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REACtOR PHYSICS DEPMTMWT '
ADVANCED OPERATIONAL P W W G -: .- I . '
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BNWL- 452
U C - 3 4 , P h y s i c s
R E L A T I V I S T I C I O N I N E L E C T R O M A G N E T I C WAVE
( B A T T E L L E - N O R T H W E S T P R O G R A M ORBIT )
Berna rd H . Duane
T h e o r e t i c a l P h y s i c s Un i t R e a c t o r P h y s i c s Department
J u n e , 1 9 6 7
PAC1 F I C NORTHWEST LABORATORY . RICHLAND, WASHINGTON
BNWL- 452
P r i n t e d i n t h e Uni t ed S t a t e s of America A v a i l a b l e from
Clea r inghouse f o r F,ederal S c i e n t i f i c and T e c h n i c a l I n f o r m a t i o n N a t i o n a l Bureau of S t a n d a r d s , U. S . Department o f Commerce
S p r i n g f i e l d , V i r g i n i a 22151 P r i c e : P r i n t e d Copy $ 3 . 0 0 ; M i c r o f i c h e $0 .65 I
iii BNWL- 452
T A B L E OF C O N T E N T S
ABSTRACT . . . . . . . . . . . . . 1
VATHEMATI CAL PHY S I CS . . . . . . . . . 2
Equa t ions o f Motion . . . . . . . 2
F i r s t I n t e g r a l s . . . . . . . . . 2
Second I n t e g r a l s . . . . . . . . 5
Bremss t r ah lung I n t e g r a l . . . . . . 6
P u l s e d Wave T r a i n s . . . . . . . . 7
Maximum Energy . . . . . . . . . 7
Mean Energy . . . . . . . . . . 11
NUMEKICS . . . . . . . . . . . . . 13
Computation Logic . . . . . . . . 13
P l o t Logic . . . . . . . . . . 14
. . . . . . . ION ORBITS IN LASER BEAMS 15
. . . . . . . Proposed Experiment 15
. . . . . . T h e o r e t i c a l P r e d i c t i o n s 1 7
. . . . . . . Proposed Measurements 23
. . . . . . . . . . ACKNOWLEDGEMENTS 23
. . . . . . . . . . . . REFERENCES 23
APPENDIX: BITS . . . . . . . . . . A-1
B N W L - 4 5 2
R E L A T I V I S T I C I O N I N E L E C T R O M A G N E T I C W A V E
( B A T T E L L E - N O R T H W E S T P R O G R A M O R B I T )
B e r n a r d H . D u a n e
A B S T R A C T
B a t t e l l e - N o r t h w e s t program O r b i t c o n s t r u c t s and p l o t s
e i g h t - d i m e n s i o n a l p h a s e - s p a c e o r b i t s f o r a r e l a t i v i s t i c
cha rged p a r t i c l e d r i v e n by an e l e c t r o m a g n e t i c p l a n e wave.
M A T H E M A T I C A L P H Y S I C S
E O U A T I O N S O F M O T I O N
C o n s i d e r t h e r e l a t i v i s t i c mo t ion o f a c h a r g e d p a r t i c l e
d r i v e n by an e l e c t r o m a g n e t i c p l a n e wave, a s i l l u s t r a t e d i n
F i g u r e 1. I n t h e f o u r - d i m e n s i o n a l s p a c e - t i m e o f s p e c i a l
r e l a t i v i t y ( ' ) s p a n n e d by t h e l i n e e l e m e n t
2 2 2 2 2 d s = dx + dy2 + d z 2 + ( d i c t ) = - c d r , ( 1 )
a c h a r g e q h a v i n g r e s t e n e r g y mc2 i s a t f o u r - p o s i t i o n - X
= (x y z i c t ) w i t h four-momentum P = (p, p p Z i E / c ) = m dX/dr - Y - a t p r o p e r t i m e T . The e l e c t r o m a g n e t i c p o t e n t i a l - m o m e n t u m f i e l d
h a s p r o p a g a t i o n v e c t o r K - = ( 0 0 k i w / c ) , a m p l i t u d e - A =
(A 0 0 O) , and p h a s e K - X = kz - w t . The p r o p a g a t i o n v e c t o r - - h a s n u l l m a g n i t u d e and i s p e r p e n d i c u l a r t o t h e wave a m p l i t u d e .
K . K = 0 = k 2 - w 2 / c 2 , and K - A = 0 . - - - - The m a g n e t i c f o r c e f i e l d [ B = kA s i n ( o t - k z ) ] and t h e e l e c -
Y t r i c f o r c e f i e l d [Ex = wA s i n ( u t - k z ) ] a p p e a r r e s p e c t i v e l y
a s t h e s p a c e - l i k e (B) - and t i m e - l i k e ( E / i c ) - components o f t h e
po t en t i a l -momen tum c u r l ,
(A - - K - K A) s i n ( K 0 X ) . - - - - ( 4 )
I n t h i s r e p r e s e n t a t i o n , E i n s t e i n ' s e q u a t i o n s o f mo t ion t a k e
t h e fo rm
F I R S T I N T E G R A L S
C o n t r a c t i n g t h i s e q u a t i o n o f mo t ion upon t h e p r o p a g a t i o n
v e c t o r - K w i t h t h e h e l p o f E q u a t i o n ( 3 ) y i e l d s t h e p h a s e
i n t e g r a l
BNWL- 452
X - = (x Y Z i c t ) , - P = ( p x Py P Z i E / c ) , A = ( A 0 0 O ) , K = ( 0 0 k i u / c ) - -
2 2 2 2 d s 2 = dx + d y 2 + d z 2 + ( d i c t ) = - c d i
d P / d ~ - = ( q / m ) (K A - A K) . P f' (K-X) - - - - - - -
Matrix-Ex~onential Solution
F I G U R E 1
ION IN E L E C T R O M A G N E T I C W A V E
With t h e h e l p o f t h i s p h a s e i n t e g r a l , t h e e q u a t i o n s o f mot ion
( 5 ) now i n t e g r a t e by i n s p e c t i o n t o t h e m a t r i x - e x p o n e n t i a l
s o l u t i o n
The m a t r i x power s e r i e s d e f i n i n g t h e m a t r i x e x p o n e n t i a l f u n c -
t i o n t e r m i n a t e s h e r e w i t h i t s s e c o n d - o r d e r t e r m , s i n c e f rom
E q u a t i o n (3)
The c o m p l e t e f i r s t i n t e g r a l , E q u a t i o n ( 7 ) , t h u s s i m p l i f i e s t o
i t s low o r d e r t e r m s ,
T r a n s l a t e d back i n t o t h r e e - s p a c e l anguage and a r r a n g e d
a s a n u m e r i c c o m p u t a t i o n s e q u e n c e , E q u a t i o n s ( 6 ) and ( 9 )
b e come
Program O r b i t c o n s t r u c t s t h e f i r s t i n t e g r a l s a s a f u n c t i o n of
p r o p e r t i m e T by d i r e c t e v a l u a t i o n o f t h e f o u r boxed e q u a t i o n s .
5
S E C O N D I N T E G R A L S
' 4 u l t i p l y i n g t h e momentum i n t e g r a l , E q u a t i o n (9), by dr /m
and i n t e g r a t i n g w i t h t h e h e l p o f t h e p h a s e i n t e g r a l , E q u a t i o n
( 6 ) , now g i v e s f o r t h e o r b i t e q u a t i o n s ,
2 - - K - u - C O S ( K - u 1 - ( ~ / z ) ( ~ A / K . P ) 2 j ~ . 1 [ 1 / 2 + cos ( I ( - x ) I - -0 - - 0 - - - -0
T r a n s l a t e d back i n t o t h r e e - s p a c e l a n g u a g e and a r r a n g e d a s a
n u m e r i c c o m p u t a t i o n s e q u e n c e , t h e s e o r b i t e q u a t i o n s become
6 BNWL- 4 5 2
Program O r b i t c o n s t r u c t s t h e second i n t e g r a l s a s a f u n c t i o n
of p r o p e r t ime T by d i r e c t e v a l u a t i o n of t h e s e boxed e q u a t i o n s
( d i v i d e d by 2 n t o s i m p l i f y phase r e c o g n i t i o n ) .
B R E M S S T R A H L U N G I N T E G R A L
An a c c e l e r a t e d charge r a d i a t e s energy from i t s r e s t frame
a t t h e p r o p e r t ime r a t e (2 )
2 d E y / d ~ = (u0c/6n) (qdP/mcdr) - , (20)
where uoc i s t h e impedance o f f r e e space (377 ohms). Making
u s e o f E q u a t i o n s ( 5 ) , ( 6 ) , and (8) r educes t h i s e x p r e s s i o n t o
2 - - K A).(P/m) - - s i n ( K . X ) - - d ~ ,
2 2 2 = (uoq /6nm) (qA/mc) (P/mc) - .K - - K O (P/m) - s i n (K-X) - - dr ,
2 2 2 = (pOq /6nm)(qA/mc) (K-P /mc) s i n (KeX) d(K.X). (21) - -0 - - - -
The r a d i a t i v e ene rgy E t h u s i n t e g r a t e s t o Y
T r a n s l a t e d back i n t o t h r e e - s p a c e language and a r r a n g e d f o r
numer ic e v a l u a t i o n a s a f u n c t i o n of p r o p e r t ime T , t h i s
i n t e g r a t e d "Beschleunigungss t r a h l u n g " energy becomes
2 where ro = il q /4nm i s t h e "charge r a d i u s " d e f i n e d c l a s s i c a l l y * 0
by e q u a t i n g i t s r e s t ene rgy mcZ t o i t s e l e c t r o s t a t i c ene rgy
q2 /4nc o r 0'
- * = (2.81785 * 0.00004) x 10 - 1 5
For an e . l e c t r o n , ro m .
P U L S E D W A V E T R A I N S -
The p r e c e d i n g m a t r i x - e x p o n e n t i a l a n a l y t i c s o l u t i o n f o r
t h e r e l a t i v i s t i c mo t ion o f an i o n d r i v e n by an e l e c t r o m a g n e t i c
wave e v o l v e d a s a r e c e n t s p i n - o f f o f some 25 y e a r s o f mathe-
m a t i c a l p h y s i c s work a t I Ianford on a f a r more i n t r i c a t e
p rob l em h a v i n g somewhat s i m i l a r m a t h e m a t i c a l s t r u c t u r e
( n u c l e a r t r a n s m u t a t i o n t h e o r y ( 3 ) ) . C o n v e r s e l y , t h e domain o f
a p p l i c a b i l i t y o f t h e s e m a t r i x - e x p o n e n t i a l i o n o r b i t s a p p e a r s
t o e x t e n d c o n s i d e r a b l y beyond t h i s f i r s t a p p l i c a t i o n , and
c e r t a i n l y i n c l u d e s i o n s d r i v e n by p u l s e d p l ane -wave t r a i n s
o f q u i t e a r b i t r a r y p u l s e s h a p e . The l e g e n d o f F i g u r e 1 d i s -
p l a y s t h i s p u l s e d wave s o l u t i o n e x p l i c i t l y , and i t can b e
e x p e c t e d t o become a v a i l a b l e i n p rogram O r l ~ i t a s t h e n e e d
a r i s e s .
M A X I M U M E N E R G Y
Ana lyz ing t h e momentum i n t e g r a l s f o r maximum a t t a i n a b l e
e n e r g y l e a d s t o combin ing E q u a t i o n s ( 1 2 ) and (13 ) i n t h e
form
2 2 2 0 ~ / m c ~ = ~ ' / m c ~ + (1/2) [ (px /mc) - (p:/mc) ] / ( ~ O / m c - p Z / m c ) . ( 24 )
Along any o r b i t , maximum e n e r g y ~ / m c ~ t h u s c o r r e s p o n d s t o
maximum x-momentum magn i tude I p /mc l . From E q u a t i o n (10 ) i t X
c an b e s e e n t h a t px/mc o s c i l l a t e s be tween t h e l i m i t s
and t h u s r e a c h e s a maximum magn i tude o f
0 I P , / ~ C l m a x = Ip,/mc + (qA/mc) cos (wto - kzo ) 1 + /qA/mc 1 . ( 2 5 )
With r e s p e c t t o v a r i a t i o n of i n i t i a l t i m e - p h a s e w t o , t h i s
e x p r e s s i o n maximizes a t
8 BNWL- 452
where t h e p r o g r e s s i v e c a p i t a l i z a t i o n (from max t o Max) r e f e r s
t o f u r t h e r max imiza t ion . The c o r r e s p o n d i n g maximum e n e r g y ,
Equa t ion ( 2 4 ) , becomes
F u r t h e r max imiza t ion w i t h r e s p e c t t o v a r i a t i o n of t h e
i n i t i a l momentum d i r e c t i o n i s c o n s i d e r a b l y s i m p l i f i e d by s h i f t -
i n g t h e r e p r e s e n t a t i o n t o four-momentum-space p o l a r c o o r d i n a t e s ,
a s d e f i n e d by
The m o t i v a t i o n f o r t h i s s h i f t , o f c o u r s e , i s t o impose t h e
r a d i a l c o n s t r a i n t .
upon t h e momentum v a r i a t i o n s . I n t h i s r e p r e s e n t a t i o n , t h e
maximum e n e r g y , Equa t ion (27), t a k e s t h e form
With r e s p e c t t o v a r i a t i o n o f t h e a z i m u t h a l momentum a n g l e
$ 0 , t h i s e x p r e s s i o n maximizes a t
- s i n h e o C O S + ~ ) , (34)
where f u r t h e r c a p i t a l i z a t i o n ("lax t o MAX) r e f e r s t o f u r t h e r
max imiza t ion .
9 BNWL- 452
D i f f e r e n t i a t i n g t h i s e x p r e s s i o n t o l o c a t e i t s maximum
w i t h r e s p e c t t o v a r i a t i o n of t h e i n i t i a l - m o m e n t u m p o l a r a n g l e
$ 0 ' and t h e n maneuve r ing t o s o l v e f o r $ , y i e l d s s e q u e n t i a l l y , 0
c o s h e o C O S $ ~ - IqA/mcl s i n $ = s i n h e o , 0
- 1 2 cos [$o + t a n ( /qA/mcl s e c h e o ) ] - ( s i n h e )/[cash e o 0
2 1 / 2 + (qA/mc) I y
- 1 - 1 $0 + t a n ( I q ~ / m c s e c h e o ) = t a n ( [ I + (qA/mc) ] c s c h e o ) ,
t a n $ = { [ l + (qA/mc) ] 0
c o s h e o
The s t r u c t u r e h e r e s u g g e s t s s e t t i n g
2 1 / 2 I qA/rnc 1 = s i n h a , [ l + (qA/mc) ] = c o s h a ,
which l e a d s t o t h e f u r t h e r s i m p l i c a t i o n ,
t a n i o = ( c o s h e o cosha - s i n h e s i n h a ) / ( c o s h e s i n h e o 0 0
+ cosha s i n h a ) ,
= c o s h ( e o - a ) / [ s i n h ( o o + a) c o s h ( f ~ ~ - a ) ] ,
o r f i n a l l y ,
10 BNWL- 452
Second d i f f e r e n t i a t i o n o f E q u a t i o n (34) v i a s i m i l a r maneuvers
y i e l d s a n e g a t i v e s e c o n d d e r i v a t i v e ,
2 a cosheMAx/a"a $ o = - 2 ( s i n h e o s i n h a C S C $ ~ ) / ( c o s h e o
- s i n h e o C O S $ ~ ) ,
which e s t a b l i s h e s t h e e x t r e m a l E q u a t i o n (38) a s a maximum.
The c o r r e s p o n d i n g maximum e n e r g y , o b t a i n a b l e now by m e n t a l l y
s l i p p i n g t h e p o l a r a n g l e E q u a t i o n ( 3 8 ) i n t o E q u a t i o n (34) w i t h
t h e h e l p o f E q u a t i o n ( 3 5 ) , becomes
cos h e b l ~ ~ = c o s h e o + 2 s i n h a s i n h ( e o + a ) ,
= c o s h [ ( e o + a ) - a ] + 2 s i n h a s i n h ( e o + a ) ,
= c o s h ( e o + a ) cosha + s i n h ( e o + a ) s i n h a ,
o r
-1 0 2 E ~ ~ x /mc2 = cosh [ c o s h (E /mc ) + 2 s i n h - ' ( 1 q ~ / m c 1 ) ] , . where a g a i n f u r t h e r c a p i t a l i z a t i o n (MAX t o MAX) r e f e r s t o
f u r t h e r m a x i m i z a t i o n .
T h i s s i m p l e and u s e f u l e x p r e s s i o n , i n resum;, g i v e s t h e
maximum a t t a i n a b l e r e l a t i v i s t i c e n e r g y E !I AX f o r an i o n o f
r e s t e n e r g y mc2 and c h a r g e q d r i v e n by an e l e c t r o m a g n e t i c
p l a n e wave h a v i n g momen tum-po ten t i a l a m p l i t u d e A . To a t t a i n
t h i s t h e o r e t i c a l maximum, t h e p a r t i c l e must b e g i n i t s o r b i t
w i t h t h e l o c a l e l e c t r i c f i e l d p a s s i n g t h r o u g h z e r o , must
have i t s i n i t i a l momentum ( i f any) i n t h e p l a n e s w e p t o u t by
t h e t r a v e l i n g e l e c t r i c f i e l d and o r i e n t e d a t an a n g l e $ o , a s
g i v e n by E q u a t i o n ( 3 8 ) , f rom t h e p r o p a g a t i o n v e c t o r t oward
t h e r i s i n g e l e c t r i c f o r c e , and must r i d e t h e wave u n t i l i t h a s
s e e n h a l f ' a wave go b y .
The u l t r a - r e l a t i v i s t i c l i m i t f o r t h e o p t i m a l i n j e c t i o n
a n g l e , E q u a t i o n ( 3 8 ) , i s d i s p l a y e d more c l e a r l y by t h e
a l t e r n a t i v e form
The maximum-energy f u n c t i o n , E q u a t i o n ( 4 0 ) , c l e a r l y d i s p l a y s
t h e o r b i t p h y s i c s a s a L o r e n t z r o t a t i o n , and t h e form o f
E q u a t i o n (41 ) i s c o n v e n i e n t f o r s l i d e - r u l e work , b u t e l e c -
t r o n i c compu te r s p r e f e r t h e e q u i v a l e n t a l g e b r a i c mess
f o r b o t h a c c u r a c y and s p e e d .
M E A N E N E R G Y
For some a p p l i c a t i o n s , mean e n e r g y may p r o v i d e a more
i n f o r m a t i v e measure o f p e r f o r m a n c e t h a n t h e p r e c e d i n g maxi-
mum e n e r g y . h l e n t a l l y a v e r a g i n g t h e e n e r g y i n t e g r a l ,
E q u a t i o n ( 1 3 ) , o v e r i t s p r o p e r t i m e p e r i o d a l o n g an o r b i t ,
w i t h t h e h e l p o f t h e momentum i n t e g r a l s , E q u a t i o n s ( 1 2 ) and
( l o ) , y i e l d s
<E/mc2> = k0/mc2 + (qA/mc) { ( p i / m c ) c o s ( a t o - kzo )
2 2 + (l/Z)(qA/mc) [(1/2) + c o s (mto - h z 1 / (EO/mc
0
- p;/mc). ( 44 )
T h i s e x p r e s s i o n g i v e s t h e a v e r a g e r e l a t i v i s t i c e n e r g y a l o n g an
o r b i t .
1 2 BNWL- 452
Fo r a random d i s t r i b u t i o n o f i n i t i a l t i m e - p h a s e w t 0 '
f u r t h e r p h a s e a v e r a g i n g now p r o v i d e s
S h i f t i n g t o four-momentum s p h e r i c a l c o o r d i n a t e s t o f a c i l i -
t a t e f u r t h e r a v e r a g i n g o v e r a random d i s t r i b u t i o n o f i n i t i a l
three-momentum d i r e c t i o n s y i e l d s , f i n a l l y ,
T h i s e x p r e s s i o n , i n resum;, g i v e s t h e mean r e l a t i v i s t i c e n e r g y
c c < E > > > f o r i o n s o f r e s t e n e r g y mc2 and c h a r g e q d r i v e n by an
e l e c t r o m a g n e t i c p l a n e wave h a v i n g m o m e n t u m - p o t e n t i a l a m p l i t u d e
A , p r o p e r - t i m e a v e r a g e d a l o n g o r b i t s , and a v e r a g e d o v e r a
random d i s t r i b u t i o n o f i n i t i a l t i m e p h a s e and i n i t i a l momentum
d i r e c t i o n .
N U M E R I C S
C O M P U T A T I O N L O G I C
The s o u r c e deck c o n s i s t s o f a b o u t 250 c a r d s ( A p p e n d i x ) ,
f o r m u l a t e d i n t h e m a c h i n e - i n d e p e n d e n t d i a l e c t a l i n t e r s e c t i o n
o f Univac-1107 F o r t r a n - IV-CSC and IBII-7090 F o r t r a n - I V - 1 3 ,
and d e s i g n e d f o r b o t h modu la r g rowth v e r s a t i l i t y and f reedom
from o b s o l e s c e n c e .
Complete i n p u t i n s t r u c t i o n s a p p e a r a t t h e b e g i n n i n g o f
t h e main program. I n p u t c o n s i s t s o f t h e e l e c t r o m a g n e t i c
p o t e n t i a l momentum qA/mc, t h e c h a r g e - r a d i u s p h a s e k r o / 2 n ,
t h e i n i t i a l p o s i t i o n - p h a s e and t i m e - p h a s e o f t h e p a r t i c l e
( k x o / 2 n , k y o / 2 n , k z o / 2 n , w t o / 2 n ) , i t s i n i t i a l momentum
(pz /mc, P ; ' m ~ , p i / m c ) , t h e p r o p e r - t ime o u t p u t p h a s e i n t e r v a l
w o A ~ / 2 n , t h e t e r m i n a l p r o p e r - t i m e p h a s e o r / 2 n , and t h e r a n g e 0
and r e s o l u t i o n o f t h e g r a p h i c a l o u t p u t .
Numeric r o u n d i n g i s u s e d t h r o u g h o u t t h e c a l c u l a t i o n s t o
min imize a c c r u a l o f t r u n c a t i o n b i a s . A s c a n be g a t h e r e d by
s c a n n i n g s u b r o u t i n e Famdr ( F l o a t i n g a d d - m u l t i p l y - d i v i d e
r o u n d ) , r o u n d i n g i s p e r f o r m e d s i m p l y by a d d i n g t w i c e t h e low
o r d e r p a r t o f e a c h a r i t h m e t i c o p e r a t i o n answer t o i t s h i g h
o r d e r p a r t p r i o r t o f i n a l t r u n c a t i o n . S u b r o u t i n e S p i l l
w r i t e s a l i n e o f w a r n i n g and d i a g n o s t i c i n f o r m a t i o n i n t h e
o u t p u t upon t h e o c c u r r e n c e o f any s p i l l o r d i v i s i o n by z e r o .
S u b r o u t i n e A l b e r t ( E i n s t e i n ) e v a l u a t e s t h e momentum
i n t e g r a l s , E q u a t i o n s ( l o ) , ( l l ) , ( 1 2 ) , (13) ; t h e p o s i t i o n
i n t e g r a l s , E q u a t i o n s ( 1 6 ) , ( 1 7 ) , ( 1 8 ) , ( 19 ) ; and t h e r a d i a -
t i o n i n t e g r a l , E q u a t i o n ( 2 3 ) , a l l a s a f u n c t i o n o f p r o p e r
t i m e . T h i s key s u b r o u t i n e h a s been q u i t e f u l l y o p t i m i z e d
w i t h emphas i s upon n u m e r i c r e l i a b i l i t y , u n r e s t r i c t e d
n u m e r i c r a n g e , and u n r e s t r i c t e d p rob l em s i z e .
P L O T L O G I C
A l l numer ic o u t p u t i s w r i t t e n i n d u p l i c a t e on two s e p a r a t e
drum ( o r d i s c ) f i l e s . I n a f u l l y developed remote t r a n s m i s s i o n
env i ronment , t h e f i r s t drum f e e d s dec ima l o u t p u t t o e i t h e r a
desk t y p e w r i t e r o r l i n e p r i n t e r under r e a l - t i m e c o n t r o l of t h e
u s i n g a n a l y s t . The second drum p e r i o d i c a l l y f e e d s a c c r u e d
b i n a r y o u t p u t t o t h e p l o t t e r l o g i c under a u t o m a t i c t i m e - l a g
c o n t r o l t o p r o v i d e c r o s s - p l o t and p l o t - o v e r l a y v e r s a t i l i t y .
S u b r o u t i n e P l o t s c a n s t h e p l o t drum f o r a l l r e l e v a n t d a t a ,
assembles e i g h t - d i m e n s i o n a l p h a s e - s p a c e c r o s s p l o t s , c a l l s
upon s u b r o u t i n e Map t o t r a n s f o r m e a c h d a t a p o i n t t o C a r t e s i a n
c o o r d i n a t e s v i a f l e x i b l e c u r v i l i n e a r c o o r d i n a t e t r a n s f o r m a t i o n
l o g i c , t r a n s l a t e s and s c a l e s t h e p l o t s t o f i t t h e d i s p l a y
domain, and f e e d s f u l l y p r o c e s s e d c r o s s p l o t s and p l o t o v e r -
l a y s t o t h e p l o t t e r i n t e r f a c e . S u b r o u t i n e Map i s p r e s e t t o
an i d e n t i t y t r a n s f o r m a t i o n b u t can be o v e r l o a d e d f r e e l y by
t h e u s i n g a n a l y s t t o produce p o l a r p l o t s , l o g a r i t h m i c s c a l e s ,
conformal mapping t r a n s f o r m a t i o n s , c o n f o c a l q u a d r i c c o o r d i n a t e
p l o t s , o r o t h e r e x o t i c p a t t e r n s .
BNWL- 4 5 2
I O N O R B I T S I N L A S E R B E A M S
P R O P O S E D E X P E R I M E N T
To i n v e s t i g a t e t h e s e e f f e c t s e x p e r i m e n t a l l y , c o n s i d e r
f o c u s i n g a l a s e r beam upon a c l o u d o f e l e c t r o n s e m i t t e d by a
h o t t u n g s t e n r i n g e n c i r c l i n g t h e f o c a l domain, a s s k e t c h e d
i n F i g u r e 2 . Peak l a s e r beam i n t e n s i t y a p p e a r s t o b e l i m i t e d
p r i n c i p a l l y by t h e d i e l e c t r i c s t r e n g t h o f t h e l a s i n g medium.
F o c u s i n g t h e l a s e r beam down t o w i t h i n t h e c o h e r e n t d i f f r a c -
t i o n l i m i t , o f t h e o r d e r o f h a l f a wave l e n g t h i n d i a m e t e r ,
' p r o v i d e s an enormous c o n t r o l l a b l e i n c r e a s e i n beam i n t e n s i t y ,
r i s i n g a s t h e i n v e r s e s q u a r e o f t h e beam d i a m e t e r .
Based upon h i s a c c r u e d measurements o f l a s e r p u l s e
e n e r g i e s and p u l s e s t r u c t u r e s , W . V a l i e s t i m a t e s ( 4 ) t h a t low
power l a s e r s p r e s e n t l y a v a i l a b l e w i t h i n B a t t e l l e - N o r t h w e s t
L a b o r a t o r i e s , o p e r a t e d i n t h e g i a n t p u l s e mode, s h o u l d
g e n e r a t e p u l s e e n e r g i e s o f a b o u t 0 . 0 1 J i n 6 x 10 - 1 3 s e c , o r 11 10 /6 W o f beam power , a t t h e neodymium wave l e n g t h o f 1 . 0 6 u .
Focused t o w i t h i n t h e f i r s t z e r o o f t h e B e s s e l f u n c t i o n
( k r o = 2 .4048) , t h i s beam power c o r r e s p o n d s t o a beam
i n t e n s i t y o f
The c o r r e s p o n d i n g e l e c t r o m a g n e t i c f i e l d a m p l i t u d e s become
C o h e r e n t D i f f r a c t i o n
Laser L e n s R i n g
FIGURE 2
ELECTRONS I N LASER BEAM
1 7 BNWL- 45 2
For an e l e c t r o n , t h e p o t e n t i a l momentum r a t i o qA/mc becomes
The p h y s i c a l c o n s t a n t s u s e d h e r e a r e p c = 4n x l o v 7 x 2.997930 0
x l o 8 ohms f o r t h e impedance o f f r e e s p a c e , mc2 = 0 .510976 YeV
f o r t h e r e s t e n e r g y o f t h e e l e c t r o n , and c = 2.997930 x 10 8
m / s e c f o r t h e v e l o c i t y o f l i g h t .
An i n f o r m a t i v e p l a u s i b i l i t y check on t h e s e f a n t a s t i c
m a g n i t u d e s i s o b t a i n a b l e q u i t e s i m p l y by n o t i n g , w i t h r e f e r e n c e
t o F i g u r e 2 , t h a t s c a l i n g t h e f o c u s e d e l e c t r i c f i e l d back t o
t h e o n e - c e n t i m e t e r d i a m e t e r o f o u r neodymium l a s e r r o d y i e l d s
f o r t h e e l e c t r i c f i e l d w i t h i n t h e l a s e r ,
j u s t below t h e d i e l e c t r i c s t r e n g t h o f q u a r t z g l a s s ( 6 . 7 8 x 10 v/m) . ( 5 )
T H E O R E T I C A L P R E D I C T I O N S
For a low d e n s i t y c l o u d o f e l e c t r o n s wh ich s t a r t f rom
r e s t ( ~ O / r n c ~ = I ) , a s i n t h e e x p e r i m e n t p r o p o s e d i n F i g u r e 2 ,
t h e maximum e n e r g y , E q u a t i o n (41 ) , and mean e n e r g y , E q u a t i o n
( 4 7 ) , r e s p e c t i v e l y , s i m p l i f y t o
S u b t r a c t i n g o f f t h e e l e c t r o n r e s t e n e r g y (mc2 = 0 .510976 \ l e v ) , ( 6 )
and t h e n making u s e o f t h e da tum, E q u a t i o n ( 5 3 ) , now g i v e s f o r
t h e maximum and mean k i n e t i c e n e r g i e s :
KINETIC ENERGY PREDICTIONS
Maximum: 2 T ~ ~ ~ / m C = 2(qA/mc) , o r
T~~~ = 2 ( - 1 . 6 2 7 0 ) ~ 0 . 5 1 0 9 7 6
= 2 .705 MeV.
2 2 Nean: <<<T/mc > > > = ( 1 / 2 ) (qA/mc) , o r
< < < T > > > = ( 1 / 2 ) ( - 1 . 6 2 7 0 ) 20.510976
= 0 .6764 MeV. i
These e l e c t r o n k i n e t i c e n e r g y p r e d i c t i o n s r i s e l i n e a r l y w i t h
l a s e r beam power , a c c o r d i n g t o E q u a t i o n s (56 ) and ( 5 8 ) .
E v a l u a t i n g t h e o r b i t i n t e g r a l s , E q u a t i o n s ( 1 6 ) , ( 1 8 1 , and
(19), f o r an e l e c t r o n which s t a r t s f rom r e s t w i t h t h e e l e c t r i c
f i e l d p a s s i n g t h r o u g h z e r o ( x o = y o = z - - t o = 0 = - 0
0 x - py - 0 2 - P z , E O = mc ) and which r i d e s t h e wave u n t i l i t h a s s e e n h a l f a wave go by (wor = n) y i e l d s a s t h e l a b o r a t o r y p o s i t i o n
/ w a v e l e n g t h and t i m e / p e r i o d r a t i o s f o r t h e maximum e n e r g y
s t a t e ,
The c o r r e s p o n d i n g momentum r a t i o s and momentum d i r e c t i o n can
b e r e a d o f f t h e momentum i n t e g r a l s , E q u a t i o n s ( 1 0 ) and ( 1 2 ) ,
a s
Two s u c h maximum e n e r g y s t a t e s a p p e a r a s t h e p r o m i n e n t l y
e n c i r c l e d p o i n t s on t h e o r b i t s shown i n F i g u r e 3 . The second
a r i s e s f o r t h e m i r r o r - i m a g e i n i t i a l t i m e - p h a s e w t = 0
T I .
For e l e c t r o n s which s t a r t from r e s t (xo = y o = z = o 0
0 - 0 - 0 - - Px - Py - p Z ) 9 t h e o r b i t i n t e g r a l s , E q u a t i o n s (16) and ( 1 8 ) , s i m p l i f y somewhat t o t h e form
T kx = (qA/mc) [wr c o s ( o t o ) - s i n ( w r + u t o ) l 0 ,
2 2 k z = (1 /2 ) (qA/mc) {wr [1 /2 + cos ( a t , ) ]
+ ( 1 / 4 ) s i n 2(wr + wto)
D e s p i t e t h e i r d e c e p t i v e a l g e b r a i c s i m p l i c i t y , t h e s e o r b i t
e q u a t i o n s d i s p l a y phenomenal ly i n t r i c a t e f u n c t i o n a l b e h a v i o r ,
a s can be g a t h e r e d by a g l a n c e a t F i g u r e 3 , which p l o t s
p o s i t i o n p h a s e ( k x / 2 ~ , k z / 2 ~ ) a s a f u n c t i o n o f b o t h p r o p e r -
t i m e p h a s e w ~ / 2 ~ and i n i t i a l t i m e - p h a s e w t / 2 n . Program 0
O r b i t c o n s t r u c t e d t h i s machine p l o t a s a m o s a i c - s u p e r p o s i t i o n
c r o s s - p l o t of t h e o u t p u t o f 24 s u c c e s s i v e change c a s e s which
swep t b o t h p r o p e r p h a s e w r / Z n and i n i t i a l p h a s e w t o / 2 n t h rough
two comple te c y c l e s a t i n t e r v a l s o f 1 / 2 4 c y c l e ( I S 0 ) , t o
g e n e r a t e t h e e n t i r e f a m i l y o f o r b i t s , E q u a t i o n s . ( 6 6 ) and ( 6 7 ) ,
i n one r u n . T h i s p l o t h a s been a r r a n g e d t o d i s p l a y t h e a c t u a l
v i s u a l a p p e a r a n c e o f t h e e l e c t r o n o r b i t s i n t h e l a s e r beam, i f
mercury v a p o r i s p e r m i t t e d t o l e a k i n t o t h e vacuum i n s u f f i -
c i e n t c o n c e n t r a t i o n t o make t h e e l e c t r o n i o n i z a t i o n t r a c k s
v i s i b l e . Each penned l i n e t r a c e s o u t an e l e c t r o n o r b i t . Each
p o i n t symbol marks a p o i n t t a b u l a t e d i n t h e n u m e r i c a l o u t p u t
(Appendix) . The p o i n t symbols c y c l e t h rough 1 2 shapes on
s u c c e s s i v e o r b i t s t o a i d t h e eye i n t r a c k i n g an e l e c t r o n
t h r a u g h i t s o r b i t . The l a s e r beam i s i n c i d e n t from t h e l e f t
o f F i g u r e 3 , w i t h i t s f o c a l domain c e n t e r e d a t t h e o r i g i n ( 0 , 0 ) .
2 1 BNWL- 4 5 2
The e l e c t r o m a g n e t i c wave h u r l s t h e e l e c t r o n s f i r s t t r a n s v e r s e l y
i n t h e d i r e c t i o n o f t h e e l e c t r i c f o r c e f i e l d and t h e n down-
s t r e a m a l o n g i n t r i c a t e l y cusped o r b i t s dependent upon i n i t i a l
phase .
Combined s c r u t i n y o f t h i s h i g h l y i n f o r m a t i v e p l o t and o f
t h e s e h i g h l y d e c e p t i v e o r b i t e q u a t i o n s r e v e a l s t h a t a l o n g each
o r b i t t h e e l e c t r o n r e a c h e s maximum r e l a t i v i s t i c ene rgy a t t h e
p o i n t s o f i n f l e c t i o n and r e t u r n s t o r e s t ene rgy a t t h e cusps !
With t h e i s o l a t e d e x c e p t i o n of two d e g e n e r a t e o r b i t s which
z igzag a s y m p t o t i c a l l y downstream ( t h e two centermos t o r b i t s i n
F i g u r e 3 ) , t h e o r b i t s t e n d g e n e r a l l y t o z igzag abou t t h e maxi-
mum energy o r b i t s which appea r i n F i g u r e 3 a s t h e dense b l a c k
l i n e s o f o r b i t c o a l e s c e n c e . The two o r b i t s a long which t h e
maximum a t t a i n a b l e e n e r g y , Equa t ion ( 5 6 ) , i s r e a c h e d a r e
t i l t e d snakes which have no c u s p s . T h e i r a n g l e of t i l t can be
i n f e r r e d from E q u a t i o n s (60) and (61) as
- 1 t a n (x/z) = * t a n - l ( 4 m ~ / 3 ~ ~ ) = * tan- '0 .8195 = * 39O20.1'. ( 6 &
The upper and r i g h t s c a l e s i n F i g u r e 3 g i v e t h e l a b o r a t o r y
d i s t a n c e s i n wave leng ths f o r t h e c o n d i t i o n s of t h e p roposed
e x n e r i m e n t , and t h e s t r u c t u r e o f t h e o r b i t Equa t ions (66) and
(67) makes i t c l e a r how t o r e s c a l e t h e same p l o t t o f i t o t h e r
e x p e r i m e n t a l c o n d i t i o n s . V a r i a t i o n of t h e d r i v i n g f i e l d qA/mc
s c a l e s t h e t r a n s v e r s e x - a x i s l i n e a r l y and t h e a x i a l z - a x i s
. q u a d r a t i c a l l y . The l e f t and bot tom s c a l e s o f F i g u r e 3 i n c r e a s e
t h e d r i v i n g f i e l d qA/mc by a f a c t o r of 1 0 0 , t o i l l u s t r a t e t h e
r e s c a l i n g p r o c e d u r e .
The p r e c e d i n g p l o t r e a p p e a r s i n F i g u r e 4 , p r e p a r e d a t
t w i c e t h e l e v e l of d e t a i l , w i t h b o t h p r o p e r t ime phase wr/2n
and i n i t i a l t ime phase o t o / 2 n swept through two c y c l e s a t i n t e r -
v a l s of 1 /48 c y c l e ( 7 . 5 ' ) , t o d i s p l a y more v i v i d l y t h e s t a t i s -
t i c a l d i s t r i b u t i o n of o r b i t s a r i s i n g from random i n i t i a l phase
c o n d i t i o n s . The den,se b l a c k l i n e s of h i g h - e n e r g y - o r b i t
2 3 BNWL- 4 5 2
c o a l e s c e n c e show up q u i t e s h a r p l y h e r e as t h e most prominent
v i s i b l e c h a r a c t e r i s t i c of t h e e l e c t r o n beam. To complete t h e
p i c t u r e , v i s u a l i z e t h e t h r e e - d i m e n s i o n a l o r b i t p l o t g e n e r a t e d
by p e r m i t t i n g t h e o r i g i n of F i g u r e 4 t o f l u t t e r about t h e
t h r e e - d i m e n s i o n a l f o c a l domain o f t h e l a s e r beam. This f i n a l
a s p e c t of t h e s t a t i s t i c a l a v e r a g i n g l o g i c l e a d s t o t h e p r e d i c -
t i o n t h a t t h e e l e c t r o n beam w i l l appea r as tw in round h i g h -
energy p rongs of t h e o r d e r o f h a l f a wavelength i n d i a m e t e r ,
t h r u s t o u t of t h e f o c a l domain o f t h e l a s e r beam i n t h e p l a n e
o f i t s e l e c t r i c f i e l d , and enve loped i n some low ene rgy f u z z .
P R O P O S E D M E A S U R E M E N T S
A d e c i s i v e (two s i g n i f i c a n t f i g u r e ) measurement o f t h e
maximum e l e c t r o n e n e r g y , f o r comparison w i t h t h e p r e d i c t i o n ,
Equa t ion ( 5 7 ) , and a pho tograph o f t h e e l e c t r o n beam, f o r
comparison w i t h F i g u r e 4 , a r e key i n i t i a l o b j e c t i v e s .
A C K N O W L E D G E M E N T S
P h y s i c s c o n s u l t a t i o n was p r o v i d e d by W . A. Reardon,
W . V a l i , H . S . Zwibel , R . E . S c h e n t e r , A . G . G ibbs , and
C . W . Lindenmeier .
R E F E R E N C E S -
I . P . G . Bergmann. I n t r o d u c t i o n t o t h e Theory o f R e l a t i v i t y , P r e n t i c e - H a l l , I n c . , New Y o r k , N . Y . , 1 9 4 8 .
2 . A . Sommerfe Zd. E l e c t r o d y n a m i c s , ~ c a d e m i c P r e s s , I n c . , New ~ o r k , N . Y . , 1 9 5 2 .
3 . B . H . Duane. " T i m e - V a r i a n t so topic T r a n s m u t a t i o n ( G E - HL Program A l c h e m y ) , I' p p . 4 - 7 , HW-80020 , P h y s i c s Research Q u a r t e r l y R e p o r t (October-November-December, 1 9 6 3 ) , Genera l E l e c t r i c Hanford L a b o r a t o r i e s , ~ i c h l a n d , Wash ing ton .
4 . W . V a l i . Unpub l i shed Measurements , P a c i f i c Nor thwes t L a b o r a t o r y , B u t t e l l e Memorial I n s t i t u t e , R i c h l a n d , Wash. ( O r a l T r a n s m i t t a l , January 1 9 6 7 ) .
5 . E . U . Condon, H . Odishaw. Handbook o f p h y s i c s , ~cGraw- ill Book Co., I n c . , New Y o r k , N . Y . , 1 9 5 8 , F igure 7 .38 .
6 . J . W . M . Dumond, R . Cohen. "Fundamental C o n s t a n t s o f A tomic Phys ics , . " Chap. 10 o f E . U . Condon, H . ~ d i s h a b , Handbook o f P h y s i c s , McGraw-Hill Book Co., I n c . , New ~ o r k , N . Y . , 1 9 5 8 .
A P P E N D I X
B I T S
A P P E N D I X
B I T S
The s o u r c e d e c k f o r p rogram O r b i t i s f o l l o w e d by n u m e r i c
i n p u t f o r t h e o r b i t s d i s p l a y e d i n F i g u r e 3 and n u m e r i c o u t p u t
f o r t h e maximum e n e r g y o r b i t ( i n i t i a l t i m e p h a s e w t 0 / 2 n = 0 )
and f o r t h e minimum e n e r g y o r b i t ( i n i t i a l t i m e p h a s e
o t o / 2 a = 1 / 4 ) .
D ELT O R B I T * l ~ h 7 0 4 0 2 t 5859
0 0 0 0 0 1 C CHARGED PARTICLE I N ELECTROMAGNETIC WAVE 000002 C B A T T F ~ I F- - NORTHWFST PROGRAM ORBIT 0 0 0 0 0 3 CBOHBIT INPUT D E F I N I T I O N NEE B I T 0QQ!L_i)4 ----.------- . ~ ~ C ~ ~ Q A ~ ~ ~ P ~ T E J ~ L I ~ ~ M O l 4 u ' ~ I ~ I U ~ ~ L H A . T l Q ~ ~ Q ~ ~ L ~ ~ ~ ~ X ~ F Q T E ~ T I ~ ~ ~ A * ~ C Q S ~ * P ~ ~ ~ ~ T ~ ~ T J ~ ~ Z l U ~ ----- 1 - U P 0 0 0 0 0 5 C (X ELECTRIC FIELO E=-L)A/DT, Y f4AG:qETIC F I E L D ki=CUHL(A)* Z PROPAGATION) 0 0 0 0 0 6 - - - _ - _ - _ - - - _ _ _ _ _ - _ --_--- C-_ Kr! - J!.IIIIA~-_X-~P~-S_I~T_~ON~~P!~!!_S_E~~X~-~~~~-I,--LS-~~_A_~~_O_RAT_O_RY- YFHQT_O_oN_--W_A-V_EE-LEhi_G_THl ----- Q--E_-W ------------- 0 0 0 0 ~ 7 C Y o I I JZT IAL Y-POSIT~OIJ PHHSE YO/L (L I S LABORATORY PHOTON WAVE LEhrGTH) 0 EXP 0 0 0 0 0 8 C Z o I IJ I 'FIAL Z-POSITIOIU PIiASE 211/L ( L 15 LABORATORY PHOTON WAVE LENGTH) 0 EXP 0 0 0 0 0 9 C TU INITIAL TIME PHASE T O / T T ( T T IS LABORATORY PHOTON PERIOD) 0 EXP 000010 C PXO I N I T I A L X-I-IOMLFJTUIVI HAT1 O f'Xn/ivlC (MZREST MASS, CZPHOTON SPEED) 0 EXP 0 0 0 0 1 1 C PY O I l 4 I T I A L Y-P~OFIEI.IT(JIVI RAT1 0 PY O / I ~ C (MZREST MASSP C=PHOTON SPEED 0 EXP
C PZO I N I T I A L 2-MOMtNTUW KATIO PZO/MC (MZREST MASS* C=PHOTON SPEED) 0 EXP 000012__ _ _ _. ._. _ _ _ _ - _ __-__. ~ -------. - - ............................................... 0 0 0 0 1 3 C DTP OIJTPUT TICK-TOCK TIlilE PHASE UTP/TTP (TTP I S PROPER PHOTON PERIOD) 1/8 EXP 0 0 0 0 1 4 ~ c TP TERMINAL PROPER TIME PHASE TP/TTP (TTP IS PROPER PHOTON PERIOD) 1 EXP 0 0 0 0 1 5 C H CHARGE R A D I l J S HAT10 R/L ( L I S LAUORATORY PHOTO14 WAVE LENGTH) 0 EXP ooo!!l_sl----_..---..-..------. --. ____-. _ _ _ _ _ _ _ - - _ . .................................. ------------------------_ ----_-_.---_I-
000017 C MAPS hLJMRER OF PHASk-SPACE CROSS PLOTS (NONE 0, MAXIMUM 1 0 0 ) 0 I N T O E . . - - c - - PLXLUS ~FLAP~~~M~~NS~II~QRL~~APS~~LATE~~~~P_LQT-~TAPE~-FI~U~QE~.ELLE~BYP_A_I~SJ -------------------------------- 0 0 0 0 1 9 C PLUS MAPS MEANS L A S T IvIAPS (PLOT-TAPE END-OF-FILE* RtWINUv UNLOAD) 000020 . - -. --
0 0 0 0 2 1 C ( ( Z Z N S S ( K * L * ~ ~ ) * K = ~ * ~ ) , L = ~ , ~ ) , M = ~ ~ M A P S SCALES (L= t=XMILS* L=2=YMILS) EXP ? P\) oQolaz - - - - _ _ CCCCENOOOPliASE. _ _ _ _ _ _ - - PriASE--4iR_--PHee5EE_C~LL~M) M ) M ) M ) M ) El\lil\lil\lilPLQT. CMLLSl---PLDT-_ENR - Q Q - Q - - - - Q Q - - - Q Q Q - Q Q - - Q - - - -
0 0 0 0 2 3 C ZZi\JSS(l*L, i4) ZZNSS(2tL*t" l Z Z Z s S ( 3 t L r M ) Z Z N S S ( 4 t L t M ) ZZNSS(5 rL rM) - o.@!!o24.~~ - - - - - - _ _ - - - - - - - C ~ ~ ~ _ c l 1 ~ L ~ X ~ 1 . 1 ~ 2 ~ ~ Y Y _ ! ~ ~ 3 ~ Z ~ ! C ~ 4 4 ~ ~ ~ ~ N ~ 5 ~ P X X ~ S P ~ P - Y ~ N ~ 3 _ ~ P 2 2 N F - B ~ E ~ N ~ 9 ~ E R - N ~ ~ Q ~ T P ~ --------_I--------------------
0 0 0 0 2 5 0 0 0 0 2 6 C DATA TRAI4SFORM FLEXIBLY V I A SUBROUTINE MAP(XY) 0 0 0 0 2 7 C THEN THANSLATE AND SCALE LINEARLY TO MATCH ENDS 0 0 0 0 2 8 ~ - -_ - - - - - - - - - - -__ C PL~~TTER~~~~IUC~RG!_?~;~~~~~S_V_M_R_O_L_L--ANB~~C~R_Y-~I;~AI,-~ 5_R_A_T_U2N-!-?PI~QNSs ...................................
0 0 0 0 2 9 C MtlSHX ( 1 0 9 8 7 6 5 4 3 2 1 ) = ( 1 2 3 4 5 6 7 8 9 1 0 ) M I L X-GRID 1 0 I N T - 0&00-4_4 - _ - _ - - - - - - - - _ _ _ C ~ ~ Y E t i : 5 ~ H Y ~ ~ ~ Y Y Y I ~ Q ~ a 9 9 9 H ~ 7 7 ~ b ~ 3 _ s _ 4 ~ ~ ~ ~ _ 2 1 ~ ~ r ~ ~ l r - 2 ~ ~ 3 3 - 4 ~ r ~ - 5 6 6 6 7 7 - d - d 9 9 1 0 D ~ - M J L ~ L Y ~ G ~ D - D D - - - D D D D - b&-_INI ------------- 0 0 0 0 3 1 C 1 M I L GRID SPAtJS 20000 MILS 2-10 M I L GRIDS SPAN 3 0 0 0 0 MILS 0 0 0 0 3 3 C MARh ( 0 1 ? 3 4 5 h 7 8 9 l n 1 1 1 , [ * ) SYblRf~ l 1 I N T - 0 0 0 0 3 3 C MARK ( 0 1 2 3 4 5 6 7 8 9 1 0 1 1 ) = ( . 1 2 3 4 5 6 7 8 9 0 -1 NUMBER 1 I N T
c M J ~ ~ ! J ~ ~ J ~ A ~ ~ K ~ ~ _ U _ P ~ R P ~ ~ E ~ ~ P L ~ ~ T ~ L ~ ~ ~ I ~ T H ~ ~ C ~ Y C ~ I ~ : ~ M A R X S _ 0_0_1)0-31) _- - - ~ .-__-----_--____--___-
0 0 0 0 3 5 C LIEJE ( 2 Y 8 ) = ( L I N E S POINTS ARCS) CURVE-SEGMENTATION MODE 2 I N T OOCr!?;i6 _ - - -- _ - - - - -- -. - --- _ _ _ .. _ - - _ - - - _ _ - _ _ _ - _ _ - - --- - - - - - - - -- - - -- - - - - - - - - - - - - - - -- -- - - -- - - - - - - - - - - - - - - - - - - - -- - . - _ - _ - - _ - _ _ - - -- _ -- _- _ - - - -- - - - - - - - -. 0 0 0 0 3 7 C PHOTON SPEED C = 2.99793+8 METER/SECOND 0 0 0 0 3 8 C ELECTRON REST ENERGY = M*C*C = 0,510976+6 ELFCTHON VOLTS 0 0 0 0 3 9 C ELECTHOid CHARGE Q = -1.60206-19 COULOMBS OOOO40 C ELECTRON RADIUS H = Q*0/(4*PI*EPSILON*M*C*C) = 2.81785-15 METER 0 0 0 0 4 1 C ELECTRON QA/MC=-398.54244 FOR lr+15 JOUL/SEC WITHIN F IRST BESSEL ZERO w
z 0 0 0 0 4 2 C PROTON REST ENERGY = M*C*C = 938.211+6 ELECTRON VOLTS 0 0 0 0 4 3
5 0 0 0 0 4 4 C IqATEHIAL LAStR WAVELENGTH L RADIUS/WAVE R / L P
wl N
000045 C AL205 CH+++ 6943.-10 M 4.0585482-9 000046 C GLASS NU+++ 1.06-6 M 2.6583490-9 000047 ----------_-_------------ ~ - - - c ~ i l ---------------- _u_f_+_f- - - - - - - - - - - -- - - - - - - - - PL~-L I -Y~ -~L~ ------------- 1~-12-z2a2a+ 9_9_--------- - - - - - - - - - -9_---9_----9_
000048 C kiE Id E lr160-6 M 2.4291810-9 000049 ........................................................................................................................................................ 000050 DIMENSION DRUM(-/) IJNIVAC 000051 CALL ETIME UNIVAC 000052 CALL SETDH (4t524268 P 262144 rUHLif.4) UNIVAC 000053 ---------__---__-_-_-____----_-_- C-AC_L_-SEETIO15-tLl - r r - - r _ _ - - - _ - _ - - ~ - _ _ _ - - _ _ - r - - - r UNLVA-C---C--- 000054 C A L L S E T I O ( 6 r 2 ) U N I VAC 000055 .................................. c-A_~L-SF1_7£9_E_EC$_j2~-6 ------~-------_----riri-----------ri-riri----ri UNIYAC ----------- 000056 C CALL MOUIFY(6) IBM 000057 000058 C ENTER OHRIT LOOP 0 0 0 0 ~ 9 ............................ LQD--REW-LNG-_Lc _LC-_LC_LC_LC_LC------_LC_LC------------------------------------------------------------------------------------9_-------
000060 C LOAD INPIIT L I S T SNPlJT COhlPUTE AkU L I S T O R B I T PLOT O R i 3 I T 0OOObl CALL LOAD 000062 CALL L I S T 000063 CALL ALBERT 000064 CALL PLOT 000065 C NEXT OHBIT ------------------------------------------------------------------------------------------------------------------------------------------------------.-
000066 GO TO 100 000067 32766 STOP - - - ~ ~ - - - - - - ~ - - _ ~ _ - ~ - - - - - - - - - - - - - - - - - - - - - - - - _ - - - - - _ - - - - - _ - _ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - YNL!l~-C--CC--C-C-. 000068 END
D ELT P A G E 1 1 ~ 6 7 0 2 2 7 t 5037b ...................................................................................................................................................
0 0 0 0 0 1 C 48-LIIUE PAGE, 2-LIrJL MARGINS TOP/BOTTOMt TIME/PAGE TOP LEFT/RIGHT 000002 SUOROUTINF PAGE (L1Nk S ) 000003 DATA LEAF/O/vLINE/O/ 000004 ---__---------- - -- ---- 1 E~LLlLJESl--30rr2Q-~lQ - - - __---~~-_~~---~~_~__~--lll-l-----------.
000005 1 0 LINEZLINE-LINES 0_0_0!!0_6_ -----_------------------- ZF-ILX_iEI--3~Q!_3_Q9cSO ---------------------------------_------------------------------------------------------ 0 0 0 0 0 7 C LIPIES=O REGIN PAGE 1 000008 3 0 LEAFZO 000009 C LINES=- TURN PAGE
3 0 LEAF=LEAF+l ooa_o_lcl----------_------------------------------------------------------------------------------------------------------------------------------- 0 0 0 0 1 1 C WRITE (6 .40 ) LEAF IBM 000012 oo0tri-3--------------------------------------------.. 40 FOHMAT( l lH1 O O H O O M O U S ~ ~ X I ~ I ) IBM
CALL ETIMEF(TIME) UNIVAC 000014 TIME=TIME/60. UNIVAC 0 o o 0 1 5 W I { I ' ~ E ( 6 t 4 O ) TII"IE,LEAF UNIVAC
6 . L I S T SPILL
C I F S P I L L OR D1vlS10r.1 t lY ZEROP SAY WHAT* WHERE* NOW WHAT 000002 SL~BHOUTINE S P I L L (iitiEHE) OOOOO3 DIMEIJSION YESNO(2) OOOOU4 D-/1T_A_-YESiJQiA~L6!i. ----i.---- ~I-'~E~!Y.Q~~~I_~~II_JCL - _ 1 _ _ -------_-------_-------_-9
000005 CALL OVERFL ( I ) 000006 ---------~__-__- --_-__--~--------- C-AbL-Y!lLHKCd1 000007 IF((I+J).EQ.~) GO TO 200 000008 CALL PAGF(1) 000009 WHITE (hr100) Y E S , V O ( I ) ~ Y E S N O ( J ) ~ W H E R E 00oalo --------____------_--_---~-- L~~_4-F-QRi.1HI~~5H-H~AD~P-QIINT--NEXT~2X43~-5;HSP~€LL~2XA3_tUti125~ISION-sY--EKQ--~~--. 000011 1N A6t2X14HNO PROPAGATION) 000012 2110 RETURN ----- 0006~3 ErJo
f * L I S T FAMDH
D ELT FAMDH111670220t 1 4 2 7 9
-------------------------------------_--------------------------------------_---------------------------------------------------------------------.
0 0 0 0 0 1 a FUNCTION ZEHO(A) HETUHNS DEAD ZLHO I F A I S MULTIPLE ZERO FAMDR*OO 000003 - 000003 * FUI~CTIOIJ FMPR (A 1 0 ) HETURNS A*B HOUNUED FAMDR 0 2 OQOaM - _ _ _ - -9 - - - ---- F~J~_C_TI.QN-FRP_R_~ALB~-.PET~R!~S~~A~H~H_D~IIWED_ - - - - - - - _ - - - - - - - - - _ - _ _ - - f_AMI!RRQ3a-aa 0 0 0 0 0 5 s METHOD ADD TWICE LOW ORDER PART TO H I G ~ ORDER PART BH DUANE BNW FAMDR 0 4
FAMDR 0 5 FAMDR 0 6
000008 __-_- 8 1 1 EQU 11 FAMDR 0 7 0000U9 8(2) L I T r ASSIGN L ITERALS TO BANK 2 FAMDR 08 000010 8 ( 1 ) ASSIGN PROGRAM TO BAhK 1 FAMDR 0 9 o-6o-ai-i---------------------------------..---------------------------------------------------------~-----------------------------.
FAuH* NOP N A I T FOR 011 REGISTER B I T S FAMDR 1 0 000012 LA A01*01B11 FLOATllvG ADD AND ROUrYD FAMOR 11
- - -~~ - - - - - - - - - - - - - - - - - - - - - ~ - - - --------------------- ~ - - ~ ~~ - - - - - - - - - - - - - - - - - - ~ - - - - - - - - - - - - - - - - - - - - ~
000013 FA A O * * l r B l l ADD A TO B FAMDR 1 2 J FRrJ 0 0 o " l ! - HOUND AND RETURN FAMDR 1 3
0%0015 FMPR* idOP * vdAIT FOR 811 REGISTER B I T S FAMDR 1 4 LA AO**O*B11 O!?(3!?16__- _ _ .. __. _ _ _ _ _ _ _ - _ _ .__. . __*-.E~_Oe__TI_NG-_M_ULTAPbYYYA~rlrlrlROoUrUru~ r,r,r,r,r,r,r,r,r,r,r,r,r,r,r, F_A_rcll!?RRR1S---
0 0 0 0 1 7 Frvl A01*11D11 8 MULTIPLY A BY B FAMDR 1 6 0 0 0 0 1 8 _ - .. _ _ _.f_H_rllL - _ FA _ - _ - A1zZA1 llllllll.lll l..llllllll 1. ---- ,- IIQ_U_E~U-LO~~IIQK~ER~PABT - _____._ _ _ _ _ _ - _ _ _ _ fC\C\YORRR~l ---- 000019 FA kO I A 1 HOUND FAMOR 1 8 000020 - - - T O P - A 0 v ( 0 4 0 0 ! k ! l U ~ ~ ~ 8 I w ! & P T I ~ - Z E L S P - - - FAMDR 19 000U21 SZ A0 SET ~ I U L T I P L E ZERO TO DEAD ZERO FAMDR 2 0 ooJo -22 _ _ _ J _ _ - - _ 3 ~ _ B l l _ _ . I-KEJU&II-AO~ANS~~K~~~IF~~NQ~ZPJLL~W-DLQ-EAMDR-~~ ---.
0 0 0 0 2 3 FDPR* NOP u A I T FOR B l l REGISTER B I T S FAMDR 2 2 o!?o@kL - _ - - - - I A ---- A-Q r _*o~_U11___-. _ _ - _ _ _ _ _ _ ._A - FLOAT_I_rll_G_ _G_Y~yIDD~~QRR-PROo€~LO~A_NR-_NR_Oo~NR~f A_M_B_S-23---- 0 0 0 0 2 5 FD A O * * l r B 1 1 8 D I V I U E A BY B FAMDR 2 4 0 0 0 0 2 6 FA &.I rA1 . tq H DO-R FAMDR 35 000027 FU A l * * 1 1 B 1 1 s D I V I D E REivlAINDEH BY B FAMDR 2 6 0 0 0 0 2 8 - - - - - - -_-_- - - - - -_ _ - - _ - ERNiL ____-. _ _ _ _ _ _ _ - _ - - _ _ - _ _ - _ r--RQUNi-AN[lN[lHEiURN _ _ _ _ _ _ _ _ _ - _ - - - _ _ _ - - - - - EAMaRaR233333 0 0 0 0 2 9 ZERO* NOP * WAIT FOR H I 1 REGISTER B I T S FAMDR 2 8 04_0__43_0 LA - _ _ - A & ~ J I Y I B ~ ~ -_-___------------- 4--tGP--M_UL_T_IPLE-~RQ--QNNDPecPecP2W0 ~ 0 - 0 - - 0 0 ~ 0 fAMRf-29 ---- 0 0 0 0 3 1 JGD B 1 1 ,FRIJ+2 DECREMENT RETURN INDEX REGISTER FAMDR 30 0 0 0 0 3 2 FND FAMDRw31
8 s L X S T L O A D
rii \
I
D ELT L I S T t l r 6 7 0 4 0 2 r 5866 --------------------------------------------------.--------------------------------------------------------------------------------------
0 0 0 0 0 1 SUBROUTINE L I S T 0 0 0 0 0 2 C O M M O N / G O / R ~ Q A ~ U T P ~ T P ~ X O ~ Y O I Z ~ B T O ~ P X O I P Y O ~ P ~ O P F O I X I Y I ~ I T ~ P X ~ P Y ~ P ~ 0 0 0 0 0 3 ~ ~ E I E R ~ P T ~ M A P S ~ Z Z N S S ( ~ ~ ~ ~ ~ ~ ~ ) ~ M E S I ~ X P M E S H Y ~ M A R K ~ ~ I N E .QQQ&QY - - .___- - . _---- CALL-PAGEI--fil-----------------------------. ---------_-----_-_-------_--_------------_-------------
0 0 0 0 0 5 WRITE ( h e l 0 0 ) RPQA~UTP~MAPS~MESHX~MESHYPMARKIL INE o-Q0_0_0_4-_ - --- --- - - --- -- -- -1fiDD-FQKI4A JJC-UXILOPHCH1!R~EU--PAHJJI CcLE-U$- ELF;cc'CRO_MAGNE~IC-~Y~1_Y5X3WRATT~ ------.
0 0 0 0 0 7 ILL-NORTHWEST PROGRAM O R B I T / / ~ X ~ ~ H B O D Y R A D I U S ~ X ~ H P O T E N T I A L ~ X ~ H T I C K - 000008 2TOCK/4X9\-iR/L WAVESSX11HQA/MC RATIO4X12HDTP/TTP CYCS4X11HPHASE-SPAC 0 0 0 0 0 9 3E4Xl lHPLOT X - G R I D ~ x L ~ H P L O T Y - G R I D ~ x ~ ~ ~ ~ P L O T S Y M R O L ~ X ~ ~ H P L O T SEGMENT 00Ool.Q ---__-------_---------- Cc/LP~E$~S~~7~1Y_X_4_t!_M_A_P_SJJ1rr~X5~Ev_lES_H~~IIU~CcX5H_M_E5HYY~~t~X~HNAH~Z_7_~3X_Y_H_L_I_N_ELSsssssss 0 0 0 0 1 1 5 0 0 0 0 1 2 I N K S = I AL3S (MAPS) --------------------------------.---------------.----------------.--------------------------------------------------- -------.-----------
0 0 0 0 1 3 IF(INKS.LT.~) GO TO 500 000014 CALL PAGE ( 3 ) 0 0 0 0 1 5 NKITE (6 ,200 ) INKS 0 0 0 0 1 6 2 0 0 F O R W A T ( 1 H /31X5Ul4PtiASE-SPACE MAPS ( ( Z Z N S S ( K P L P M ) ~ K = ~ ~ ~ ) P L = ~ , ~ ) , M = ~ ......................................................................................................................................... 0 0 0 0 1 7 l , I h / 2 5 X 9 H E t ~ R PHASE6X9HPHASE ENDBX~HPHASERX~~HEND PLOT ( M I L S ) PLOT POOO-U% - - -__-_-_--- -_--- - -~--- P E I C Q ~ .................................................................................................. 0 0 0 0 1 9 DO 3 0 0 M = l r INKS 000020 - 0 0 0 0 2 1 3110 WHITE ( 6 , 4 0 0 ) ( (ZLNSS(KIL~M) @ ~ = 1 , 5 ) r ~ = 1 , 2 ) OaC!0-2_2_ - - - - _ _ - - - - - - - - - - _ _ - 40-QQ EQRMATIIH- L L ~ . I K ~ P ~ L L ~ _ C ~ ~ ~ - ~ H HuaX1P_[iE1517~_12HHY-i J- -- --- ----- -------- ---------- ------ 0 0 0 0 2 3 5 0 0 CALL PAGE(4) 0_0_00-2L( __-__--_----------------- U R X T E - - C ~ J - ~ ~ Q ~ ..................................................................................... 0 0 0 0 2 5 600 FOHMAT(1H /120H LAB ENERGY MOMENTUM MOMENTUM MOMENTUM P 0 0 0 0 2 6 IOSITION POSITION POSITION LAB TIMF BREMSSTRAHL PROPER T 0 0 0 0 2 7 21ME/120H E/MCC RATIO PX/MC RATIO PY/MC RATIO P7/MC RATIO X/L WAV 0 0 0 0 2 8 --------_---_----__-------------- 3ES-SYChh-hhhWA_V_E_S_-L/I, WA_V~SSS~~T~~CYS;bESsEI~C~C~R~T~P~~p1T'I~PPCY~IIbH ------- 0 0 0 0 2 9 0 0 0 0 0 3 0 .------------_---_-------_----~--- REIURrd . . . . . . . . . . . . . . . . . . . . . JJJJJJJJJJJJJJJJJJJJJ _ _ _ _ - _ _ _ _ - ~ _ - - - - _ - - - - JJJJJJJJJJJJJJJ
0 0 0 0 3 1 END
10. L I S T ALBERT
W ELT ALBEHT111670402e 5872 ..............................................................................................................................................
............................................................................................................................................... 0 0 0 0 0 1 C INTEGRATE F L N S T t 1 1 4 HA~IIILTONIAIJ H= ( P-Q*A ( X ) **2/2*M=-M*C**2./2 0 0 0 0 ~ 2 SURK~UTXNF ALRFKT 0 0 0 0 0 3 C O M M O ~ ~ / G O / R ~ Q A ~ U T P I T P ~ X O I Y O ~ Z ~ ~ T O ~ P X O I P Y O ~ P Z O I E O ~ X ~ Y ~ Z ~ T ~ P X ~ P Y I P Z 9LQDC)Oci - - - - - - - - - - _ o _ - - - _ o _ _ o _ _ o _ - - - - - - - ~IEIE~Y-PILMAI?SJZD~SSJ~~~I_~_[I~~~*-MES~~XJMESHYIMARKLUW ----------------------------------- 000005 DIMENSION Q P T ( I u ) _OQ@_Oti ......................... ELQLUYALE.UE--IUF?J-LXL~ --------_----------------------------------------------------------------------- 000007 DATA PI2/6.2031i3531/
~ -
000020 -- SIrdU=SIiJ (PHASE) 0 0 0 0 2 1 S I N ~ O = F ~ ~ I P R ( ~ . * S ~ N O P C O S O ) 000043 --------_-_--_-----__--- C~-5z~:EAnR_~~3rFJJP~<J-c:P-S0_or_C-~S-0_1-L ---------------------------------------------------------------- 0 0 0 0 2 3 PT=-UTP
C . .- 00 !?o?lc--- -_ - -- - - --- - -- .. --- -Er\J.TLU--PPPQPPEn-- .!-LME_E_,F.IEEP-F_'i,_O-QP.. - - ---- -- ------ --- --- --- --------- --- - ----- ---------- ----------------- 0 0 0 0 2 5 ~ n n PV=FAIJR(DTPIPT) - o o o G 2 ~ ~ PHASE=FMPH (FAUH (CYCLE0 P P T ) ~ f ' I 2 ) -
0 0 0 0 2 7 DPXZFMPR ( O A I FADH (COSO I -COS ( F'liASE) 1 .Qo-o!h% ---_-_. _ _ - PX~AUKL PX.O_cDPXI - _ - - - - - 0 0 0 0 2 9 fJY=PY0 [email protected] ---_--------------.i.i.i--.i- PZ=FAO~~~PZCI~LFYPI~J~_~PB~IDP~B~€ADH~~ZI~W~~IPK~I-L~COJ~~ 0 0 0 0 3 1 E=FADH(COIPZ) 0 0 0 0 3 2 CYCLF=FUPH(PTtCO) 000033 DSIN=FADR ( S I N (PHASE) I-SIN0 O _ Q O O ~ ~ ~~LLVL;FYJPR~P_T-~-~L~I - - - - - - - - . - - - _ ~ _ - - _ ~ - - l ~ - - - - - - - - - -
0 0 0 0 3 5 DX=FMPR(CX~FAUR(FMPK(~~'AVE~COSO)~-USIN)) 0-QQO46 - - - -__ - -_ - X~IA[IKLXR~E~R~~_EL~I<~~~D-C~-'~U,~~LF~DPC(,U)XLP-I~~I~~ ..........................................
0 0 0 0 3 7 Y = F A D H ( Y ~ ~ F M P H ( P Y D ~ C Y C L E ) ) 000038 DSIN?=FAnH(SIN(3.*Pi iA5F) ?-SEFJ2fl)/?. 0 0 0 0 3 9 DL=FDPR(FADF~(FMPR(PXO~)~FMPR(FMPR(C~/~.~QA)~FADK(FMPR(WAVEICOS~O &Q@u ---__------------------- tlfi!UKL ~ U . J E ~ ~ C I E E M _ ~ ~ ~ ~ L _ * - C Q ~ Y ~ L ~ U ~ ~ ~ ~ ~ I J - C ~ I ----_-------.---------------------------------
0 0 0 0 4 1 Z=FAOK(ZOtFADRIFMPR(PZOtCYCLE)rUZ))
0 0 0 0 4 4 CAI I qPII I (6Hkl REHT)
000045 .CALLPAGFo 000046 WHITE (6r2Q0) E I P X ~ P Y ~ P Z ~ X I Y P Z ~ T ~ E R , P T 0QQB4z --_-__------------ ~ I L O - X D R ~ T - L ~ I P ~ O U ~ L S L ~ 000048 WRITE (4) (WPT(N)rN=lrlO) OQQD-99 ......................... IEL AUSlP-Tl~LT.~ABS1v1l-l--GQ-TU~1DQ ----------------------------------------------------- 000050 C CLOSE PROPFH TIME LOOP (PLOT LAST TP/DTP LOGICAL RECORDS ON UNIT 4) 000051 FrdD FI I F Q 000052 REWIND 4 .QQo@53 -____.---_-------------. Rk2URL.C .----------------------------------------------------------------.------------------------- 000054 END
11. LIST PLOT
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. - - - - - - -
- RUN 5 9 C U B 0 6 8 r l U t 1 0 0 BH D U A N E * . 7 0 3 B L D G D - E X T 6-4448. . O R E I T 0 - T E L BNW JOB B T A P E S U 0 3 5 6 9 P L O T ORB1 J 1 -RX ASG A = U 0 3 5 6 9 H = P L O T O R B I T 2 -N XQT CUR - ORBlf 3
I N A O R B I T 4 T R I A _ _ - _ - - _ _ _ O R B l f _ S _ _
-N XQT O R B I T O R B I T 6 B O R B I T X O = u . * YO=U., ZO=Oo, Q A = - 1 . 6 2 7 0 4 2 7 , D I P = 4 . 1 6 6 6 6 4 7 - 2 * _ 1 P = 2 * 9 D O C U M t N T Z Z N S S ( 1 9 1 9 1 ) = -.29 2 - 3 9 3.9 0.9 9 8 4 2 . 5 9 X=Z Z Z N S S ( 1 9 2 , 1 ) = -1 .89 1.8, 1 . 9 0.9 7 0 8 6 . 6 9 _ _ _ _ __- - YEX_-_ ---_.
M A P S = - 1 9 M A R K = - 1 9 TO=-. 4 5 8 3 3 3 3 3 9 T O = 1 1 / 2 4 R z 2 . 6 5 8 3 4 9 0 - 9 , P X O = 0 . 0 0 0 0 0 0 0 + 0 9 P Y O = 0 . 0 0 0 0 0 0 0 + 0 ~ P Z O = 0 . 0 0 0 0 0 0 0 + 0 ~ B ND+++ $ O R B I T T O - - - 4 1 6 6 6 6 6 7 , B T O = 1 0 / 2 4 $ O R B I T T C = - - 3 7 5 , B T D = Q 9 / 2 4 $ O R B I T T O = - - 3 3 3 3 3 3 3 3 , B T 0 = 0 8 / 2 4 $ O R B I T T b = - e 2 9 1 6 6 6 6 7 9 5 J Q = 0 7 / 2 4 $ O R B I T T O = - - 2 5 9 B T 0 = 0 6 / 2 4 B O R B I T T O = - e 2 0 8 3 3 3 3 3 9 $ T O = D 5 / 2 4 B O R d I T T U = - - 1 6 6 6 6 6 6 7 , B T 0 = 0 4 / 2 4 B O R B I T T O = - 0 1 2 5 , B T O = Q 3 / 2 4 $ O R B I T T O = - 8 . 3 3 3 3 3 3 3 - 2 , $ T 0 = 0 2 / 2 4 S O R B I T T O = - 4 . 1 6 6 6 6 6 7 - 2 9 B T O = D 1 / 2 4 B O R B I T TO=O., $ T 0 = 0 0 / 2 4 S O R B I T T 0 ~ 4 . 1 6 6 6 6 6 7 - 2 9 B T D = 0 1 / 2 4 BORBIT ~ 0 = 8 . 3 3 3 3 3 3 3 - 2 , B T 0 = 0 2 / 2 4 B O R B I T T O = . 1 2 5 9 S 5-0=03/24 B O R E I T T 0 = . 1 6 6 6 6 6 6 7 9 B T 0 = 0 4 / 2 4 B O R B I T T 0 = . 2 U 8 3 3 3 3 3 9 B T 0 = 0 5 / 2 4 $ O R B I T T O = . 2 5 + B T 0 = 0 6 / 2 4 B O R B I T T 0 z . 2 9 1 6 6 6 6 7 , B J 0 = 0 7 / 2 4 B O R B I T T O z . 3 3 3 3 3 3 3 3 , B T 0 = 0 8 / 2 4 B O R B I T T O z . 3 7 5 , . - -_ - - _ - _ $=aPL24 B O R B I T T 0 = . 4 1 6 6 6 6 6 7 9 B T 0 = 1 0 / 2 4 B O R B I T T 0 = . 4 5 8 3 3 3 3 3 9 B T O = 1 1 / 2 4 B O R B I T T b z . 5 9 M A P S = l * B T 0 = 1 2 / 2 4
- MSG L A B E L T A P E H P L O T TAPE H ON BENSEN-LEHNER P L O T T E R - PLOT 1 - MSG B H D U A N E ( 6 - 4 4 4 8 ) C U B 0 6 8 7 0 3 B L D G 7 0 0 A R k A 3 1 M A R 6 7 PLOT 2 - MSG 1 P L O T K E - 4 6 - 1 5 1 0 ( 1 0 X l O / C M 1 8 x 2 5 CM) H O L E S A T TOP PLQT 9 - MSG SYMBOL H E A D S A V E TAPE P L O T 4 - F I N X
7 I M t v 3 6 0 8 3 9 8 - 0 1 h 2 3 ....................................... _CJ~_A_F:GEP_o_P_A__R_RTJ_IC_CCF=F=_I_N~NEL5_C_IKO!~A6N~T_I_C__c__c_W~VE ----------------------------------------------------------.
BATTELLE-NORTHWEST PROGRAM ORBIT .............................................................................. ...................................................................................................
BODY RADIUS PGTENTTAL TICK-TbCK H / L WAVES Q A / M C R k l l O DTP/TTP CYCS PWASE-SPACE PLOT X-GRIU PLOT Y-GRID PLOT SYMBOL PI OT SFGMFNT 2.6583489-09 -1.6270427106 4,1666666-02 MAPS -1 MESHX 1 0 MESHY 1 0 MARK -0 LINE 2
LAB ENERGY MOMEII~TI iL: I~IOME~!TI)P PIOMENTUM POSIT~ ON POSITION POSIT I O N LAB TIME BREMSSTRAHL PROPER TIME E/KCC ~ R A T I O PX/r.?C R h l I C PY/kiC RATIO P L / I ~ C R A T I O X/L WAVES Y/L - --.--------------------------------------------------------------------------------- NAVES Z / L WAVES T/TT CYCLES E/MCC RATIO TP/TTP CYCS
T I M E 1.4315918+OOM 3 5 -_--_--____-_----------------------------------------------- CH~-B~ED_oP~~~eTI~~LELE~NNNEE~TKOlulAFFNEETI22L~YE ...........................................................
BATTELLE-NORTHWEST PROGRAM ORBIT ---------------------------------------------------------.---------------------------------------------------.--------------------------------------------------------------------
BODY RADIUS POTENTIAL TICK-TOCK R / L WAVES QA/F'IC RATIO DTP/TTP CYCS PHASE-SPACE PI OT X-GRID PLOT Y-GRXD PI OT SYMBOL PI OT <FGMFNT
2 .6583489-09 -1eh270427+00 4 .1666666-02 MAPS -1 MESHX 1 0 MESHY 1 0 MARK - 6 L I N E 2
PHASE-SPACE MAPS ( ( Z Z N S S ( K ~ L * M ) ~ K = ~ ~ ~ ) . L = ~ * ~ ) ~ M = ~ ~ 1 __-_________-______------------------ ENUUU@HA5EEEEEEEEEEPHA5LLENDDDDDDDDDDDDDPHASE E.E.E.E.E.E.E.E.E.E.E. EW-PLQTTTLMSl--PLODTTEM hlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIlhlIl-hlIlhlIlhlIlhlIlhlIlhlIl-hlIlhlIlhlIlhlIl-
LAB ENERGY MO%~ENTIIM MOil.lEF?TUM T.IOMENTUM P O S I T ~ ~ ~ \ ~ POSITION P O S I T I O N LAB TIME BREMSSTRAHL PROPER TIME E/MCC RATIO PX/iqC RATTO PY/Mc RATIO PZ/,dC HUTXO X/L WAVES Y/L WAVES Z/L WAVES T/lT ............................... CYCLES E/MCC RATIO Tp/_T_TP CYCS-
TIME 1 . 4 5 2 7 1 ~ 1 + 0 0 ~ 36,
DO PLOT 1 TIME 1.463h06A+OOM
B-1
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