Interaction between low energy cesium ion beam and thermal cesium plasm

Baker, D.

Sellen, J. M.

Wong, A. W.

English

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Report on Program Supported by 
NASA Grant NGR- 05 - 00 7+6 
Interaction Between Ion Beams and Plasmas 
December 1 ,  1966 
A. Y .  IVong 
Principal Investigator 
Progress Report N-2  
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? 
. 
In t e rac t ions  Between Ion Beams and Plasmas 
D. Baker and A. Y. IJong 
Department of  ?hysics ,  University o f  Ca l i fo rn ia ,  Los Angeles, Ca l i fo rn ia  
and 
J. II. Sel len  
TPJJ Systems, Redondo Beach, Ca l i fo rn ia  
I. INTRODUCTION 
In t h i s  paper we w i s h  t o  repor t  t h e  prel iminary r e s u l t s  o f  the  i n t e r -  
a c t i o n  between a low energy cesium ion  beam (1 t o  30 ev) and a thermal cesium 
plasma (.25ev). A schematic o f  the system used is  shown i n  Fig. 1. 
The cesium plasma i s  produced by contac t  i on iza t ion  on a hot  tungsten 
p l a t e  i n  one end o f  a Q machine.' 
which i s  e s s e n t i a l l y  t h e  same as the  one developed by Se l l en  e t  a1.2 The 
ions  are formed on the  su r face  of a porous tungsten plug which i s  fed by a 
beam of C 
e r a t e d  by t h e  acce le ra t ing  g r i d  and then dece lera ted  t o  t h e  plasma p o t e n t i a l .  
The beam ve loc i ty  can be va r i ed  from 1 t o  15 t i n e s  t h e  plasma ion thermal 
v e l o c i t y  (a i ) .  
mum beam dens i ty  was 5x10 /cc. 
The cesium ion  beam is  produced by a gun 
atoms from an oven behind t h e  plug. The C ions are then accel-  
S S 
llie beam and plasma width is  approximately 2.5cm. The maxi- 
9 9 The plasma dens i ty  ranged from 5x10 /cc  t o  
11 10 /cc. 
The experimental work can be broken down i n t o  two main ca tagor ies .  
The first catagory is t h e  inves t iga t ion  o f  s t a b i l i t y  limits for low f r e -  
quency o s c i l l a t i o n s  i n  an ion beam-plasma system confined by a magnetic f i e l d .  
The ion  beam i s  d i r ec t ed  along the magnetic f i e l d .  The dens i ty  grad ien ts  
c 
-upported by the  magne i c  f i e l d  give r ise t o  an aximuthal component t o  t h e  
uns tab le  wave, thus changing t h e  wave charac te r  from t h a t  i n  a homogeneous 
i n f i n i t e  plasma. 
The second catagory i s  the  inves t iga t ion  o f  t h e  a t t enua t ion  and t h e  phase 
ve loc i ty  o f  low frequency "ion a c o u s t i d t  waves i n  a s t a b l e  ion  beam-plasma 
system. The waves are exc i t ed  and received by g r ids  immersed i n  the  bean- 
plasma system. 
11. Density P r o f i l e s  
The cross-sect ion dens i ty  p r o f i l e s  of t he  beam and the  plasma were 
measured sepa ra t e ly  i n  order  t o  a sce r t a in  t h a t  t h e  beam was centered i n  the  
plasma, 
any misalignment. 
i n  Fig. 2. 
"'lie pos i t i on  o f  t he  plasma i n  the  chamber can be ad jus ted  t o  remedy 
The dens i ty  p r o f i l e s  a f t e r  t he  f i n a l  adjustment are shown 
111. S t a b i l i t y  L i m i t s  of an Ion Beam-Plasma System 
Confined by a blagnetic F ie ld  
--- 
-- -
One of t h e  i n i t i a l  goals of t h i s  experiment was t o  v e r i f y  the  t h e o r e t i c a l  
work by Fr ied  and \long3 which predic ted  the  s t a b i l i t y  limits f o r  e l ec t ro -  
s ta t ic  "ion acous t ic t t  waves propagating p a r a l l e l  t o  a ilaxwellian ion  beam 
which i s  i n j e c t e d  through an i n f i n i t e  homogeneous Ilaxwellian plasma with no 
magnetic f i e l d .  
dens i ty  grad ien ts  give rise t o  addi t iona l  terms i n  the  d ispers ion  r e l a t i o n  
which can change the  s t a b i l i t y  limits of  the  system. 
a l s o  r e s u l t  i n  a component of the wave which is perpendicular  t o  t h e  magnetic 
f i e l d ,  thus giving a h e l i c a l  wave of  t h e  type described by K a d o m t s e ~ . ~  
However t h e  presence of the  magnetic f i e l d  and t h e  r e s u l t i n g  
4 
These addi t iona l  terms 
In 
- 3 -  
t h e  l i m i t  of zero dens i ty  gradients  t h e  h e l i c a l  waves go over i n t o  ordinary 
ion  acous t i c  waves. 
experimental observat ions.  
The presence of t h i s  type of wave i s  borne out  by two 
1. A spontaneous o s c i l l a t i o n  was observed which had s t a b i l i t y  l i m i t s  
c lo se  t o  those  pred ic ted  by Fried and !:rang. (See Fig. 3 ) .  A t  a beam t o  
plasma dens i ty  r a t i o  of .27 and abeam ve loc i ty  of 2.6  a. (a. is t h e  plasma 
ion  thermal ve loc i ty ) ,  t he re  were no o s c i l l a t i o n s  i n  t h e  plasma. 
ve loc i ty  was increased an o s c i l l a t i o n  appeared with a frequency of Z 20 Kc. 
The amplitude of t h e  o s c i l l a t i o n  increased with increas ing  beam ve loc i ty  u n t i l  
a beam ve loc i ty  of 4.a 
s u l t e d  i n  a decrease of the  o s c i l l a t i o n  amplitude. 
5.2ai t h e  o s c i l l a t i o n  amplitude had returned t o  zero. The f a c t  t h a t  t h e  
o s c i l l a t i o n -  had a maximum amplitude a t  beam v e l o c i t i e s  s l i g h t l y  g r e a t e r  than 
the  phase ve loc i ty  of an ion  acous t ic  wave ind ica t e s  t h a t  t he  i n s t a b i l i t y  i s  
caused by a resonance of  t h e  beam p a r t i c l e s  with t h e  ion acous t i c  wave. 
t h e  beam ve loc i ty  i s  increased the p a r t i c l e s  go out  of resonance with t h e  wave 
and the  o s c i l l a t i o n  disappears.  
1 1  
A s  t h e  beam 
was reached. Further  increase  i n  beam ve loc i ty  re- i 
A t  a beam ve loc i ty  of 
A s  
The o s c i l l a t i o n  was detected by a p lanar  g r i d  s i t u a t e d  perpendicular  
t o  t h e  magnetic f i e l d  and beam di rec t ion .  
showed t h a t  t h e  o s c i l l a t i o n  amplitude was maximum i n  the  cen te r  o f  t h e  plasma 
column. This i nd ica t e s  a wave propagating along the  magnetic f i e l d .  
on t h e  edge of the  plasma, where t h e r e  were l a rge  dens i ty  grad ien ts ,  phase 
measurements showed t h a t  the  o s c i l l a t i o n  had an azimuthal component. This 
i n d i c a t e s  a h e l i c a l  type wave or  two uncoupled waves-- an a x i a l  wave i n  the  
c e n t e r  of t h e  plasma and an azi:.iuthal wave on the  edge. 
p4easurements with a small probe 
Also, 
- 4 -  
2.  Phase measurement of a similar o s c i l l a t i o n  under s l i g h t l y  d i f f -  
e r e n t  condi t ions gave another ind ica t ion  of t h e  presence of a azimuthal 
wave. 
s i t u a t e d  i n  a common a x i a l  plane but  with a 90' azimuthal angle between 
them (see Fig. 4) .  
t h e  phase d i f fe rence  between t h e  two probes changes smoothly. 
cates t h a t  t he  phase ve loc i ty  or  t h e  wave number of  t h e  azimuthal component 
i s  dependent on beam ve loc i ty  , 
The phase change of the  o s c i l l a t i o n  was measured between two probes 
As t he  beam ve loc i ty  is  increased  from 2.6a t o  8.ai, i 
This ind i -  
The two phenomena discussed above were observed on t h e  las t  day of  
opera t ion  and w i l l  be inves t iga ted  thoroughly i n  subsequent runs. 
IV. Damping of  Low Frequency Longitudinal ;;raves 
In order  t o  study the  a t tenuat ion  o f  ion waves i n  an ion  beam-plasma 
system, low frequency e l e c t r o s t a t i c  waves were exc i t ed  on a la rge  plane g r i d  
and received on a similar movable large plane g r i d  i n  a manner similar t o  
:;long, D'Angelo and rlotley. 6 
Attenuation and phase ve loc i ty  measurements were made for various 
values  of beam v e l o c i t y  and bean t o  plasma dens i ty  r a t i o .  
rate is  less than f o r  ion acoust ic  waves i n  a plasma with no beam. 
Fig.  5). 
i nve r se ly  with the  r a t i o  of beam dens i ty  t o  plasma dens i ty ,  
i n  terms of t h e  dimensionless parameter Z = - the  a t tenuat ion  rate is 
i 
independent of frequency. 
t h e  waves were e s s e n t i a l l y  undamped. 
follows. There i s  an instantaneous conduction s i g n a l  between the  e x c i t i n g  
The a t tenuat ion  
(See 
c8a.)  t he  a t t enua t ion  rate va r i e s  For low bean ve loc i ty  (Vbeam 
1 
When p l o t t e d  
w x 
a 
(See Fig. 5) .  For high beam v e l o c i t i e s  (V beam '12ai) 
The explanat ion of t h i s  may be as 
- 5 -  
g r i d  and the  receiving gr id .  
propagated wave the  t i n e  between the  end of the  e x c i t a t i o n  and t k e  end o f  
t he  received propagations must be g r e a t e r  than the  time of a h a l f  cycle. 
Since the  phase ve loc i ty  of  these  waves is high t h e  two g r ids  must be  far  
apa r t  t o  s ee  a h a l f  cycle  d i f fe rence  between the  two s i g n a l s .  A t  these  
d is tances  we would expect t o  see the  "electron contr ibut ion" t o  the  ion 
acous t i c  wave. 
In  order  t o  measure the  amplitude of  t he  
This wave is very slowly damped. 
The phase ve loc i ty  of t h e  wave depends s t rong ly  on the  beam ve loc i ty .  
The dependence on dens i ty  is small. 
t h e  beam ve loc i ty  and increases  with increas ing  beam ve loc i ty .  
erence between phase ve loc i ty  and beam ve loc i ty  a l s o  increases  with in-  
c reas ing  beam ve loc i ty .  If the  wave w 8 s  an ion acous t i c  wave t r ave l ing  
backwards i n  the  beam, the  phase ve loc i ty  i n  the  lab frame would be l e s s  
than t h e  beam ve loc i ty ,  as  observed, bu t  the  d i f f e rence  between the  two 
would remain constant,  This i s  cont ra ry  t o  observation. The observed 
dependence o f  phase ve loc i ty  on beam ve loc i ty  ind ica t e s  t he  wave is  t r ave l -  
i n g  i n  the  combined beam plasma system. 
The phase ve loc i ty  i s  always less than 
The d i f f -  
V. :.ii crowave Detect ion  System 
A microwave de tec t ion  system was used i n  p lace  of  t he  receiving g r i d  
t o  measure the  amplitude o f  t h e  waves. The r e s u l t s  were e s s e n t i a l l y  the  
same as t h e  g r i d  de t ec t ion  system. One d i f f i c u l t y  encountered i n  using the  
microwave system was t h a t  a s ing le  measurement took s o  long t h a t  t h e  plasma 
parameters would change over the course of a s e r i e s  o f  measurements, thus  
l i m i t i n g  the usefulness  of t he  microwave system. The microwave system was 
. 
- 6 -  
a l s o  used i n  an attempt t o  detect  t h e  response o f  t he  bean-plasma t o  o s c i l -  
l a t i o n s  exc i ted  a t  amplitudes approximating those of thermal f luc tua t ions .  
140 conclusive r e s u l t s  were obtained. 
V I .  Noise Spectrum of  Beam-Plasma System -
Observations were made of the frequency spectrum of  the  plasma with 
and without t he  beam, and f o r  severa l  beam v e l o c i t i e s .  
quencies examined was from 0 t o  4 Xllz. 
not iceable  d i f f e rence  i n  noise  spectrum i n  t h i s  range. 
"lie range of fre- 
The presence of t h e  beam made no 
VII. Computer Program 
A computer program is being w r i t t e n  t o  ca l cu la t e  t he  s p a t i a l  behavior 
A method similar t o  o f  the  amplitude and t h e  phase of  t he  wave p o t e n t i a l .  
t h a t  descr ibed by Gould4 
i n  the  numerical i n t eg ra t ion  of t h e  inverse  Fourier  transform 
f a c t  t h a t  t he  d ispers ion  r e l a t i o n  va r i e s  r ap id ly  with wave number. 
r e s u l t s  give phase v e l o c i t i e s  which agree approximately with experiment. 
lfowever t h e  computer r e s u l t s  for  amplitude v a r i a t i o n  is  considerably d i f f -  
e r e n t  from t h a t  obtained by experiment. 
reasons.  
is being used. D i f f i c u l t i e s  have been encountered 
due t o  the  
Present 
Tnis may be  due t o  a number of  
1. 
2. 
3.  Col l i s iona l  e f f e c t s  (not accounted f o r  i n  theory) .  
; lagnetic f i e l d  and dens i ty  gradient  e f f e c t s .  
Boundary e f f e c t s  a t  g r i d  and a t  ends of plasma columns. 
- 7 -  
VIII. Future 1:ork -
Further  experimental work i s  necessary t o  determine t h e  c h a r a c t e r i s t i c s  
o f  t h e  uns tab le  wave. Phase measurements w i l l  be macle t o  determine i f  t h e  
Nave i s  h e l i c a l  o r  is two separa te  waves, one i n  t h e  c e n t e r  of the  plasma 
and one on the  edge. S t a b i l i t y  limits w i l l  be determined and t h e  amplitude 
and frequency dependence on t h e  various system parameters w i l l  be measured. 
Concurrently w i t h  t h i s  experimental work, a t h e o r e t i c a l  ana lys i s  of the  
complete d ispers ion  r e l a t i o n  will continue, including dens i ty  grad ien t  and 
magnetic f i e l d  e f f e c t s .  Solutions will be obtained i n  the asymptotic l i m i t s  
o f  t he  various system parameters. Subsequent t o  t h e  results obtained i n  t h e  
asymptotic l i m i t s  a numerical so lu t ion  of the  exact  d i spers ion  r e l a t i o n  w i l l  
be obtained e i t h e r  on the  UCLA on-l ine computer f a c i l i t y  o r  by a Fortran 
program wr i t t en  f o r  t he  UCLA I311 7094. 
Other experimental work considered f o r  t he  fu tu re :  
1. 
2. 
3.  
4 .  
Effec t  of an ion beam on t h e  damping o f  azimuthal d r i f t  waves i n  
a plasma w i t h  dens i ty  gradients  i n  a magnetic f i e l d .  
Inves t iga t ion  of  t he  e f f e c t  of  an ion  beam on t h e  noise  spectrum 
o f  a plasma. 
Yegahert z range. 
He w i l l  extend the  observed spectrum i n t o  t h e  10 
Inves t iga t ion  of the  electron-ion wave predic ted  by Ohnuma and 
Hat ta  8 f o r  high ve loc i ty  ion beams. 
Continued inves t iga t ion  of a t tenuat ion  of  ion acous t ic  waves i n  
a s t a b l e  beam-plasma systeci. 
References 
1. 11. D’Angelo and 14. Rynn, Phys. Fluids  4, 1303 (1961). -
2. J. PI. Se l len ,  Jr , ,  I J .  Dernstein and R. F. Kemp, Rev. o f  Sc i .  I n s t r .  36, -
(1965) . 
3. B. Fr ied  and A. Y. \;long: S t a b i l i t y  L i m i t s  f o r  Longitudinal IVaves i n  Ion 
Uean-Plasma In te rac t ion ,  Physics of Fluids  9,  p. 1084, June 1966. 
4. L. Enriques: On t h e  In t e rac t ion  of an Ion Beam with a Plasma. Matt-366 
Plasnia Physics Lab. Princeton Universi ty  Sept . 1965. 
5. iz. B. Kadomtsev, Soviet  Phys. JETP Vole 16 1191 (1963). -’ 
6. A. Y. ;long, N. D’Angelo and R. f lotley: Phys. Rev. 133 A436, (1964). -’ 
7 .  R. Gould: Exci ta t ion  of Ion-Acoustic ;Javes: Phys. Rev. Vol. 136 U4A 
16, Nov. 1964. 
8. T. Ohnuma and Y. iiatta: I n s t a b i l i t y  i n  Three Component Plasma System, 
Physics of Fluids  E, p. 1422 J u l y  1966. 
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A 50kc 
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Fig. 5 , -  Dahping of Longitudinal \\rave VS. -Longitudinal Distance *- 


Interaction Between Ion Beams and Plasmas

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