Electron beam compression with electrostatic and magnetostatic field

Johnson, C. C.

Talbot, K. I.

English

NASA Technical Reports Server

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ELECTRON BEAM COMPRESSION WITH 
ELECTRIC AND MAGNETIC FIELDS 
\ 
K .  I .  T a l b o t  
and 
C .  C .  Johnson 
GPO PRICE $ 
CFSTI PRICEIS)  $ 
Microfiche (MF) 39 - 
f f653 July65 
MICROWAVE DEVICE AND PHYSICAL ELECTRONICS LABORATORY 
ELECTRICAL ENGINEERING DEPARTMENT 
UNIVERSITY OF UTAH 
Salt L a k e  C i t y ,  U t a h  
A u g u s t  1964 
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INTRODUCTION 
Elec t ron  beams a r e  v e r y  important  i n  microwave devices such a s  
a m p l i f i e r s  and o s c i l l a t o r s ,  i n  radar  and communication equipment, plasma 
i n t e r a c t i o n  d e v i c e s ,  micro-welding dev ices  f o r  welding small p a r t s ,  and 
i n  h igh  power e l e c t r o n  tubes .  
a p p l i c a t i o n s ,  e l e c t r o n  beams with smal l  d iameters  and l a r g e  c u r r e n t  and 
power d e n s i t i e s  a r e  r equ i r ed .  
duced by a compression mechanism employing both e l e c t r o s t a t i c  and magne- 
t i c  f i e l d s ,  Th i s  paper p r e s e n t s  des ign  and t e s t  in format ion  on a 
c y l i n d r i c a l l y  focused beam wi th  a c u r r e n t  d e n s i t y  o f  2000 amps/cm2. The 
beam en t r ance  cond i t ions  and t h e  magnetic f i e l d  i n t e n s i t y  a t  t h e  ca thode  
a r e  c r i t i c a l  parameters  i n  t h e  gun des ign .  Under proper  c o n d i t i o n s ,  t h e  
beam produced i s  w e l l  focused with l i t t l e  r i p p l e .  
For microwave dev ice  and micro-welding 
Elec t ron  beams o f  t h i s  type  may be pro-  
ANALYSIS 
1 
The beam compression system c o n s i s t s  o f  an e l e c t r o s t a t i c a l l y  con- ..- v ~ r g 2 i i t  e l e c t r m  gux with  E! subsequent magnetic compression r eg ion  a s  
shown i n  F i g .  1. The magnetic f i e l d  i n  t h e  t r a n s i s t i o n  r eg ion  0 < z < R 
i sassumed t o  be  
- Bk 
2 - cos  ?)+ Bk B =  z 
I n  t h e  r e g i o n  x > R ,  B 
n e t i c  f i e l d  i s  assumed: B 
= Bo,  and i n  t h e  r eg ion  z < 0 ,  a cons t an t  mag- 
i s  t h e  ca thode  f l u x  d e n s i t y .  = Bk, where B 
Z k 
The beam r o t a t e s  as it  e n t e r s  t h e  t r a n s i t i o n  r eg ion  because f l u x  
is cut during the e l e c t r o s t a t i c  compression process .  The angular  v e l o c i t y  
o f  t h e  beam i n  t h e  t r a n s i t i o n  reg ion  i s  given by Busch's theorem 
t t h e  c where B i s  t h e  f l u x  d e n s i t y  a t  z = 0,  and r i k k t h e  r d i u s  th 
I 
L.  Kikushima and c .  C .  Johnson, "A High Current  Dens i ty  B r i l l o u i n  
Focused E lec t ron  Beam," Proceedings --- o f  t h e  IEEE , Vol.  52 ,  January 
1964, pp. 82-83. 
d e .  
..4 1 
Convergent 
/- gun 
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B z 
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Focused beam 
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F i g .  1. Electron beam compression system. 
- 2 -  
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. a  1 .  
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Bnce t h e  angular  v e l o c i t y  i s  known, t h e  equat ions  sf metion fo r  t h e  
edge e l e c t r o n  may be w r i t t e n  i n  a convenient  ferm. 
equat ions  of  motion a r e  
The normalized 
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whar e 
2 4  
k k l  
3 
2aB r 
B r  0 
+ 2 4  
0 0  
I"' 2 Bk rk  1 
0 
- 
2 2 + i; + c o s  5) - 
Bo ro ! 0' 
E 
u - r l r  
r = f i n a l  beam rad ius  
Z = xz / ro  
0 
0 
T = nu t lr  
0 0  
u = a x i a l  beam v e l o c i t y  
0 
n 
U) = beam plasma frequency 
P 
- 3 -  
The above equat ions were programmed f o r  an I B M  1620 computer u s ing  
Figure 2 shows some t r a j e c t o r y  p l o t s  f o r  t h e  o u t e r  e l e c t r o n  f e r  v a r i o u s  
va lues  o f  cathode f l u x .  
and t h e s e  curves show t h a t  the cathode must be w e l l  shielded t o  o b t a i n  
a near  -Br i l l o u i n  beam. 
t h e  Runge-Kutta-Gill method. The va lue  of perveance used was 2.4 x 10- 6 . 
The f i n a l  magnetic f i e l d  Bo i s  7,500 gauss ,  
F igu re  3 shows a p l o t  of 28/u where LU = e B  / m  i s  t he  e l e c t r o n  
C Y  cyc lo t ron  frequency. 
of design curves g iv ing  the  required en t r ance  s l o p e  and r a d i u s  f o r  a 
smoothly focused beam. 
The computer r e s u l t s  wzre usgd t o  formulate a se t  
The equa t ions  o f  motion have been modified t o  account f o r  i n i t i a l  
thermal v e l o c i t i e s  a t  t h e  cathode. 
t h e  equat ions in  t h e  same way the cathode f l u x  term does.  Curves have 
been published2 which g i v e  t h e  per c e n t  of charge l y i n g  o u t s i d e  a given 
r a d i u s  f o r  a given beam v o l t a g e ,  c u r r e n t ,  and temperature .  For a t y p i -  
c a l  case of 1OOO:l convergence, 30 per c e n t  of t h e  beam c u r r e n t  l i e s  o u t -  
s i d e  of t h e  Bri l louin-focused diameter.  
The thermal v e l o c i t y  terms appear i n  
EXPERIMENTAL RESULTS 
A high perveance and high area compression e l e c t r o n  gun designed 
by F r o s t ,  P u r l ,  and Johnson3 was s e l e c t e d  f o r  u s e  i n  t h e  magneto-electr ic  
compression system. Beam perveance and p r o f i l e  measurements were made 
on t h e  new gun i n  a demountable beam t e s t e r .  I n  o rde r  t o  make tes t s  i n  
a so leno id ,  a hard tube wi th  an i n t e r n a l  po le  p i ece  was designed from 
t h e  curves obtained i n  t h e  computer s tudy .  The tube was designed t o  
o p e r a t e  a t  10 kv and 2 . 4  amps with a f i n a l  beam diameter of .0136 inches 
i n  a magnetic f i e l d  o f  7,500 gauss.  
The f i r s t  beam t e s t e r  was operated with t h e  beam impinging d i r e c t l y  
on a f l a t  copper c o l l e c t o r .  A measure of t h e  beam diameter was achieved 
The e ros ion  p a t t e r n  was s l i g h t l y  sma l l e r  than t h e  .0136 inch diameter 
c a l c u l a t e d  v a l u e ,  bu t  t h i s  was probably due t o  t h e  dec rease  i n  c u r r e n t  
d e n s i t y  near t h e  beam edges.  
L _ _  uy 1ilea.iiriiig t h e  erosiori pattzrr ;  G;; t h e  c o l l c c t c x  9s s h n m  c32 Fig. 4 .  
A second t e s t  was conducted i n  which t h e  beam was allowed t o  burn 
J. R .  P i e r c e  and L.  R .  Walker, I' ' B r i l l o u i n  Flow' with Thermal V e l o c i t i e s , "  2 
J o u r n a l  of Applied Phys ic s ,  Vol. 2 4 ,  p. 1328. 
R. D .  F r o s t ,  0. T.  P u r l ,  and H.  R .  Johnson, "Electron Guns f o r  Forming 
So l id  B e a m s  of High Perveance and High Convergence," Proc.  I.R.E., --
V O ~ .  56 ,  August 1962, p p .  1800-07. 
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Fig. 4 .  Beam impression on a flat copper collector. The 
theoretically calculated beam diameter of 13.6 mills 
is shown. 
- 7 -  
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4 4 '  
h o l e s  through a s t a c k  of t h i n  carbon-paper f o i l s .  Four f o i l s  made of 
carbon paper were placed i n  t h e  tube perpendicular  t o  t h e  beam a x i s  
I and between t h e  e l e c t r o n  gun and t h e  f i n a l  c o l l e c t o r .  The beam burned 
ho le s  i n  the  four  carbon f o i l s  of diameters  .028,  .024,  ,024,  and .023 
i nches .  
Some experimental  r e s u l t s  by Brewer' have ind ica t ed  t h a t  t h e  
l 
Pierce-Walker t heo ry  f o r  thermal spreading e f f e c t s  i n  e l e c t r o n  beams 
i s  f a i r l y  a c c u r a t e  up t o  about 95 per c e n t  of t h e  enclosed beam c u r r e n t .  
The Pierce-Walker curve i s  shown i n  F i g .  5 as t h e  s o l i d  cu rve ,  and t h e  
Brewer experimental  curve as t h e  dashed curve.  The v e r t i c a l  a x i s  i s  
t h e  normalized c u r r e n t  o u t s i d e  a given r a d i u s .  
l i n e  i n  F i g .  5 r e p r e s e n t s  0.024 inches,  t h e  experimental ly  determined 
beam d iame te r .  C a l c u l a t i o n s  o f  the  carbon f o i l  temperature  from i n f o r -  
mation given by t h e  Pierce-Walker curve shows t h a t  t h e  v a p o r i z a t i o n  
temperature  of carbon paper would n o t  b e  reached.  I f  t h e  Brewer curve 
i s  used f o r  t h e  c a l c u l a t i o n ,  t h e  c a l c u l a t e d  temperature a t  t h e  edge 
of t h e  h o l e  i s  near t h e  vapor i za t ion  temperature .  Th i s  experiment shows 
t h a t  t h e  beam i s  f a i r l y  w e l l  focused a t  t h e  expected d i ame te r ,  and tends 
t o  v e r i f y  t h e  Brewer curve f o r  t h e  thermal t a i l .  
The v e r t i c a l  do t t ed  
A combined e l e c t r o s t a t i c  and magne tos t a t i c  compression system 
may be employed t o  y i e l d  e l e c t r o n  beams of very small d i ame te r s  and 
v e r y  l a r g e  c u r r e n t  and power d e n s i t i e s .  Ana ly t i ca l  r e s u l t s  have been 
obtained which g i v e  design curves f o r  a minimum-ripple beam. 
of small design e r r o r s  i n  i n i t i a l  beam s l o p e  and r a d i u s  have been in -  
v e s t i g a t e d ,  a s  we l l  as e f f e c t s  due t o  thermal v e l o c i t i e s  and cathode 
f l u x .  
The e f f e c t s  
-6 
Experimental r e s u l t s  have been obtained on a perveance 2.4 x 10 
beam o p e r a t i n g  a t  10 kv. A f i n a l  beam diameter of  .013 inches was 
obtained i n  a magnetic f i e l d  of 7,500 gauss .  An a r e a  compression of 
1350: l  was obtained with a f i n a l  c u r r e n t  d e n s i t y  of 2,000 amps p e r  square 
c e n t i m e t e r .  The beam s i z e  was detected by copper c o l l e c t o r  e ros ion  
p a t t e r n s  and ho le s  burned i n  carbon-paper d i s c s .  
George R .  Brewer, "Some C h a r a c t e r i s t i c s  of a Magnet ical ly  Focused 4 
Elec t ron  Beam," J o u r n a l  of Applied Phys ic s ,  Vo l .  30,  p .  1330. 
- 8 -  
. 
Fig .  5 .  P l o t  o f  t h e  normalized c u r r e n t  o u t s i d e  a given normalized 
rad i u s .  
- 9 -  


Electron beam compression with electric and magnetic fields

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