david neuffer- an exploration of phase stability in the "surfatron" accelerator

8/3/2019 David Neuffer- An Exploration of Phase Stability in the "Surfatron" Accelerator

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Reports to business, industry, theacademic community, ariid federal,state and local governments.

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P a r t i c l e s t r a p p e d b y t h e ma g n e t i c f i e l d o s c i l l a t e i n13x a b o u t 1 3 p wh i l e By , t h e Y v e l OCi t y , increases follow-I n g ( f r o me q . 4 ) :

I n t h e r e l a t i v i s t i c l l mi t 1 3 = - l / y p s - ( 1 - 1 3 f ) 1 2wi t h B x = 1 3 p , e q s . ( 4) a n d i 5 ) c a n h e c o mb i n e d t oo b t a i n

I n t r o d uc t I o n1 2 h a v e d e v e l o pe d a mo d i -a t s ou l e as a n d Da ws o n ,f i c a t l o n o f t h e p l a s ma b e a t - w a v e a c c e l e r a t o r , 3 c a l l e d as u r f a t r o n , t h a t a d d s a ma g n e t i c f i e l d t o t h e p l a s mab e a t - w a v e f i e l d to ma l n t . a ~ np ar t i c l e mo t f c m d nc t h e wa v e .n a l e l e c t r i c f i e l d 1 5

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o r , w i t h $ = k p x - wp t a n d E y = - 1 / Yp ,a n d d e v ~ l o p s f r mn p l a s ma - wa v e o s c i l l a t i o n s e x c i t e d b yl a s e r Du l s es o f f r e q u e n c i e s w a l l u ) + b a n d wa v e v e c - f9m!.P!+(s~n@s i n $.)d t : ~ YYP ( 8 )f r e qu e n c y a n d k p ; s ~ 1 - ~ 2 . E . c a n b e e x p r e s s e d a s wi t hwi t h Z, t h e p l a s ma - wa v e a mp l i t u de , S 1 . I n t h e s u r f a -t r o n , a c o n s t a n t t r a n s v e r s e ma g n e t i c f i e l ~ i s a d d e d T h e mo t i o n i s s t a b l a i f I s i n $ 10 1 < 1 o r y p l l < L o , wn i c hi s p r e c i s e l y t h e c o n d i t i o n f o r ma g n e t i c t r a p p i n g i nr e f . ( l ) . Eq u a t i o n ( B) i s t h e e x p r e s s i o n f o r p h a s eOs : i l l d t i o n s a b o u t d Central S t d b l e p h a s e I & I a t wn l c hp a r t i c i e s g a i n e n e r s y e t a r a t e g i v e n b y; s F , ; , ( 3 )wh e r e ; , ; a r e u n i t v e c t o r s ,

T h e e q u a t i o n s o f mo t i o n f o r d p d r l i c l e wi t h ma s sM i n t h e s e f i e l d s a r e YC2 !& sEo 3 p c s l n$ o ~ q y p l $ CL I , \ 9 )~ ( Y 3 x ) s & s i n ( k p x - wp t ) + & f3y , a n d a n d e n ? r g y Os c i l l a t i o n s a b o u t t h e c e n t r a l e n e r g y dref ; u r d f r o m

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# m# f i x s i n ( k p x - ~ t )@2 - 1 / ?He r n y ~ ( l - q ) .

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T h e b u c k e t a r e a ( i n @ - AY s Pa c e ) i n c r e a s es a s Wi n a c c e l e r a t i o n , s o t r a p p e d p a r t i c l e s r e ma i n t r a pp e d .I n a d i a b a t i c a c c e l e r a t i o n , t h e a r e a o f a t r a pp e d b u n c h~ ~ ? ~ n ~h ~~ s ~~ e n~ ~ ~ y ~ ~ ~ ~ h ~ ~ h i ~ ~ e ~ ~ ~ ~ e ~ ~ e ~~ / ~ ~T h e ma j o r d i f f e r e n c e b e t we e n s u r f a t r o n a nd s y n c h r o t r o nso s c i l l a t i o n s i s t h a t s u r f a t r o n a c c e l e r a t i o n i s f a s t a n dn Ot e n t i r e l Y a d i a ba t i c ; t h e a p p r o x i ma t i o n c o n d i t i o n;Wly ( 1 3 )

i s n o t a l w a y s v a l i d .T h e o s c i l l a t i o n s a r r s ub s t a n t i a l l y d i f f e r e n t f r o ml i n a c p ; : a s e o s c i l l a t i o n s . I n a n u l c r a r e l a t i v i s t i cl i n a c , t h e o s c i l l a t i o n f r e qu e n c y ( Q%y - 3 / * ) b e c o me sq u i t e s l o w a n d p ar t i c l e s I MI D T Oa Ch a n d Sy r n P t o t i c p h as ea s t * - . In t h e s u r f a t r o n , ( Qs ~ Y - 1 / 2 ) o s c i l l a t i o n s: g ; : ~ d e , a l t h o u q h s l o we d , a n d n o a s y mp t o t i c p h a s e i s. :?9 = ~ f ! s d t i n c r e a s e s i n d e f i n i t e l y .o

T h e f e a t . u - e s [ I f s u r f a t r o n o s c i l l a t i o n s d e s c r i b e da b o v e h a v e b e e n c on f i mn e d i n t s i mu l a t i o n s i n t e g r a t i n gt h e e x ac t e q u a t i o n < o f mo t i o n .

S y nc h r o t r g ~ Ra d i a t i o n i n a Su r f a t r o nRa d i a t i o n i n a t r a n s v e r s e ma g n e t i c f i e l d l l m i t se l e c t r o n a c c e l e r a t i o n i n a s y n c h r o t r o n s t o < l o o - G ev

f i n a l e n e r q v . I t i s i mDo r t a n t t o d e t t ? r mi n e wh e t h e r as i mi l a r l i mi t e x i s t s i n a s u r f a t r o n .T h e o o we r r a d i a t e d b y a Pa r t i c l e i s g i v e n h y ~

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T h i s s a me r e s u l t i s o b t a i n e d i n t h e c o r r e s p o n c l ] n gl i n ac ,= d i n b o t h c a s e s i s q u i t e s ma l l a l , d d o e s n o tc h a n ge a s p ar t i c l e e ne r g i e s i n c r e a s e .T h e s e c o n d t e r m o t e q . ( 1 5 ) , wh i c h Co r r e s po n d s t or a d i a t i o n f r u m t h e t r a n s v e r s e B - f i e l d mo d i ~ i e a t I y t h eE - f i e l d , i s n o v a n i s h i n g wi t h f i n i t e Ph a s e Wr o r s a n di n c r e a s e s cs yf, b e c omi n g i mPo r t a n ~~ n t ~ ~e h ~~ t ~ ~ ~ ~ ~~

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( )2 2 { n - i n $ 0 2@- %c y ~ ( 1 7 )a n d a c c e l e r a t i o n r e q u i r e s t h a t t h i s t t = r mb e l e s s t h a nt h e s y n c h r o n o u s r a t e o f e n e r g y g a i n , T h i s i , l l P l l e s f o re l e c t r o n s )

( 2L @w i n 0 - i n os i n + 0 ) < 2 . 3 X 1 0 5 , ( 1 8 )YPwh e r e E i s t h e e l e c t r o n e n e r g y .

T h e p h a s e e r r o r t e r m ( s l r I $ - s , n$ . ) w i l l De e x -Ci t e d b y t h e b e a m Ph a s e s p r e a d a s we l l a s f l u c t u a t l o n bi n t h e p l a s ma - wa v e p n a s e a n d a mp l i t u d e , . S u c n f l u c t u a -t i o n s a r e e x p e c t e d a t a b o u t t h e 1 0 % l e v e l i n a r t ~ s u n -a b l y u n i f o r m p l a sma : x c i t a t i o n . Ui t h B = 1 0 T a n dYp = 1 0 ( t y p i c a l v a l u e s ) , E c 5 T e J i s l mp l l e d .S u r f a t r o n o s c i l l a t i o n s a r e n o t d i r e c t l y d f f e Ct e db y t h e r a d i a t i o n ; h o we v e r t h e p l a s ma c ou l d b e d i s t u r be db y i n t e n s e p a r t i c l e r a d i a t i o n . He a v i e r p a r t i c l e s ( P,p , P t c . ) c an o b t a i n mu c h ] a r ] e r e n e r g i e s b e f o * e e n c o u n -t e r , 9 r a d i a t i o n d i f f i [ l l t i e ; .

Nu me r i c a l E x amp l e s u f Su r f a t r o n s- - . - - - Pr e v i o u s l y , s i mu l a t i o n r e s u l t s d e mo n s t r a t i n g p a r -t i c l e t r a p p i n g a n d s u r f a t r o n o s c i l l a t i o n s h a v e b e e np r e s e n t e d , a n d p a r a me t e r s f o r h i g h - e ne r g y h n d d e mo n -s t r a t i o n a c c e l e r a t o r s h a v e b e e n s uq g e s t e d . b B e c au s e Jf u n c t i o n a l s u r f a t r o n c omb i n e s h i g h - i n t e n s i t y s y n c h o -n i ~ e d l a s e r p u l s e s , a u n i f o r m me d i u m- d e n s i t y pldsma,a n i n j e c t e d b e a m, a n d a u n i f o r m h i g h ma g n e t i c t i c l d , ap r e c i s e f o r mu l a t i o n o f o p t i mu m p a r a me t e r s I s n u t yulp n s ~ t b l e . I n t h i s s e c t i o n wc o u t l l n e t wo p u s s l b l us u r f a t r o n s t o d c mo n s h a t e t h e t e c h n i q ue U( PJ r a n wt e r

c y n c r a t i o n oT h r mo s l . ~ i f f i c u l l r p q u i r e n wn t s a r u L h u l a s e rc h a r o c t c r i s t l ~ s . I i i g h - p u u c r l d s e r s wi t h v u r y s h u r lp u l s e , a r ~ r p q t i i r ml . T h e t i me s c a l e n f t h e I J u l > e 1 $s e t I ) y t h o f d c t t h a t t h r p l a wn p W. I V V r c l n ( l l u s u h c r ( wto n l y for a t!mu lPss L h s n t h e ton o!.clllatiuu LIIIMI!

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