satisfactory cooling of atoms is obtained only at a discharge power P ~< 0.3 kW cm -3. We assume that the observed strong dependence of the atom temperature on the discharge power is due to the penetration of the plasma from the area of the rf discharge into the cooling channel and to an increase of the plasma density with the increase of the discharge power. The most typical measured H atom velocity distributions are shown in fig. 15 together with the Maxwell velocity distribution calculated for TO= 300 K and corresponding to an effusion-type flow from the dissocia-
452
A.S. Belov et al. / Velocity distribution in a pulsed hydrogen beam
T,~
V, ~O.Scr~.s -'
~0 45 12, e111."3
o
9~0
•
L .............
2.4
900 ~.0
t60 4.6
10 42
M 4.5 ~0
80
• i
2
3
3~5
/
3.0
4
5 P,kW
40 ~
Fig. 14. Parameters of the atom velocity distributions vs the rf discharge power. Tch = 77 K, t m e a s = 0 . 5 m s . O: 2.5X1017 molecules per pulse, +: 3.3x 1017 molecules per pulse, D: 5.4x1017 molecules per pulse, ix: 6.7x1017 molecules per pulse, × : 8 X 1017 molecules per pulse, e: 1 X 10 TM molecules per pulse.
tor. As far as we know, a supersonic b e a m of hydrogen atoms with a M a c h n u m b e r Mii > 4 was o b t a i n e d for the first time in our experiments. 4.4. Intensity o f the atomic beam The density in a b e a m of hydrogen atoms was measured by the mass spectrometer described in sect. 2.3. The distance between the nozzle and the center of the ionization region of the mass spectrometer was 17.8 cm.
z
i i
i
~3
i L
4
6
a
O ' 4 0 S e m ' s -(
Fig. 15. Typical velocity distributions of atoms. I : the tube
without the cooling channel, N = 2.5 x 1018 molecules per pulse, 2: T~h = 300 K, N = I . 0 × 1 0 TM molecules per pulse, 3: T~h = 77 K, N = 5.4x l0 z7 molecules per pulse, 4: Maxwell distribution for TO= 300 K.
40 Iz
40 ~8
N, mot 14 p0r ptt£so Fig. 16. Density of the atomic beam vs gas consumption. 0: T~h = 300 K, x : Tch = 77 K; t . . . . = 0.5 ms, x = 0.85.
The results of measurements are presented in fig. 16. U n d e r our conditions, for N < 1 x ]01"/ molecules per pulse the time during which the dissociator tube is filled with gas i n c r e a s e with decreasing N. Thus, for a fixed time interval between the m o m e n t s of triggering the gas valve and the rf discharge, this leads to a sharper increase of the b e a m density measured at the m o m e n t corresponding to the middle of the rf discharge pulse in comparison with a linear dependence. In a b e a m of cooled atoms, for N from 1 x 1017 to 5 x 1017 molecules per pulse, the density is higher than in a b e a m of warm atoms. This is due to the fact that for the same gas consumption, the M a c h n u m b e r in a b e a m of cooled atoms is greater than in a b e a m of w a r m atoms. The m a x i m u m achievable density of the b.eam is approximately the same for b o t h the warm a n d the cooled atomic beams. For a b e a m of cooled atoms it is achieved at Net - 5 x 1017 molecules per pulse, while for w a r m atoms at Nor - 1 x 10 TM molecules per pulse. Apparently, the increase of the b e a m density is h a m p e r e d by the scattering of atoms (the b e a m - s k i m m e r interference). In the atomic beam-type polarized ion sources operated in a continuous mode, the scattering of atoms in the region between the nozzle a n d the skimmer is, probably, the main factor h a m p e r i n g the increase of the a t o m b e a m intensity [26,27]. In our experiments the scattering of atoms by the'residual gas in the dissociator v a c u u m c h a m b e r was negligible, since, at N = 1 x 10 TM molecules per pulse, the pressure in this c h a m b e r was not greater than 1.5 × 10 -4 Torr. However, it was pos-
A.S. Beloo et al. / Velocity distribution in a pulsed hydrogen beam sible to increase the density of the atomic beam by 1.7 times by increasing the height of the skimmer from 12 to 30 mm, which indicates that the scattering of the beam by the gas, reflected by the skimmer, was considerable. Apparently, it is possible to decrease the scattering of atoms by the further optimization of the skimmer geometry, which was not fully done in the present work. The intensity of the atomic beam, I (atoms sr -~ s - l ) , is given by the expression
t(0)=
- 2 n msVtms,
where nms is the density of the beam measured by the mass spectrometer, ~ is the average velocity of atoms in the beam, and Lms is the distance between the atom source and the center of the ionization region of the mass spectrometer. For a beam of cooled atoms at N = 3.3 × 1017 molecules per pulse and P = 0.23 kW Cm -3 (the conditions under which factor nms/V2p approximately has a maximum), we find that I ( 0 ) = (2.8 + 0.8)× 1020 atoms sr -1 s -1. The other parameters of the beam under such conditions are: VMp= (1.97 + 0.07)×105cm s -1, T1 = ( 1 4 . 4 + 1) K, T 0 = ( 9 6 + 10) K, and M = 4.14 _ 0.35. "Theoretical intensity" of a nozzle beam (without accounting for the decrease in the beam intensity due to the scattering of atoms) is given by the expression [19] (for M > 3)
I(o) = As~o,o r (Y~)'/~
M3
y+l
453
cross-sections of atoms and molecules. Nevertheless, for determining n o we assumed that x - = x 0. This approximation is justified by the fact that the relative fraction of atoms in the beam was sufficiently large (x >t 0.8), and the relative error of this approximation is unlikely to exceed - 25%. The value of the ratio n o / n d was determined from the measurements of the characteristic time of the gas escaping from the dissociator with the rf discharge turned on, as was described in sect. 4.1 for the case of a molecular beam. For T~h = 77 K, N = 3.3 × 1017 molecules per pulse and P = 0.23 kW cm -3, it was found that ~-1= (0.75 +__0.05) ×10 -3 s. From formula (8) under these conditions (TO= 96 K, a 0 = 1.15 × 105 cm s -1) we get n o / n d ---4.0. Formulae (10) and (11) for MI1=4.14, x 0 = 0 . 8 , y = 5 / 3 and N = 3.3 × 1017 molecules per pulse give Ith(0)= 1.1 X 10 21 atoms sr - I s -1. The big difference between the experimentally measured beam intensity (I(0)exp = (2.8 + 0.8)× 10 20 atoms sr -1 s -1) and the intensity predicted by formulae (10) and (11), apparently, cannot be explained only by the uncertainty in the values of the quantities entering formulae (10) and (11). On the one hand, the inevitable decrease of the beam intensity due to the scattering of atoms must be taken into account in formula (10), and on the other hand, in the real beam this decrease possible can be reduced by the optimization of the skimmer geometry.
), 5. Conclusion (10)
where A s is the skimmer orifice area, and n o and a 0 are the stagnation density and the speed of sound respectively. In order to use formula (10) for calculating the peak intensity of a pulsed beam of hydrogen atoms let us express approximately the atom density n 0 through the experimentally measured parameter N:
N
no-
2x__.q_o ( n o ]
Vd 2-~¢o \ na]"
(11)
Here Vd is the volume of the dissociator tube and ~¢0 is the relative fraction of atoms in the tube. The first factor in eq. (11) is equal to the peak density of hydrogen molecules in the tube; the second one accounts for the dissociation of molecules; while the third factor accounts for the increase in the density of atoms when the latter are cooled in the channel, x 0 may not be equal to the measured parameter x, since the angular distributions of atoms and molecules in the gas flow from the dissociator are not necessarily the same. Furthermore, the decrease in the intensity of the atomic and the molecular beams due to scattering can also be different due to the difference in the collision
When the pressure in the tube and the power applied to the rf discharge are increased, the hydrogen dissociator with the rf discharge usually used in the atomic beam-type PPS is similar to the thermal dissociator, since in this case the hydrogen temperature rises up to a few thousand degrees and the thermal dissociation of hydrogen molecules plays an essential role. In such a dissociator it is possible to obtain a high dissociation degree of hydrogen - at least in the pulsed mode when the initial density of hydrogen molecules in the dissociator tube is under 5 × 1017cm -s. In this case, in order to obtain a high dissociation degree of hydrogen in the rf discharge it is necessary to supply a power up to 0.8 kW cm -3. The high temperature of the gas is a negative feature of this dissociator, since the acceptance angle of the separating magnet in the PPS is inversely proportional to the energy of atoms in the beam. The cooling of atoms is achieved by letting the hot gas pass through a sufficiently long cooling channel. When the atoms are cooled, the density of atoms in the channel increases. This "compression" effect favours the formation of a supersonic atom flow. We have obtained a supersonic beam of hydrogen atoms with a Mach number Mtl = 2.7 + 0.25 for the temperature of
454
A.S. Beloo et al. / Velocity distribution in a pulsed hydrogen beam
the cooling channel walls 300 K, a n d with Mfl = 4.14 + 0.35 for a temperature of 77 K. In a b e a m of cooled hydrogen molecules for the chosen dissociator geometry at N = 2 x 10 ~8 molecules per pulse, we have measured a M a c h n u m b e r M H= 6.8 + 0.6. The distribution of atom velocities depends on the rf discharge power a n d on the pressure inside the dissociator tube and varies during the rf discharge pulse. For a b e a m of cooled atoms the main factor is the discharge power. T e m p e r a t u r e TO to which the atoms are cooled in the channel at T~h = 77 K changes from TO = 85 K at P = 0.23 kW cm -3 to TO - 220 K at P - 0.7 kW cm -3. Apparently, the main reason for an incomplete cooling of atoms is the p e n e t r a t i o n of the plasma from the region of the rf discharge into the cooling channel. The decrease of the nozzle orifice radius must lead to a more complete cooling of atoms. However, due to the surface and volume r e c o m b i n a t i o n of atoms in the cooling channel, this leads to a decrease of the relative fraction of atoms in the beam. U n d e r the conditions optimal for the focusing of the atomic beam by the separating PPS magnet (i.e. in the case when the factor n n / v ~ p is m a x i m u m ) we have o b t a i n e d a b e a m of atoms with intensity I(0) = (2.8 + 0.8) x 10 20 atoms sr 1 s - 1 the most p r o b a b l e velocity vMp = (1.97 + 0.07) × t05 cm s 1, a n d temperatures T~ = (14.4 + 1) K, TO = (96 + 10) K. Apparently, the intensity of the b e a m can be increased by the optimization of the skimmer geometry and, thus, by reducing the effect of the atom scattering. The authors are grateful to Prof. S.K. Esin a n d to Prof. V.M. Lobashev for support a n d for their c o n s t a n t interest in our work. We are grateful to Prof. G. Clausnitzer for his useful criticism of the first variant of this paper.
[5]
[6]
[7] [8]
[9] [10] [11] [12] [13] [14] [15]
[16] [17] [18] [19]
[20]
[21] [22]
References [23] [1] P.A. Schmelzbach, W. Gr~ebler, V. K6nig and B. Jenny, Nucl. Instr. and Meth. 186 (1981) 655. [2] H.G. Mathews, A. Kruger, S. Penselin and A. Weinig, Nucl. Instr. and Meth. 213 (1983) 155. [3] E. Grorud, J.-L. Laclare, G. Leleux, A. Nakach and A. Ropert, Int. Symp. on High Energy Spin Physics (1982) ed., Gerry M. Bunce, AlP Conf. Proc. no. 95 (ALP, New York, 1983) p. 407. [4] L.G. Rather, Int. Symp. on High Energy Spin Physics
[24] [25] [26] [27]
(1982) ed., Gerry MI Bunce, AlP Conf. Proc. no. 95 (ALP, New York, 1983) p. 412. S. Hiramatsu et al., Int. Symp. on High Energy Spin Physics (1982) ed., Gerry M. Bunce, AIP Conf. Proc. no. 95 (AIP, New York, 1983) p. 419. N.G. Anishchenko et al., Int. Symp. on High Energy Spin Physics (1982) ed., Gerry M. Bunce, AIP Conf. Proc. no. 95 (ALP, New York, 1983) p. 445. Yu.M. Ado et al., IFVE 82-54, O U K / O P Serpukhov (1982). C. Bovet, D. M6hl and R. Ruth, Workshop on SPS Fixed-Target Physics, CERN 83-02, vol. II (Geneva, 1983) p. 396. E.F. Parker, N.Q. Sesol, and R.E. Timm, IEEE Trans. Nucl. Sci. NS-22 (1975) 1718. Yu.A. Plis and L.M. Soroko, Uspekhi Fiz. Nauk. 107 (1972) 281. B.P. Ad'yasevich, V.G. Antonenko, Yu.P. Polunin and D.E. Fomenko, Atomnaya Energiya 17 (1964) 17. M. Perrenoud, W. G~ebler and V. K0nig, Helv. Phys. Acta 44 (1971) 594. W. Kibishta, CERN PS/DL/Note, 77-5 (Geneva, 1977). S.G. Popov and D.K. Toporkov, Preprint IYaF SO AN SSSR, 80-129, (Novosibirsk, 1980). P.F. Schultz, E.F. Parker and J.J. Madsen, Proc. 5th Int. Symp. on Polarization Phenomena in Nuclear Physics, Santa Fe, eds., G.G. Ohlsen et al., AlP Proc. no. 69 (ALP, New York, 1981) p. 909. A. Kantrowitz and J. Grey, Rev. Sci. Instr. 22 (1951) 328. V.B. Leonas, Uspekhi Fiz. Nauk, 127 (1979) 319. R. Keller, L. Dick and M. Fidecaro, Report CERN 60-2 (Geneva, 1960). H.F. Glavish, Proc. 3rd Int. Symp. on Polarization Phenomena in Nuclear Reactions, Madison, eds., H.H. Barshall and W. Haeberli (University of Wisconsin Press, Madison, 1971) p. 267. A.S. Belov, S.A. Kubalov, V.E. Kuzik and V.P. Yakushev, IYaI AN SSSR, Preprint-0272 (Moscow, 1983) Nucl. Instr. and Meth. 227 (1984) 11. G.E. Derevyankin, V.G. Dudnikov and P.A. Zhuravlev, Pribory i Tekhnika Eksperimenta 5 (1975) 168. A.S. Belov, S.A. Kubalov, V.E. Kuzik and V.P. Yakushev, IYaI AN SSSR, Preprint-0247 (Moscow, 1982). W.L. Fite and R.T. Brackmaun, Phys. Rev. 112 (1958) 1149. K. Teshima and Y. Yasunaga, Jap. J. Appl. Phys. 22 (1983) 1. L. Valyi, Atom and Ion Sources (Wiley, New York, 1977) p. 75. Yu.A. Plis and L.M. Soroko, JINR, R9-10312 (Dubna, 1976). A.V. Evstigneev, S.G. Popov and D.K. Toporkov, Preprint IYaF SO AN SSSR, 84-51 (Novosibirsk, 1984).
STUDY OF THE VELOCITY A.S. B E L O V , S.A. K U B A L O V ,
DISTRIBUTION V.E. K U Z I K
IN AN INTENSE
443
PULSED
HYDROGEN
BEAM
a n d V.P. Y A K U S H E V
Institute for Nuclear Research of the Academy of Sciences of the USSR, 60th October Anniversary prospect 7a, Moscow 117312, USSR Rrceived 24 October 1983 and in revised form 6 March 1985
We present the results of measurements of the velocity distributions of particles in a pulsed hydrogen beam obtained from a dissociator with a radio frequency discharge (duration 1.0 ms, repetition rate 1 Hz). It is shown that the hydrogen inside the dissociator is heated up to - 2800 K, so the thermal dissociation of hydrogen molecules is essential. In order to cool the atoms, the gas was let through a pyrex channel 5 mm in diameter. The cooling channel walls being at room temperature and the channel having a length of 50 ram, we have obtained a supersonic beam of hydrogen atoms with a Mach number n i l = 2.7 +0.25. When the channel walls were cooled by the flowing liquid nitrogen and the channel was 70 mm long we obtained a beam of cooled atoms with a Mach number MII = 4.14 + 0.35. The velocity distribution of atoms depends on the power of the rf discharge inside the dissociator and on the gas consumption per pulse, and varies during the discharge pulse. For a temperature of the cooling channel walls Tch = 77 K, a gas consumption N = 3.3 × 1017 molecules per pulse and a discharge power of 0.23 kWcm -3, we have obtained an atomic beam with intensity I(0)= (2.8 + 0.8);,< 1020 atoms sr-1 s-1 and a most probable velocity oMp = (1.97 + 0.07)× 105 cm s-1.
1. Introduction The constant improvement of the atomic beam-type polarized proton sources (PPS) has resulted in the development of sources with a beam current greater than 100 /~A [1,21. At present, the acceleration of polarized protons in high energy accelerators [3-8] makes the development of pulsed PPS a very important problem. Earlier, Parker et al. [9] have shown that for a pulsed source with a low repetition frequency it is possible to obtain an improvement in the beam intensity of a factor of - 3 by operating the dissociator in the pulsed mode. Since the acceptance angle of the separating magnet in the atomic beam-type PPS is inversely proportional to the energy of the atoms [10], the current of the polarized ion beam increases as the hydrogen temperature falls, so in a number of PPS the dissociator was cooled by liquid nitrogen [2,11-14]. For a pulsed source the cooling of the dissociator nozzle to 28 K has led to an increase in the current of the polarized proton beam by a factor of 2.5 [15]. One more way to increase the beam current in the PPS is to obtain a supersonic flow of atoms from the dissociator. The nozzle sources of supersonic molecular beams proposed by Kantrowitz and Grey [16] give beams with intensity as high as 10 21 particles sr -1 s -1 [17], i.e. nearly two orders of magnitude higher than the intensity of beams in effusion sources. As far back as 1960, Keller et al. [18] have proposed to use supersonic beams in the PPS. At an adequate selection of the 0168-9002/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
nozzle and skimmer geometry the improvement in the intensity of an ideal supersonic beam in comparison with effusion beams is proportional to the Mach number squared [19]. The better monochromaticity of the supersonic beam [16] must lead to an additional increase of the atom density behind the separating magnet due to the smaller chromatic aberration during the focusing of atoms. U p to now the advantages of supersonic flows have not been fully used in PPS. Partially, this is due to the low hydrogen pressure ( - 1 Torr) in the PPS dissociator. For a beam of hydrogen atoms obtained from a microwave pulsed dissociator cooled to 77 K, the measured Mach number was about 1.5 [13]. As was discussed in ref. [19], the experimental investigation of conditions necessary for the formation of a supersonic flow at low gas pressures is an imperative necessity. A high intensity beam of hydrogen atoms was obtained from the pulsed dissociator designed for the PPS of the Moscow Institute for Nuclear Research [20]. In the present paper we present the results of the time-offlight measurements of the velocity distributions in supersonic flows of atomic hydrogen obtained from this dissociator. The aim of our work was to study experimentally the effect of such factors as the rf discharge power, gas consumption and atom cooling on the atom velocity distribution and on the density of a pulsed atomic beam. The time-of-flight measurements of the atom velocity are also a direct method to obtain information necessary for designing the optimal polarization system of the atomic beam in PPS.
444
A.S. Belov et aL / Velocity distribution in a pulsed hydrogen beam
2.1. General description o f the set
_y..The scheme of the set is shown in fig. 1. The electromagnetic valve injected molecular hydrogen into the dissociator tube, where the H 2 molecules were dissociated in pulsed rf discharge, excited inside the tube. The rf generator was pulsed by modulation of the anode voltage. The atomic beam was formed by the skimmer and the collimator. The dissociator tube and the rf coil of the generator were installed in a vacuum chamber, evacuated by a titanium sublimation pump with a pumping speed of ~ 4000 1 s -1 (H2). The apparatus for measuring the beam parameters was installed in the second vacuum chamber, evacuated by the same pump. The pulsed pressure in the chambers and the gas consumption in the dissociator were measured by a fast ionization-type pressure gauge. The beam density was measured by the time-of-flight mass spectrometer. For measuring the velocity distribution the beam was chopped into short segments by a mechanical chopper. The segments were detected by an ionization gauge whose signals were amplified and recorded by a storage-type oscilloscope. In the measurements of the particle density by the mass spectrometer the chopper was moved out of the beam. The zero-time signal for the time-of-flight velocity measurements produced by the light emitting diode-photodiode pair was also used to trigger the set. 2.2. Dissociator
In its main features the dissociator was similar to the one described in ref. [20]. The measurements were performed for three different dissociator tubes shown in fig. 2. The tubes were made of pyrex glass and, before installation into the vacuum chamber, were treated by hydrofluoric acid and after that by distilled water in order to lessen the surface recombination of atoms.
ELECT::~A~E NET]O ]~ANJ6Z~ETION/~oILM~I~;O~SDEC~NSETER
VOLTAr,,E D ' 6 " E u ~
"1 ' II ~ ~ It >- -PI.iOTOI)IODE
DISS0CIAT0O tIagr EMITTIN6
ASSEMBLY
DIOI~E
OOLLINATOP
4 9. 3 4 5 er~ 9ISS0OlATOQ TUEE I-I. O. /
2. Experimental apparatus
SEAM
OIAOPPEQ
Fig. 1. Scheme of the experimental set.
c~
IONI::ATION GAUBEP-
~',-
%
.
000LING N= t~ OI-IANNEL
j J
80NII] NOZZLE
Fig. 2. Scaled drawing of the dissociator tube and of the system forming the atomic beam.
The geometry of the tube in fig. 2a was selected in view of measuring the gas temperature inside the tube. In the dissociator shown in fig. 2b the atoms were cooled as the beam was let through a channel with a length of 50 mm, an inner diameter of 5 mm and a wall temperature of 300 K. In the dissociator shown in fig. 2c the walls of a 70 mm long channel were cooled, by the flowing liquid nitrogen to 77 K. In all three cases the orifice diameter of the nozzle was 2.3 mm. The beam was formed by a skimmer made of stainless steel - a truncated hollow cone with an inlet diameter of 4 mm and internal and external angles of 45 ° and 50 ° respectively. A collimator ( ~ 6 ram) was installed for lowering the pulsed pressure in the apparatus chamber. For short, we will call the beams obtained from the dissociators shown in figs. 2a, 2b and 2c the hot, the warm and the cooled beams, respectively. The rf power was fed to the dissociator by a coil (5 turns, ~ 15 mm) inductively coupled with the rf discharge and supplied by the rf voltage with a frequency of 70 MHz from the rf generator. The modulator of the anode voltage of the rf generator produced voltage pulses with a height up to 6 kV and a duration varying from 0.05 to 3 ms. In the present work the measurements were done for a pulse duration of 1 ms and a repetition frequency of 1 Hz. The rf discharge was supplied by a power up to 0.8 kW cm -3 (the volume of the dissociator tube was 8 cm3). The highest rate of hydrogen dissociation was observed when the rf discharge was turned on simultaneously with the gas injection into the dissociator tube [20]. The fast electromagnetic valve used for injecting hydrogen into the dissociator was similar to the one designed by Dudnikov et al. [21]. The usual pressure of hydrogen inside the valve was about 2 atm. The amount of gas injected into the dissociator tube could be varied
445
A.S. Belov et al. / Velocity distribution in a pulsed hydrogen beam
from 1017 to 5 × 10 's molecules per pulse by changing the height of the current pulses fed to the winding of the valve electromagnet. The duration of these pulses at half-height was 140 #s. The gas was injected into the tube in - 600/Ls after the corresponding current pulse was fed to the winding, which is due to the mechanical inertia of the valve. The time during which the tube was filled with hydrogen was determined by the rise time of the molecular beam density and was about 100 #s. The gas consumption per pulse N was determined from the following formula
(1 - r,/r2) N = An,/I1 [exp( - Atm/,2) -- exp( - a tin/z,) ] '
[LEOTItON AOOEL[PATING OOLLEOTOROF 6UN
..i
-300V
/
where a t m is the time interval between the moment the gas is injected into the tube and the moment the pressure in the dissociator chamber reaches its maximum, An, is the change in the density of the gas in the dissociator chamber during the time at=, r~ is the characteristic time of the gas escaping from the dissociator tube, % is the characteristic time of the hydrogen evacuation from the dissociator chamber by the pump, and V, is the volume of the vacuum chamber containing the dissociator. For the values of parameters typical for our set, i.e. % - 1.5 ms, r= = 60 ms and atm - 5 ms, the gas consumption is N = 1.1 x An I V~ with a few percent accuracy. The gas consumption was measured with the rf discharge turned off (in units of H 2 molecules per pulse), since, when the rf discharge is on, the gas in the dissociator chamber consists of a mixture of atoms and molecules, and the recombination of atoms in the chamber makes the interpretation of the measurement results difficult. The pulsed pressure in the vacuum chambers was measured by the ionization gauges with sensitivity 1.1 X 10 4 #A T o r r - ' for an emission current of 1 mA. The systematic measurement error of about 30% was due to the accuracy of gauges guaranteed by the manufacturers. For the typical gas consumption N---10 ,8 molecules per pulse the amplitude of the pulsed pressure in the dissociator chamber was about 1.5 × 10 -4 Tort. Due to the differential pumping of the apparatus chamber the amplitude of the pressure in this chamber was about 130 times smaller than in the dissociator chamber. This ratio changed slightly as the nozzleskimmer distance was varied. The dissociator was mounted on a movable flange which made it possible to vary the nozzle-skimmer distance and to adjust the dissociator to the axis of the skimmer and the measuring apparatus. 2.3. M a s s spectrometer
The time-of-flight mass spectrometer was designed specially for measuring the density and the composition of a pulsed hydrogen beam [22]. The scheme of the mass
/
-50 V
/ MOnULATOg
/
J
\ \HOLEOULAP
ELEOTI~OgE t
BEAM
OOLLIHATOI~
II j
(1)
ELECTPONBEIP1
ELEffI'I~OI]E
IO, 1 I 1
,
OOLLEOTOli ,
l_.L.-0nms
Fig. 3. Scheme of the time-of-flightmass spectrometer.
spectrometer is presented in fig. 3. The axis of the molecular beam is perpendicular to the plane of the drawing as well as to the direction of the electron beam and to the direction of the ion flow from the ionization region. At the input of the mass spectrometer the molecular beam was collimated by a ~ 1 2 mm diaphragm. The electron beam with an energy of 250 eV and a current of 0.6 mA was produced by an electron gun with an indirectly heated flat cathode and was modulated by the voltage supplied to the modulator electrode. The duration of the electron current pulses could be varied from 2 to 14 #s; the repetition time was 100 #s. Before intersecting the molecular beam, the electron beam was collimated by a 6 × 17 mmz diaphragm. During the pulse of the electron beam, H + and H~ions and the ions of the residual gas are formed in the ionization region and are retained in this region by the electric field of the space charge of electrons. After the end of the electron pulse a short voltage pulse with a height of 110 V and half-height duration - 0.1/~s is fed to the accelerating electrode, and the ions accumulated in the ionization region are accelerated towards the collector by the electric field between the accelerating electrode and the grounded grid. During the acceleration the ions have no time to leave the region between the accelerating electrode and the grid, which ensures the monochromaticity of the ions with the same charge-mass ratio. During the drift (L d = 17 cm) from the ionization region to the collector the ions in the bunches are separated with respect I t the mass according to their time of flight. The collector of ions was shielded from the electrons scattered in the ionization region by a grid with a potential of - 3 0 0 V. The amplitude and duration of the accelerating voltage pulse
446
A.S. Belov et al. / Velocity distribution in a pulsed hydrogen beam
hydrogen atoms [23] o i H = 3 . 9 × 10 -17 cm2), C is a coefficient accounting for the transparency of the mass spectrometer grids. The ion charge
Qk=-~Ff_?ukout dt,
Fig. 4. Characteristic oscillogram of the mass spectrometer pulses; rf discharge turned on; N =1 x10 TM molecules per puls; Pre = 3.6 kW, Tch= 300 K. From left to right: electron beam current pulse (0.2 mA/div.), accelerating voltage pulse, and ion current pulses of the atomic and molecular hydrogen (50 mV/div.). Horizontal scale: 0.5 ~s/div.
as well as the dimensions of the ion collector (40 × 60 mm 2) were selected on the grounds of experimental tests to minimize the ion losses during the path from the ionization region to the collector; this is important for the absolute density measurements in the molecular beam. The transparency of the mass spectrometer in the direction of the molecular beam (inside O 12 mm) is 100%. From the collector the ion current pulses were fed to the amplifier (pass band 10 MHz, sensitivity 200 mV /~A -1) and were recorded by a storage-type oscilloscope. A typical oscillogram of recorded signals is shown in fig. 4 (the signal of the electron current and the pulse of the accelerating voltage were fed to an inverting input of the oscilloscope). Since the current of the electron beam is measured in the mass spectrometer and the dimensions of the beams are known, we can determine the density of the molecular beam from the values of parameters of the recorded ion current pulses. One can easily derive the following expression for the density of particles n k of the kth kind: N k = Ok//CIetaecZioik,
(2)
where Qk is the charge of the bunch of ions of the kth kind exhausted out of the ionization region during a pulse of the accelerating voltage, I e is the electron beam current, ta,~ is the time during which the ions are accumulated in the ionization region, which is equal to the duration of the electron beam pulse, 7.i is the average length of the intersection region of the electron and the molecular beams along the electron beam axis, eik is the ionization cross-section for particles of the kth kind by electrons with an energy of 250 eV (for
where R F is the feedback resistance of the current amplifier and uokut is the voltage of the pulse for particles of the k th kind at the output of the amplifier. The relative error of our measurements was determined by the accuracy with which the quantities in formula (2) were measured and amounted to about _ 27%. In addition, the mass spectrometer was calibrated by filling the vacuum chamber with hydrogen and taking account of the difference in the effective ionization volumes (a factor of 3.2) for particles of the molecular beam and for molecules of the residual gas. The mass spectrometer was also calibrated by the ionization gauge 2 (see fig. 1), by which the density of the molecular hydrogen beam was measured independently. The resuits of these calibrations differ from the values given by formula (2) by no more than 20% in the region of gas consumptions N - 2 × 1017 to 2 × 1018 molecules per pulse.
2.4. Apparatus for measuring the velocity distribution of particles The velocity distribution of particles in the beam was measured by the usual time-of-flight method (see fig. 1). The chopper disk with a diameter of 13 cm and rotational speed up to 24000 r.p.m, had two diametrically opposite slits each 3 mm wide. The beam was collimated by a 3 x 15 mm2 diaphragm installed before the chopper disk. The time-of-flight signal was detected by an ionization gauge placed at a distance of 79.5 cm downstream from the disk. The electron emitting filament of the gauge was parallel to the beam axis. The cylindrical ion collector had a diameter of 27 mm and a length of 26 mm. The optical transparency of the gauge in the direction of the beam was about 94%, its sensitivity being 4.4 × 104 /~A Torr -~ for an emission current of 4 mA. The current signal from the collector gauge was amplified by a wide-band amplifier and recorded by a storage-type oscilloscope. The zero-time signal was produced by the light emitting diode-photodiode pair placed near the chopper disk, diametrically opposite to the point where the disk intersects the molecular beam. When the rf discharge in the dissociator was turned on a current signal appeared in the gauge collector simultaneously with the signal from the photodiode. This signal was apparently due to the photoemission of electrons in the gauge caused by the ultraviolet emission produced
A.S. Beloo et al. / Velocitydistribution in a pulsed hydrogen beam 3. Processing of the time-of-flight signals
I ~,+"p"
O"
£8 ,
,o
I !
A typical oscillogram of the time-of-flight signal for warm hydrogen atoms is shown in fig. 6. In processing the signals it was assumed that the chopper function is of triangular form with pulse duration at the base At = d/~rfR, where d is the width of the slits in the chopper disk and in the collimato r, f is the rotation frequency of the chopper disk, and R is the distance between the axes of the beam and the disk (R = 5.4
i
:i
I
+
0.6
/
o'
,+
!,
I
+-
3.3.4047
cm).
The time-of-flight signal ~ ( t ) is related to the distribution function of particles in the beam f ( v ) by the well-known equations
mot W2 per ptttse
0.~
i
~ _ o - 6.~.40 ~' -- 4 7"404~
l,
x -
4
~
447
3
4
4.O'f .01~ •
5
t
6
7
~(t)
=f~ c(r)F(t-r)
dr,
f ( v ) = f ( L / t ) cx F ( t ) t 2. Fig. 5. Relative fraction of atoms in the beam vs the rf discharge power.
by the rf discharge; it was used as a zero-time signal in the measurements with the rf discharge turned on. The signal from the chopper photodiode, the repetition frequency of which (400 Hz) was reduced to 1 Hz by the frequency devider, triggered the feeding system of the dissociator, synchronizing the latter with the chopper. By varying the time delay of triggering of dissociator units with respect to the photodiode signal it was possible to "shift" the moment of turning on the dissociator with respect to the moment the disk slit intersected the molecular beam, and, thus, to study the variations of parameters of the atom velocity distributions during the pulse of the discharge. The employed ionization gauge was not mass-sensitive. This was not essential when the rf discharge was turned off, since in this case the b e a m consists of only the H 2 molecules. However, in the atom velocity measurements with the rf discharge turned on the relative fraction of atoms in the beam had to be large, since the time-of-flight separation in bunches of hydrogen atoms and molecules is not sufficiently good for a supersonic beam with a small Mach number. Fig. 5 shows the relative fraction of atoms x in the beam for the studied dissociator versus the rf discharge power for different N. x is determined as x = n H / ( n H + nil2 ), where n H and nil2 are the densities of atoms and molecules in the beam respectively. The density of the beam was measured by the mass spectrometer. The dotted lines in fig. 5 and in other figures below are plotted for clarity. In order to avoid errors in the measurements of the atom velocity distribution the latter were done for such an rf discharge power that x was not less than 0.8.
(3a) (3b)
Here c(r) is the chopper function, F(t) is the signal for a delta-shaped chopper function, and L is the distance between the chopper disk and the center of the ionization gauge. The pass bands of both the ionization gauge amplifier (A f = 0-100 kHz) and the oscilloscope (A f = 0 - 1 MHz) were sufficiently wide and were not taken into account when the signals were processed, as well as the effect of the finite dimensions of the ionization gauge on the form of the signal. The distribution function of the longitudinal velocities of particles in the beam was approximated by the function usually used for a supersonic particle flow (see, e.g., [13]) f ( v ) = Bv 2 exp[ - m ( v - u ) 2 / 2 k T 1],
(4)
where B is the normalization constant, m and v are the mass and the velocity of particles, respectively, u is the mass velocity of the flow, T1 is the temperature corre-
Fig. 6. Oscillogram of the time-of-flight signal; rf discharge turned on; N = I ×10 TM molecules per pulse, Prr = 3.2 kW, Tch = 300 K. Vertical scale: 2 mV/div., horizontal scale: 50 #s/div.
448
A.S. Belov et aL / Velocity distribution in a pulsed hydrogen beam distribution (4) are related by the expression
tO
u
~ o.8
VMp = ~- +
~ 0.6
The errors in the measurements of VMe, M and To presented below consist of the error connected with the accuracy with which parameters u and T a were determined from the apparatus Signal by a computer, and the error connected with the accuracy of the calibration of the oscilloscope time scale. The relative error A u / u was about _+3.5%, and A T 1 / T a - _+7%.
\
N 0.~
0.9
2
5
5
""~.1..... 6 z t,t0-~
Fig. 7. Comparison of the apparatus signal with the signal corresponding to the approximating velocity distribution function (4). Solid fine: apparatus signal (Tch = 77 K, N = 4 X 1017 molecules per pulse) normalized to unity; circles: signal corresponding to the approximating velocity distribution function for u =1.93×10 S cm s -t, T~ =18.3 K; rf discharge is on.
sponding to the longitudinal movement of particles in the center-of-mass frame of reference, and k is the Boltzmann constant. Function (4) is normalized to the density of the particle beam n; the intensity of the beam is expressed through f ( v ) as
= fo~Of(o)do. When processing the apparatus signal on a computer the parameters of the distribution function (4) - T 1 and u - were selected in such a way that the mean-square deviation of the signal corresponding to the approximating function from the apparatus signal would be minimal with account of relations (3a) and (3b). Fig. 7 shows the signal corresponding to the velocity distribution function found in this way; the apparatus signal is normalized to unity. F r o m fig. 7 one can see that distribution (4) is in good agreement with the experimental time-offlight signal everywhere except in the region of large. times of flight i.e., the experimental spectrum has a deficit of slow atoms. The processing has shown that the greater the Mach number, the better distribution (4) agrees with experimental results. Using the known values of parameters T 1 and u we calculated the Mach number 3,/11 and the temperature To of the gas in the dissociator [16]: MII = u /
~ykr m
'
To= T , ( I + ~ - ~ J - M , ~ ) ,
(5) (6)
where "y is the specific heat ratio. VeLocity u and the most probable velocity vMp for
+ -
(7)
m
4. Results and discussion
4.1. Velocity distribution of particles in a molecular hydrogen beam The measurments were performed first for a molecular hydrogen beam with the rf discharge turned off. In this case the dissociator is similar to the usual source of supersonic molecular beams. The aim of our measurements was to determine the parameters of velocity distributions in the molecular beam for relatively low pressures in the tube, typical for a dissociator in which it is still possible to obtain a beam with a large fraction. of hydrogen atoms. Fig. 8 shows the parameters of velocity distributions for warm molecules versus the gas consumption per pulse N for a fixed nozzle-skimmer distance. The maxim u m Mach number M = 3.5 + 0.3 was obtained at N =
T,I~
M
V,,~OSern..s-'
IJ.44~""/4f
I ,yl
.I ]," I
r'Ll t!il, !
,rhli¢
,.o
,oo
[,,
80
:
t'J IIIII (o
9
.'[I
t
5
/*
-~.+_o .~'[ tO~
9
5
I
t0 ~s
N, mot H,per pu~se Fig. 8. Parameters of the velocity distributions of molecules vs the gas consumption per pulse. Tch = 293 K.
449
A.S. Belov et al. / Velocity distribution in a pulsed hydrogen beam 4 x 1018 molecules per pulse. As the gas consumption was increased further, the Mach number decreased, while temperature Tz grew. Apparently, the decrease of M is due to the so-called beam-skimmer interference. This effect was also observed in the usual nozzle sources of supersonic beams at high gas pressures in the source (see e.g. ref. [24]). However, we must note that in our experiments we did not observe the pronounced sharp dependence of the beam density on the nozzle-skimmer distance XNs, typical for the supersonic beam sources in which the stagnation gas pressure P0 > 100 Torr. The density of the molecular hydrogen beam depended weakly on XNs and reached its maximum at XNS = 15 mm. It is for this optimal distance that the measurements of the velocity distributions of molecules and atoms were performed. The cooling of the channel walls to 77 K has led to an increase of the Mach number in the molecular beam. For a gas consumption of 2 × 1018 molecules per pulse we have obtained a beam of cooled molecules with a Mach number MII = 6.8 _ 0.6, velocity VMa = (1.30 _+ 0.05) X 105 cm s -1 and temperature T1 = (5.9 _ 0.4) K. The measurements of the temperature TO showed that it coincides with the temperature of the cooling channel walls (77 K) within the error of the measurements for a gas consumption up to N = 2 x 1018 molecules per pulse. For higher gas consumptions TO grows due to the incomplete cooling of molecules at high gas densities in the cooling channel. One of the factors leading to an increase in the Mach number when the gas is cooled, is the increase of the density of the gas in the cooling channel in comparison with a warm flow for the same gas consumption per pulse. This assertion was tested by measuring the hydrogen flow rate from the dissociator (see sect. 2.2 and ref. [20]). The characteristic time of the gas escaping from the tube can be presented as
Td/ ro. This "compression" effect plays an even greater role in the dissociator with the rf discharge turned on, since, as will be shown in the next section, the gas in the rf discharge is heated to a considerably high temperature. 4.2. Temperatuie of hydrogen in the dissociator with the rf discharge turned on As was established in ref. [20] (see also fig. 5), in order to obtain a high dissociation degree of hydrogen molecules at a gas consumption up to 4 x 1018 molecules per pulse, one must feed the rf discharge with a power up to 0.8 kW cm -3. For determining the gas temperature in the tube under such conditions the measurements of the atom velocity distributions were done for the tube without the cooling channel (fig. 2a). The results of the measurements are presented in fig. 9. The measurements were made at the moment corresponding to the middle of the discharge pulse (tm~ s = 0.5 ms). According to the results presented in fig. 9, temperature TO strongly depends on the power of the rf discharge and reaches - 2800 K, so the pulsed pressure of the gas in the volume occupied by the rf discharge is about 30 Tort (for N = 6.6 X 1017 molecules per pulse).
T~
7+1
vo ~ a o A n / ~ no]
hydrogen in the channel is cooled, the increase in the gas density is greater than the decrease of the speed of sound. Obviously, the increase of the density in the cooled gas is due to a gas temperature gradient in the cooling channel. According to our measurements, the degree of compression of hydrogen also depends on the diameter of the nozzle orifice. For a sufficiently small nozzle orifice area, and, consequently, for a small gas flow through the channel, the pressure gradient in the channel must also be small and we must have n o/n a -
...4h •
(8)
where a 0 is the speed of sound at gas temperature TO in the cooling channel, n d and n o are the gas densities in the dissociator and in the cooling channel respectively, Vd is the volume of the dissociator tube, and A , is the area of the nozzle orifice. At a temperature of the cooling channel walls Tch = 293 K the factor n d / n o is close to unity and the experimentally measured value of zI is in agreement with formula (8) within a 10% error. At Tch = 77 K our measurements give ~.77= 0.8~.293, where the upper indices indicate the temperature of the cooling channel walls. Since a o tx I"ol/2, from this result it follows that n o / n d > (Td/TO) 1/2, where T~ and TO are the temperatures of the gas in the dissociator tube and the cooling channel respectively. This means that as the molecular
,9500
1¢/
~"1!'
I!
1500
;/
~000
o~ +
L,
e
P~,~W
Fig. 9. Atom temperature in the dissociator tube vs the rf discharge power, tm~s = 0.5 ms. O: 3.3x1017 molecules per pulse, + : 6.6 x 101-/ molecules per pulse, e: 1.7 × 1018 molecules per pulse.
A.S. Belou et al. / Velocity distribution in a pulsed hydrogen beam
450
It is worth noting that the temperature of the dissociator tube walls ( - 3 0 0 K) differs greatly from the temperature of the gas, and there is no thermal equilibrium in the tube. Obviously, the temperature distribution of the gas in the tube must be inhomogeneous, and the temperature in the center of the dissociator tube must be higher than in the outlying areas of the discharge, including the vicinity of the nozzle where the gas temperature was measured. As is known, the degree of hydrogen dissociation depends on the temperature. For a gas density n = 3 × 1017 cm -3 and a temperature of 2800 K, the dissociation degree exceeds 80% [25]: F r o m fig. 9 it follows that in the considered dissociator the thermal mechanism of hydrogen dissociation is essential. This is confirmed by the observed dependence of the relative fraction x of atoms in the beam on the power of the rf discharge (see fig. 5). Comparing figs. 5 and 9 one can see that x increases in the same range of the rf discharge power where the gas temperature grows. Because of this, the considered dissociator can be called a dissociator of the combined type, since it is also a thermal dissociator. The dynamics of heating and cooling of atoms are shown in fig. 10, from which one can see that the temperature of the atoms increases during the rf discharge, and after the latter is turned off, the atoms are cooled during - 2 0 0 Vs. A beam of hot atoms is an effusion-type beam; after the discharge is turned off, the Mach number increases as atoms are cooled. The time variation of the atomic beam density for this dissociator geometry was described in ref. [20]. In particular, a sharp increase of the beam density after the rf discharge is turned off is explained by the results of the present work concerning the changing of the Mach number after the rf discharge is turned off.
T~
t
g F dLseborge
4.3. Velocity distribution in beams o f warm and cooled H atoms
In the measurements for beams of warm and cooled atoms it was found that the velocity distributions of atoms depend on gas consumption and on the rf discharge power and vary during the discharge pulse. The fact that the velocity distributions of atoms depend on the named parameters is explained by the heating of the gas in the rf discharge of the dissociator which was described in the previous section. This effect modifies the typical dependence of the particle velocity distribution parameters on the pressure in comparison with a source which has a constant stagnation gas temperature. Fig. 11 shows the velocity distribution parameters versus the gas consumption for warm atoms. F r o m the results presented in fig. 11 it follows that, at N < 1018 molecules per pulse, the atoms are cooled practically to room temperature. The value of TO calculated from (6) at N ~< 1018 molecules per pulse, is systematically smaller than the temperature of the cooling channel walls (T~h = 300 K). The reason for this discrepancy is not clear to US.
For gas consumption N = 1 × 1018 molecules per pulse the Mach number of the atom flow reaches MII = 2.7 + 0.25, while the most probable atom velocity is Vup = (3.05 ___0.12) × 105 cm s -a and the atom temperature in the beam is T 1 = (71 + 5) K. For gas consumptions higher than 1018 molecules per pulse the cooling of atoms is not sufficiently effective. As N grows, temperature TO rises and reaches 423 K at N = 5 × 1018 molecules per pulse. Temperature T 1
M
T, I~
V,~OScm.s"' &8
i
3.4
9000
3
i
4500
/
I! :1|
0
/
4000 500 --
3
;¢
,
"" °
e
~00
5.0
590 ~
2.6
240
1
9
1
6
0
~
%.
4.o t9 4.~ t.6 t~ ~
t, ms
Fig. 10. Changes in the atom temperature TO (1) and in the Mach number (2) of the beam during the rf discharge pulse for a tube without the cooling channel. N = 2.5 × 1018 molecules per pul.se, P,f = 6 kW.
2
5
t0 ~
~
5
tO~g
N, tool W=por p={s0 Fig. ] l . Parameters o f the atom v e l o c i t y distributions vs the gas
consumption per pulse. ~h = 300 K, tmeas = 0.5 ms, x = 0.85.
451
A.S. Belov et aL / Velocity distribution in a pulsed hydrogen beam
also rises, while the Mach number decreases to M = 2.1. The length of the cooling channel Lch was selected using the following estimation [20] Lc h -- 0.4R2/-•,
(9)
where R , is the radius of the nozzle orifice and ~ is the mean free path length of atoms in the channel, which was calculated from the value o f the atom density averaged over the length of the cooling channel. As N increases, the density of atoms in the channel grows and ~, decreases. Consequently, the time of diffusion of atoms towards the cooling channel wall increases and the efficiency of cooling falls. This is in qualitative agreement with the obtained experimental results. A more complete cooling of atoms at large N can be achieved by either increasing the channel length L~h or, as it follows from formula (9), by reducing the radius of the nozzle orifice R . . In both cases the time during which the atoms pass through the channel increases, but unfortunately, this leads to a decrease of the relative fraction of atoms in the beam due to the recombination of atoms in the channel. Fig. 12 shows the dependence of x on N for different radii of the dissociator nozzle orifice R , . For each value of N, the power of the rf discharge is the same for different R , . F r o m fig. 12 it follows that the possibility of achieving a more complete cooling of atoms by modifying the channel and nozzle geometry is limited by the recombination of atoms. The incomplete cooling of atoms at large N is also due to the increase in the rf discharge power necessary
,I.0 ~ o.g
'--
0.8
•
liH',, , l
0.6
2
5
lOm
~
5
I0m
N, mot I-l~pgr ptdsg Fig. 12. Relative fraction of atoms in the beam vs the gas consumption per pulse for dissociator tubes with different nozzle orifice radii R n" T~h = 300 K, tm¢as= 0.5 ms.
M
T.~4
l'0 11( ~ )/
L~O0
2.fi
300
_
t
2.~
200
"
2.0
T4 -'('~ 0..-- - 0
400
O" " 0
3
~-
4
"~/
5
6
7
8
P,~, kW Fig. 13. Parameters of the atom velocity distributions vs the rf discharge power at fixed N = 2.5 × 10 Is molecules per pulse, Tch = 300 K, trneas 0.5 ms. =
for obtaining a high degree of hydrogen dissociation. This is illustrated in fig. 13, which shows the parameters of the atom velocity distribution versus the rf discharge power for a fixed value of N = 2.5 × 1018 molecules per pulse. As the rf discharge power grows, one observes a nearly linear increase of temperatures TO and T 1, and a weak decrease of the Mach number. The temperature TO of warm H atoms increase during the rf discharge by 10-20%, depending on the gas consumption, and the Mach number slightly decreases, but the variations of these parameters are considerably weaker than in the case of a beam of hot atoms. The rf discharge power in the dissociator tube becomes the main factor determining the parameters of the velocity distribution for cooled atoms, since the relative variations of these parameters versus the rf discharge power for a beam of cooled atoms are a few times greater than in the beam of warm atoms. For this reason in fig. 14 parameters VMp, M and TO for a beam of cooled atoms are presented as functions of the rf discharge power. A satisfactory cooling of atoms is obtained only at a discharge power P ~< 0.3 kW cm -3. We assume that the observed strong dependence of the atom temperature on the discharge power is due to the penetration of the plasma from the area of the rf discharge into the cooling channel and to an increase of the plasma density with the increase of the discharge power. The most typical measured H atom velocity distributions are shown in fig. 15 together with the Maxwell velocity distribution calculated for TO= 300 K and corresponding to an effusion-type flow from the dissocia-
452
A.S. Belov et al. / Velocity distribution in a pulsed hydrogen beam
T,~
V, ~O.Scr~.s -'
~0 45 12, e111."3
o
9~0
•
L .............
2.4
900 ~.0
t60 4.6
10 42
M 4.5 ~0
80
• i
2
3
3~5
/
3.0
4
5 P,kW
40 ~
Fig. 14. Parameters of the atom velocity distributions vs the rf discharge power. Tch = 77 K, t m e a s = 0 . 5 m s . O: 2.5X1017 molecules per pulse, +: 3.3x 1017 molecules per pulse, D: 5.4x1017 molecules per pulse, ix: 6.7x1017 molecules per pulse, × : 8 X 1017 molecules per pulse, e: 1 X 10 TM molecules per pulse.
tor. As far as we know, a supersonic b e a m of hydrogen atoms with a M a c h n u m b e r Mii > 4 was o b t a i n e d for the first time in our experiments. 4.4. Intensity o f the atomic beam The density in a b e a m of hydrogen atoms was measured by the mass spectrometer described in sect. 2.3. The distance between the nozzle and the center of the ionization region of the mass spectrometer was 17.8 cm.
z
i i
i
~3
i L
4
6
a
O ' 4 0 S e m ' s -(
Fig. 15. Typical velocity distributions of atoms. I : the tube
without the cooling channel, N = 2.5 x 1018 molecules per pulse, 2: T~h = 300 K, N = I . 0 × 1 0 TM molecules per pulse, 3: T~h = 77 K, N = 5.4x l0 z7 molecules per pulse, 4: Maxwell distribution for TO= 300 K.
40 Iz
40 ~8
N, mot 14 p0r ptt£so Fig. 16. Density of the atomic beam vs gas consumption. 0: T~h = 300 K, x : Tch = 77 K; t . . . . = 0.5 ms, x = 0.85.
The results of measurements are presented in fig. 16. U n d e r our conditions, for N < 1 x ]01"/ molecules per pulse the time during which the dissociator tube is filled with gas i n c r e a s e with decreasing N. Thus, for a fixed time interval between the m o m e n t s of triggering the gas valve and the rf discharge, this leads to a sharper increase of the b e a m density measured at the m o m e n t corresponding to the middle of the rf discharge pulse in comparison with a linear dependence. In a b e a m of cooled atoms, for N from 1 x 1017 to 5 x 1017 molecules per pulse, the density is higher than in a b e a m of warm atoms. This is due to the fact that for the same gas consumption, the M a c h n u m b e r in a b e a m of cooled atoms is greater than in a b e a m of w a r m atoms. The m a x i m u m achievable density of the b.eam is approximately the same for b o t h the warm a n d the cooled atomic beams. For a b e a m of cooled atoms it is achieved at Net - 5 x 1017 molecules per pulse, while for w a r m atoms at Nor - 1 x 10 TM molecules per pulse. Apparently, the increase of the b e a m density is h a m p e r e d by the scattering of atoms (the b e a m - s k i m m e r interference). In the atomic beam-type polarized ion sources operated in a continuous mode, the scattering of atoms in the region between the nozzle a n d the skimmer is, probably, the main factor h a m p e r i n g the increase of the a t o m b e a m intensity [26,27]. In our experiments the scattering of atoms by the'residual gas in the dissociator v a c u u m c h a m b e r was negligible, since, at N = 1 x 10 TM molecules per pulse, the pressure in this c h a m b e r was not greater than 1.5 × 10 -4 Torr. However, it was pos-
A.S. Beloo et al. / Velocity distribution in a pulsed hydrogen beam sible to increase the density of the atomic beam by 1.7 times by increasing the height of the skimmer from 12 to 30 mm, which indicates that the scattering of the beam by the gas, reflected by the skimmer, was considerable. Apparently, it is possible to decrease the scattering of atoms by the further optimization of the skimmer geometry, which was not fully done in the present work. The intensity of the atomic beam, I (atoms sr -~ s - l ) , is given by the expression
t(0)=
- 2 n msVtms,
where nms is the density of the beam measured by the mass spectrometer, ~ is the average velocity of atoms in the beam, and Lms is the distance between the atom source and the center of the ionization region of the mass spectrometer. For a beam of cooled atoms at N = 3.3 × 1017 molecules per pulse and P = 0.23 kW Cm -3 (the conditions under which factor nms/V2p approximately has a maximum), we find that I ( 0 ) = (2.8 + 0.8)× 1020 atoms sr -1 s -1. The other parameters of the beam under such conditions are: VMp= (1.97 + 0.07)×105cm s -1, T1 = ( 1 4 . 4 + 1) K, T 0 = ( 9 6 + 10) K, and M = 4.14 _ 0.35. "Theoretical intensity" of a nozzle beam (without accounting for the decrease in the beam intensity due to the scattering of atoms) is given by the expression [19] (for M > 3)
I(o) = As~o,o r (Y~)'/~
M3
y+l
453
cross-sections of atoms and molecules. Nevertheless, for determining n o we assumed that x - = x 0. This approximation is justified by the fact that the relative fraction of atoms in the beam was sufficiently large (x >t 0.8), and the relative error of this approximation is unlikely to exceed - 25%. The value of the ratio n o / n d was determined from the measurements of the characteristic time of the gas escaping from the dissociator with the rf discharge turned on, as was described in sect. 4.1 for the case of a molecular beam. For T~h = 77 K, N = 3.3 × 1017 molecules per pulse and P = 0.23 kW cm -3, it was found that ~-1= (0.75 +__0.05) ×10 -3 s. From formula (8) under these conditions (TO= 96 K, a 0 = 1.15 × 105 cm s -1) we get n o / n d ---4.0. Formulae (10) and (11) for MI1=4.14, x 0 = 0 . 8 , y = 5 / 3 and N = 3.3 × 1017 molecules per pulse give Ith(0)= 1.1 X 10 21 atoms sr - I s -1. The big difference between the experimentally measured beam intensity (I(0)exp = (2.8 + 0.8)× 10 20 atoms sr -1 s -1) and the intensity predicted by formulae (10) and (11), apparently, cannot be explained only by the uncertainty in the values of the quantities entering formulae (10) and (11). On the one hand, the inevitable decrease of the beam intensity due to the scattering of atoms must be taken into account in formula (10), and on the other hand, in the real beam this decrease possible can be reduced by the optimization of the skimmer geometry.
), 5. Conclusion (10)
where A s is the skimmer orifice area, and n o and a 0 are the stagnation density and the speed of sound respectively. In order to use formula (10) for calculating the peak intensity of a pulsed beam of hydrogen atoms let us express approximately the atom density n 0 through the experimentally measured parameter N:
N
no-
2x__.q_o ( n o ]
Vd 2-~¢o \ na]"
(11)
Here Vd is the volume of the dissociator tube and ~¢0 is the relative fraction of atoms in the tube. The first factor in eq. (11) is equal to the peak density of hydrogen molecules in the tube; the second one accounts for the dissociation of molecules; while the third factor accounts for the increase in the density of atoms when the latter are cooled in the channel, x 0 may not be equal to the measured parameter x, since the angular distributions of atoms and molecules in the gas flow from the dissociator are not necessarily the same. Furthermore, the decrease in the intensity of the atomic and the molecular beams due to scattering can also be different due to the difference in the collision
When the pressure in the tube and the power applied to the rf discharge are increased, the hydrogen dissociator with the rf discharge usually used in the atomic beam-type PPS is similar to the thermal dissociator, since in this case the hydrogen temperature rises up to a few thousand degrees and the thermal dissociation of hydrogen molecules plays an essential role. In such a dissociator it is possible to obtain a high dissociation degree of hydrogen - at least in the pulsed mode when the initial density of hydrogen molecules in the dissociator tube is under 5 × 1017cm -s. In this case, in order to obtain a high dissociation degree of hydrogen in the rf discharge it is necessary to supply a power up to 0.8 kW cm -3. The high temperature of the gas is a negative feature of this dissociator, since the acceptance angle of the separating magnet in the PPS is inversely proportional to the energy of atoms in the beam. The cooling of atoms is achieved by letting the hot gas pass through a sufficiently long cooling channel. When the atoms are cooled, the density of atoms in the channel increases. This "compression" effect favours the formation of a supersonic atom flow. We have obtained a supersonic beam of hydrogen atoms with a Mach number Mtl = 2.7 + 0.25 for the temperature of
454
A.S. Beloo et al. / Velocity distribution in a pulsed hydrogen beam
the cooling channel walls 300 K, a n d with Mfl = 4.14 + 0.35 for a temperature of 77 K. In a b e a m of cooled hydrogen molecules for the chosen dissociator geometry at N = 2 x 10 ~8 molecules per pulse, we have measured a M a c h n u m b e r M H= 6.8 + 0.6. The distribution of atom velocities depends on the rf discharge power a n d on the pressure inside the dissociator tube and varies during the rf discharge pulse. For a b e a m of cooled atoms the main factor is the discharge power. T e m p e r a t u r e TO to which the atoms are cooled in the channel at T~h = 77 K changes from TO = 85 K at P = 0.23 kW cm -3 to TO - 220 K at P - 0.7 kW cm -3. Apparently, the main reason for an incomplete cooling of atoms is the p e n e t r a t i o n of the plasma from the region of the rf discharge into the cooling channel. The decrease of the nozzle orifice radius must lead to a more complete cooling of atoms. However, due to the surface and volume r e c o m b i n a t i o n of atoms in the cooling channel, this leads to a decrease of the relative fraction of atoms in the beam. U n d e r the conditions optimal for the focusing of the atomic beam by the separating PPS magnet (i.e. in the case when the factor n n / v ~ p is m a x i m u m ) we have o b t a i n e d a b e a m of atoms with intensity I(0) = (2.8 + 0.8) x 10 20 atoms sr 1 s - 1 the most p r o b a b l e velocity vMp = (1.97 + 0.07) × t05 cm s 1, a n d temperatures T~ = (14.4 + 1) K, TO = (96 + 10) K. Apparently, the intensity of the b e a m can be increased by the optimization of the skimmer geometry and, thus, by reducing the effect of the atom scattering. The authors are grateful to Prof. S.K. Esin a n d to Prof. V.M. Lobashev for support a n d for their c o n s t a n t interest in our work. We are grateful to Prof. G. Clausnitzer for his useful criticism of the first variant of this paper.
[5]
[6]
[7] [8]
[9] [10] [11] [12] [13] [14] [15]
[16] [17] [18] [19]
[20]
[21] [22]
References [23] [1] P.A. Schmelzbach, W. Gr~ebler, V. K6nig and B. Jenny, Nucl. Instr. and Meth. 186 (1981) 655. [2] H.G. Mathews, A. Kruger, S. Penselin and A. Weinig, Nucl. Instr. and Meth. 213 (1983) 155. [3] E. Grorud, J.-L. Laclare, G. Leleux, A. Nakach and A. Ropert, Int. Symp. on High Energy Spin Physics (1982) ed., Gerry M. Bunce, AlP Conf. Proc. no. 95 (ALP, New York, 1983) p. 407. [4] L.G. Rather, Int. Symp. on High Energy Spin Physics
[24] [25] [26] [27]
(1982) ed., Gerry MI Bunce, AlP Conf. Proc. no. 95 (ALP, New York, 1983) p. 412. S. Hiramatsu et al., Int. Symp. on High Energy Spin Physics (1982) ed., Gerry M. Bunce, AIP Conf. Proc. no. 95 (AIP, New York, 1983) p. 419. N.G. Anishchenko et al., Int. Symp. on High Energy Spin Physics (1982) ed., Gerry M. Bunce, AIP Conf. Proc. no. 95 (ALP, New York, 1983) p. 445. Yu.M. Ado et al., IFVE 82-54, O U K / O P Serpukhov (1982). C. Bovet, D. M6hl and R. Ruth, Workshop on SPS Fixed-Target Physics, CERN 83-02, vol. II (Geneva, 1983) p. 396. E.F. Parker, N.Q. Sesol, and R.E. Timm, IEEE Trans. Nucl. Sci. NS-22 (1975) 1718. Yu.A. Plis and L.M. Soroko, Uspekhi Fiz. Nauk. 107 (1972) 281. B.P. Ad'yasevich, V.G. Antonenko, Yu.P. Polunin and D.E. Fomenko, Atomnaya Energiya 17 (1964) 17. M. Perrenoud, W. G~ebler and V. K0nig, Helv. Phys. Acta 44 (1971) 594. W. Kibishta, CERN PS/DL/Note, 77-5 (Geneva, 1977). S.G. Popov and D.K. Toporkov, Preprint IYaF SO AN SSSR, 80-129, (Novosibirsk, 1980). P.F. Schultz, E.F. Parker and J.J. Madsen, Proc. 5th Int. Symp. on Polarization Phenomena in Nuclear Physics, Santa Fe, eds., G.G. Ohlsen et al., AlP Proc. no. 69 (ALP, New York, 1981) p. 909. A. Kantrowitz and J. Grey, Rev. Sci. Instr. 22 (1951) 328. V.B. Leonas, Uspekhi Fiz. Nauk, 127 (1979) 319. R. Keller, L. Dick and M. Fidecaro, Report CERN 60-2 (Geneva, 1960). H.F. Glavish, Proc. 3rd Int. Symp. on Polarization Phenomena in Nuclear Reactions, Madison, eds., H.H. Barshall and W. Haeberli (University of Wisconsin Press, Madison, 1971) p. 267. A.S. Belov, S.A. Kubalov, V.E. Kuzik and V.P. Yakushev, IYaI AN SSSR, Preprint-0272 (Moscow, 1983) Nucl. Instr. and Meth. 227 (1984) 11. G.E. Derevyankin, V.G. Dudnikov and P.A. Zhuravlev, Pribory i Tekhnika Eksperimenta 5 (1975) 168. A.S. Belov, S.A. Kubalov, V.E. Kuzik and V.P. Yakushev, IYaI AN SSSR, Preprint-0247 (Moscow, 1982). W.L. Fite and R.T. Brackmaun, Phys. Rev. 112 (1958) 1149. K. Teshima and Y. Yasunaga, Jap. J. Appl. Phys. 22 (1983) 1. L. Valyi, Atom and Ion Sources (Wiley, New York, 1977) p. 75. Yu.A. Plis and L.M. Soroko, JINR, R9-10312 (Dubna, 1976). A.V. Evstigneev, S.G. Popov and D.K. Toporkov, Preprint IYaF SO AN SSSR, 84-51 (Novosibirsk, 1984).