RELATIVISTIC ELECTRONS AND COHERENT RADIATION

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RELATIVISTIC ELECTRONS AND COHERENT RADIATION

Y. Petroff

To cite this version:

Y. Petroff. RELATIVISTIC ELECTRONS AND COHERENT RADIATION. Journal de Physique

Colloques, 1985, 46 (C1), pp.C1-153-C1-162. �10.1051/jphyscol:1985116�. �jpa-00224487�

J O U R N A L D E PHYSIQUE

Colloque C1, suppl6ment a u nOl, Tome 46, janvier 1985 _page Cl-153

R E L A T I V I S T I C ELECTRONS A N D COHERENT R A D I A T I O N

Y . P e t r o f f

L a b o r a t o i r e pour Z ' U t i Z i s a t i o n du Rayonnement ~ Z e c t r o m a ~ n d t i ~ u e ' , Betiment 209c, Universite' de Paris-Sud, 91405 Orsay Cedex, France

RQsumk - Nous d e c r i v o n s dans c e t a r t i c l e t r o i s manisres d ' o b t e n i r une emis- s i o n cohgrente de r a d i a t i o n dans l e domaine de l t u t r a v i o l e t sous v i d e e t d e s rayons X mous : t o u t e s s o n t bas6es s u r l T e x i s t e n c e d'un f a i s c e a u d 1 6 1 e c t r o n s r e l a t i v i s t e s c i r c u l a n t dans un anneau de stockage e t un systsme magnktique

appelg onduleur

.

A b s t r a c t - I n t h i s paper we d e s c r i b e t h r e e ways t o o b t a i n coherent r a d i a t i o n i n t h e vacuum u l t r a v i o l e t and t h e s o f t X r a y s : a l l o f them a r e based on r e l a t i v i s t i c e l e c t r o n s c i r c u l a t i n g i n a s t o r a g e r i n g and a magnetic d e v i c e c a l l e d u n d u l a t o r .

INTRODUCTION

I n t h i s paper I w i l l d e s c r i b e some r e c e n t work done a t Orsay t o o b t a i n cohe- r e n t r a d i a t i o n i n t h e vacuum u l t r a v i o l e t . Three ways a r e considered : t h e y a r e based on a s t o r a g e r i n g and a magnetic d e v i c e c a l l e d u n d u l a t o r .

In t h e f i r s t p a r t of t h e paper I w i l l g i v e t h e main c h a r a c t e r i s t i c s of t h e s t o r a g e r i h g and t h e u n d u l a t o r and t h e n d e s c r i b e t h e d i f f e r e n t methods.

When an e l e c t r o n ( o r a p o s i t r o n ) i s a c c e l e r a t e d i n a magnetic f i e l d t h e r e is emission of r a d i a t i o n . The wavelength o f t h i s r a d i a t i o n w i l l depend e s s e n t i a l l y of t h e energy E of t h e e l e c t r o n s . For E of t h e o r d e r o f few GeV one can r e a c h t h e hard X r a y s , f o r E % 500 MeV t h e spectrum i s c o n c e n t r a t e d i n t h e vacuum u l t r a v i o l e t and t h e s o f t X r a y s . This emission i s c a l l e d synchrotron r a d i a t i o n and i s e m i t t e d i n any s t o r a g e r i n g .

A schematic of a s t o r a g e r i n g (A.C.O.) i s shown i n Fig. 1. I t i s made w i t h 8 bending magnets and some " o p t i c s " t o keep t h e beam t o a r e s o n a b l e s i z e (quadrupoles and h e x a p o l e s ) . A r a d i o frequency c a v i t y a l l o w s t o keep c o n s t a n t t h e energy o f t h e e l e c t r o n s . One of t h e s t r a i g h t s e c t i o n s has been used t o i n s t a l l a magneticundulator.

Let s e e w h a t a r e t h e i m p o r t a n t p a r a m e t e r s f o r a s t o r a g e r i n g . We suppose t h a t t h e e l e c t r o n s h a v e a g a u s s i a n d i s t r i b u t i o n . The p o s i t i o n of an e- and i t s a n g l e (measured r e l a t i v e t o t h e e q u i l i b r i u m o r b i t ) a r e c o r r e l a t e d . The s i z e o f t h e e l e c t r o n b e a m i n t h e ~ ( z ) p l a n e i s c h a r a c t e r i z e d by o X ( o Z ) which i s t h e s t a n d a r d d e v i a t i o n of t h e e- displacements and i t s divergence oh(u;), t h e s t a n d a r d d e v i a t i o n o f the d i r e c t i o n a n g l e , A t f o c u s , t h e product a x x o;( (a, x oh) i s e q u a l t o t h e h o r i z o n t a l ( v e r t i c a l ) e m i t t - ance E ~ ( E ~ ) .

The h o r i z o n t a l e m i t t a n c e i s t h e r e s u l t o f a balance between t h e o s c i l l a t i o n s induced by t h e quantum emission of r a d i a t i o n and t h e damping which i s c r e a t e d by t h e average l o s s of energy. I n an i d e a l s t o r a g e r i n g t h e r e i s no r a d i a t i o n i n t h e v e r t i -

I L . P . CNRS 008

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985116

C1-154 J O U R N A L DE PHYSIQUE

c a l p l a n e and t h e v e r t i c a l e m i t t a n c e should be very s m a l l . However i n a r e a l machine, i m p e r f e c t i o n s cause coupling of t h e motions between t h e two p l a n e s .

e (bunch 2 )

R F

I ^-a-*

s i l i c a e-(bunch 1 )

window , m i r r o r

/

u n d u l a t o r

F i g . 1 - Schematic of a s t o r a g e r i n g with an u n d u l a t o r and an o p t i c a l c a v i t y f o r a f r e e e l e c t r o n l a s e r .

A t r e l a t i v i s t i c e n e r g i e s t h e d i p o l e p a t t e r n r a d i a t e d by t h e e l e c t r o n s i s s h a r p - l y peaked i n t h e d i r e c t i o n of motion of t h e e l e c t r o n s with a t y p i c a l h a l f - a n g l e

opening o f t h e o r d e r o f y-' where y = ~ / m c ~ = 1.96 E(MeV). This i s important because i t shows t h a t synchrotron r a d i a t i o n h a s , a t l e a s t i n t h e v e r t i c a l p l a n e , a very good s p a t i a l ( o r t r a n s v e r s e ) coherence.

I . UNDULATOR

The term u n d u l a t o r i s used f o r a p e r i o d i c t r a n s v e r s e magnetic f i e l d ( q u i t e o f t e n q u a s i - s i n u s o i d a l ) with many p e r i o d s (10 t o 100) intended t o produce a spectrum which i s composed of one o r s e v e r a l narrow l i n e s (harmonics). These a r e due t o t h e i n t e r f e r e n c e from e l e c t r o m a g n e t i c f i e l d s e m i t t e d by t h e same e l e c t r o n a t d i f f e r e n t p o i n t s o f i t s t r a j e c t o r y . The main p r o p e r t i e s /1/ can be summarised a s f o l l o w s :

a ) t h e wave l e n g t h of t h e l i n e s is given by ( a l o n g t h e a x i s )

where A. i s t h e magnet p e r i o d , y = ~ / m c ~ , K i s a p a r a m e t e r which d e f i n e s i t s f i e l d s t r e n g t h (K = 93.4BAo, MKSA)

b ) i f t h e e m i t t a n c e o f t h e s t o r a g e r i n g i s s m a l l e n o u g h , t h e i n c r e a s e i n s p e c - t r a l b r i g h t n e s s , compared w i t h a b e n d i n g magnet, i s N 2 where N i s t h e number o f p e - r i o d s .

C ) t h e b a n d w i d t h o f t h e l i n e s i s ?.

nN

d ) t h e power i n t h e nth harmonic which p a s s e s t h r o u g h a p i n h o l e s e l e c t i n g a band ny << 1 i s g i v e n by

Y

P . = 1 0 9 ~ ~ 1 ~ &- ^F (K)/Xo w a t t s Y n

where I i s t h e c u r r e n t and F,(K) a c o m b i n a t i o n o f B e s s e l f u n c t i o n s /2/.

A s a n e3ample w i t h E = 5GeV it i s p o s s i b l e t o o b t a i n e a s i l y P1

*

11. FIRST METHOD

L e t t r y t o s e e now how we c a n o b t a i n c o h e r e n t r a d i a t i o n w i t h an u n d u l a t o r . We have a complete c o h e r e n c e f o r an o p t i c a l beam i f we have s p a t i a l ( o r t r a n s v e r s e ) co- h e r e n c e a n d t e m p o r a l ( o r l o n g i t u d i n a l ) c o h e r e n c e .

The s p a t i a l c o h e r e n c e i s r e l a t e d t o t h e d i v e r s e n c e o f t h e s o u r c e , t h e t e m p o r a l t o i t s m o n o c h r o m a t i c i t y .

The u n d u l a t o r i s t h e o n l y s o u r c e w i t h t h e l a s e r h a v i n g a rernarquable s p a t i a l c o h e r e n c e , o f t h e o r d e r o f - 1 % 0 . 1 mrad f o r E = 5 GeV !

Y

I t i s e a s y t o u n d e r s t a n d t h a t t h e d i v e r g e n c e o f t h e s o u r c e i s a l s o i m p o r t a n t . I f we a r e l i m i t e d by t h e d i f f r a c t i o n we must have

T h i s c o n d i t i o n shows t h a t w i t h i n c r e a s i n g photon e n e r g y s m a l l e r e m i t t a n c e s a r e r e q u i r e d . A s examples f o r t h e European p r o j e c t E = 5 GeV

s X = 6 . 1 0 f 9 mrad

E, = 6 . l o - l o mrad

0

g o r A >, 19 A t h e s o u r c e h a s a s p a t i a l c o h e r e n c e . Is i s p o s s i b l e t o go down t o 1 o r 2 A by i n s e r t i n g p i n h o l e , w i t h a l o s s o f i n t e n s i t y p r o p o r t i o n a l t o t h e r e d u c t i o n i n E . That means t h a t powers o f t h g o r d e r o f 1 w a t t w i t h t o t a l s p a r i a l c o h e r e n c e s h o u l d be a v a i l a b l e a r o u n d 1 o r 2 A .

A t t h e e x i t o f t h e u n d u l a t o r t h e o p t i c a l beam h a s a p o o r t e m p o r a l c o h e r e n c e . B u t t h i s c a n b e c o r r e c t e d e a s i l y by a d d i n g a monochromator. Around lOKeV r e s o l u t i o n o f ImeV a r e a l r e a d y p o s s i b l e which g i v e s a c o h e r e n t l e n g t h

h 2

lcoh = AA ^?. 1 o r 2 mm.

I t i s c l e a r t h a t w i t h t h e a p p e a r a n c e o f s t o r a g e r i n g w i t h v e r y low e m i t t a n c e a s Bessy ( B e r l i n ) , Super ACO ( P a r i s ) o r t h e European p r o j e c t t h e y w i l l b e i n t h e n e x t few y e a r s a 1-ot of e x c i t e m e n t i h t h e f i e l d o f m i c r o s c o p y , h o l o g r a p h y and p r o t e i n c r y s t a l l o g r a p h y .

C1-156 JOURNAL DE _PHYSIQUE

111. ULTRAVIOLET GENERATION FROM AN OPTICAL KLYSTRON

We w i l l s e e i n t h e l a s t p a r t of t h i s t a l k t b a t it i s n o t very e a s y f o r t h e moment t o make a f r e e e l e c t r o n l a s e r f o r A s 1550 A. However coherent r a d i a t i o n w i l l be very u s e f u l f o r spectroscopy of atoms and molecules, microscopy and holography.

We have seen i n t h e f i r s t p a r t of t h i s paper t h a t by u s i n g an u n d u l a t o r and a mono- chromator i t was p o s s i b l e t o o b t a i n coherent r a d i a t i o n with a good average power.

However,if one i s i n t e r e s t e d b y peak p o w e r , t h i s i s not a good t e c h n i q u e . This i s t h e r e a s o n o f t h e experiment t h a t I w i l l d e s c r i b e now : it i s based on t h e f a c t t h a t i n an u n d u l a t o r it i s p o s s i b l e t o c r e a t e a bunching of t h e e l e c t r o n s by an e x t e r n a l powerful l a s e r .

Let t a k e an u n d u l a t o r a t resonance :

a s seen p r e v i o u s l y .

I f t h e e l e c t r o n s a r e uniformly d i s t r i b u t e d over a l a r g e number o f o p t i c a l wavelengths, A , (which i s t h e c a s e i n any s t o r a g e r i n g where X < 1 u m and o,, t h e FWHM bunch l e n g t h , i s between 1 cm and 10 cm), t h e n t h e r a d i a t i o n f i e l d s of two

i n d i v i d u a l e l e c t r o n s a r e n o t c o r r e l a t e d . Thus, f o r a n u n i f o r m distributionofelectrons, t h e t o t a l r a d i a t e d power i s only p r o p o r t i o n a l t o t h e number of e l e c t r o n s i n t h e bunch.

On t h e o t h e r hand, i f t h e e l e c t r o n s p a t i a l d i s t r i b u t i o n i s no l o n g e r uniform b u t i s modulated w i t h a p e r i o d i c i t y corresponding t o t h e r e s o n a n t wavelength, t h e average r a d i a t i o n f i e l d f o r a given harmonic from t h e whole bunch i s no l o n g e r z e r o . I n f a c t , t h e e m i t t e d power P i s p r o p o r t i o n a l t o t h e s q u a r e of t h e number o f e l e c t r o n s t i m e s t h e s q u a r e o f t h e F o u r i e r c o e f f i c i e n t f o r t h i s harmonic. I n t h i s c a s e , t h e sponta- neous emission o f t h e u n d u l a t o r i s s t r o n g l y enhanced, a n d , i n a d d i t i o n , t h e coherence p r o p e r t i e s of t h e r a d i a t i o n a r e modified. The coherence l e n g t h of t h e r a d i a t i o n (which i s N A i n t h e former c a s e , where N i s t h e number of p e r i o d s of t h e u n d u l a t o r ) i s , i n t h e l a t t e r c a s e , given by t h e coherence l e n g t h o f t h e e l e c t r o n bunch modula- t i o n . This e f f e c t was s t u d i e d s e v e r a l y e a r s ago f o r t h e microwave range and allowed f o r t h e development of k l y s t r o n d e v i c e s / 3 / .

S e v e r a l a u t h o r s have p u b l i s h e d t h e o r e t i c a l p r o p o s a l s , applying t h i s i d e a t o t h e o p t i c a l range /4/. These a u t h o r s proposed ( F i g . 2 ) t o i l l u m i n a t e an e l e c t r o n b u n c h

space

. _,,- Second undulator orift

first undubtor or magnerrc disperstve section

WrrtiltL mtrr!tl

/'-

,, ^{e t ~ -} ,,pmi~t~rnl ^{i ~ ~}

Focused bunch electron

pulsed laser trajectory

Fig. 2 - Schematic of t h e harmonic g e n e r a t i o n experiment u s i n g an o p t i c a l k l y s t r o n .

t r a v e l l i n g a l o n g an u n d u l a t o r with l a s e r l i g h t t h e wavelength o f which i s e q u a l t o t h e r e s o n a n t wavelength o f t h e u n d u l a t o r . According t o t h e FEL t h e o r y / 5 / , t h i s r e s u l t s i n an'energy modulation o f t h e e l e c t r o n beam (and p o s s i b l y t o some s p a t i a l modulation).

This energy modulation can be converted t o a s p a t i a l modulation u s i n g a d r i f t s e c t r o n ( a s i n microwave t u b e s where e l e c t r o n s a r e non r e l a t i v i s t i c ) o r u s i n g a d i s p e r s i v e magnetic s e c t i o n ( t h e o p t i c a l k l y s t r o n c o n f i g u r a t i o n ) /6/ f o r u l t r a r e l a t i v i s t i c e l e c t r o n s ( F i g . 2 ) . A t t h e end of t h i s s e c t i o n , t h e modulated e l e c t r o n beam e n t e r s i n t o a second u n d u l a t o r ; t h e spontaneous emission of t h i s u n d u l a t o r a t wavelength X/n i s t h e r e f o r e modified a s d e s c r i b e d above. This t e c h n i q u e a v o i d s t h e use of m i r r o r s , a s i n t h e f r e e e l e c t r o n l a s e r c a s e , t o produce UV l i g h t . I t should be e f f i - c i e n t on most of thg e x i s t i n g s t o r a g e r i n g t o produce l i g h t of wavelength between about 100 and 2000 A by s t a r t i n g with a v i s i b l e o r U . V . commercially a v a i l a b l e l a s e r . Although t h i s p r o c e s s i s o f t e n c a l l e d " m u l t i p l i c a t i o n " o r "up-conversionU,it i s d i f - f e r e n t from u s u a l h a r m o n i c p r o d u c t i o n s i n c e t h e coherent output power i s t a k e n from t h e e l e c t r o n energy and not from t h e pumping l a s e r .

Let us only r e c a l l t h a t , i n t h e c a s e of t h e O . K . , t h e r a t i o , R,, of t h e cohe- r e n t over t h e i n c o h e r e n t (spontaneous) emission, f o r t h e harmonic n of t h e l a s e r f r e - quency, f o r a given l a s e r power and w i t h i n t h e bandwidth of t h e coherent emission, i s p r o p o r t i o n a l t o :

where N i s t h e number of p e r i o d s o f t h e r a d i a t o b and I t h e r i n g c u r r e n t . f n i s t h e spontaneous emission modulation r a t e , r e s u l t i n g from t h e i n t e r f e r e n c e o f t h e two u n d u l a t o r s c o n s t i t u t i n g t h e O . K . , a t wavelength A L / n This i n t e r f e r e n c e i s d r i v e n by t h e s t r e n g t h of t h e d i s p e r s i v e s e c t i o n and t h e energy s p r e a d of t h e e l e c t r o n s and :

where Nd i s t h e number o f wavelength of t h e YAG l a s e r p a s s i n g over an e l e c t r o n i n t h e d i s p e r s ~ v e s e c t i o n and c h a r a c t e r i z e s t h e d i s p e r s i v e s e c t i o n s t r e n g t h /6/ and

kis

Y t h e r e l a t i v e energy d i s p e r s i o n of t h e beam. Thus t h i s d i s p e r s i o n , which does vary much with I on A . C . O . , i s a very c r u c i a l parameter.

The g o a l of t h e A . C . O . experiment was t o demonstrate t h e f e a s a b i l i t y o f t h e harmonic p r o d u c t i o n . Although t h e r e i s no t h e o r e t i c a l l i m i t a t i o n i n going i n t o t h e V . U . V . s p e c t r a l range (by u s i n g a h i g h e r e l e c t r o n e n e r g y ) , we chose t o work i n t h e v i s i b l e p a r t of t h e spectrum f o r convenience o f t h e d e t e c t i o n . We used t h e 1.06 p fundamental l i n e of a p u l s e d Nd : YAG l a s e r ( F i g . 3 ) focused i n t o our o p t i c 1 k l y s t r o n on t h e s t o r a g e r i n g A . C . O . working a t 166 MeV and looked a t t h e 3 ~ ' harmonic a t 355 nm. A t t h i s energy, t h e modulation r a t e , f3: i s much s m a l l e r t h a n one. This i s due t o t h e anomalous bunch l e n t h e n i n g on A . C . O . whlch makes t h e energy s p r e a d t o be much l a r g e r t h a n t h e nominal energy spread a t 166 MeV ( 1 . 4 10V4 f o r I 'i: c0.01 mA).

Also t h e r e i s an a d d i t i o n n a l energy spread due t o t h e i n t e r a c t i o n with t h e YAG p u l s e , s i n c e t h e r i n g energy damping time i s 180 msec a t 166 MeV and t h e YAG r e p e t i t i o n r a t e was 20 Hz i n our c a s e .

The low l a s e r r e p e t i t i o n r a t e (20 Hz) makes t h e long time average coherent emission very weak compared t o t h e i n c o h e r e n t spontaneous emission whose r e p e t i t i o n r a t e i s 13.6.MHz. Thus t h e coherent power has t o be measured on a f a s t time s c a l e .

The coherent emission p u l s e was s e n t on a box-car a v e r a g e r i n o r d e r t o o b t a i n an o u t p u t p r o p o r t i o n a l t o t h e coherent power and i n t e g r a t e d over many YAG p u l s e s .

The t o t a l a n g u l a r divergence of t h e coherent emission has been found t o be c l o s e t o 1 mrad i n good agreement w i t h t h e d i f f r a c t i o n l i m i t (A f i / I I q where a, a o, % 200um a r e t h e bunch RMS t r a n s v e r s e d i m e n s i o n s ) . The s p e c t r a l wldth of t h e coherent emission was t o o s m a l l t o be measured by our d e t e c t i o n system. By u s i n g a nionochromator of s p e c t r a l r e s o l u t i o n A X % 0.3 we could only s e t an upper l i m i t of

J O U R N A L DE PHYSIQUE

G.P. H.W

Electron bunch

!

I O.K.

Pr. S ! light pulse Pr,

,.,

Monochromator

F i g . 3

-

0 0

0 . 1 A . S i n c e t h e s p o n t a n e o u s e m i s s i o n i s v e r y b r o a d (Ah % 200 A),the measured v a l u e s o f R3 depends l i n e a r l y on t h e s p e c t r a l r e s o l u t i o n u s e d and a n a b s o l u t e v a l u e c a n b e s e t o n l y by assuming a g i v e n v a l u e f o r t h e c o h e r e n t e m i s s i o n s p e c t r a l w i d t h . The v a l u e o f Rg ( c o r r e s p o n d i n g t o a s m a l l s o l i d a n g l e ) , f o r Ah % 0 . 7

8 ,

f o r = 12. lo-'' a t I % 10mA). The c o m b i n a t i o n o f t h e s e two f a c t o r s p r o d u c e s t h e maximum o b s e r v e d a t a b o u t 1 mA. The maximum measured v a l u e o f R3 i n a p p r o x i m a t e l y 4 . 1 0 ~ ( f o r Ah = 0 . 7 A) a l t h o u g h t h e t h e o r e t i c a l v a l u e i s a b o u t 5 t o 6 t i m e s more.

W e . e x p l a i n e d t h i s e f f e c t by c o n s i d e r i n g t h e p u l s e t o p u l s e f l u c t u a t i o n s o f t h e co- h e r e n t e m i s s i o n when r e c o r d e d on a f a s t s c o p e .

The maximum number o f c o h e r e n t p h o t o n s e m i t t e d p e r p u l s e i s a b o u t l o 5 t h e o r e - t i c a l l y and 2 . l o 4 e x p e r i m e n t a l l y / 7 / . T h i s r a t h e r s m a l l number i s due t o v a r i o u s l o s s e s : ( i ) due t o t h e l a r g e e n e r g y d i s p e r s i o n o f t h e r i n g a t low e n e r g y t h e maxi- mum i s r e a c h e d a t 1 mA o f r i n g c u r r e n t where f 3 2 i s o n l y ( i i ) we worked a t a l o w e r l a s e r power (PL % 15 MW). T h i s a c c o u n t s f o r a l o s s o f a f a c t o r % l o 2

(PL ^% 100 MW and o p t i m i z e d d i s p e r s i v e s e c t i o n ) . ( i i i ) we have a l i m i t e d number of p e r i o d s i n t h e " r a d i a t o r " s e c t i o n (N = 7 ) . Thus a f a c t o r l o 6 - 10' i s l o s t when we compare w i t h an o p t i m i z e d k l y s t r o n p l a c e d on a s t o r a g e r i n g e x h i b i t i n g no anomalous bunch l e n g t h e n i n g . I n o u r c a s e t h e O . K . h a d b e e n o p t i m i z e d f o r f r e e e l e c t r o n l a s e r s t u d i e s and t h e p a r a m e t e r Nd i s t o o s t r o n g f o r t h i s e x p e r i m e n t . Moreover t h e e n e r g y o f 166 MeV i s v e r y f a r from t h e nominal working e n e r g y o f A.C.O. (540 MeV).

B - F u t u r e o f t h e e x p e r i m e n t s ---

On ACO we e x p e c t t o u s e a s h o r t e r p u l s e ( 3 n a n o s e c ) Nd:YAG l a s e r a s a pump.

F i g . 4 - E x p e r i m e n t a l v a l u e o f t h e c o h e r e n t e m i s s i o n r a t i o R3 ( p o i n t s w i t h e r r o r b a r s ) , m o d u l a t i o n f a c t o r o f t h e t h i r d harmonic i n c o h e r e n t e m i s s i o n w i t h t h e l a s e r o f f ( a ) and on ( b ) . The t h r e e c u r v e s a r e p l o t t e d v e r s u s t h e s t o r e d c u r r e n t .

T h e r e f o r e t h e a v a i l a b l e power, f o r a b o u t t h e same i n p u t e n e r g y , w i l l be h i g h e r . By working between 240 and 350 MeV t h e n u m e r i c a l c a l c u l a t i o n s show t h a t t h e r e g i o n 10-20 eV c a n b e r e a c h e d and t h a t 10' - l o 8 c o h e r e n t p h o t o n s / p u l s e w i l l b e produced f o r a n i n p u t power o f 50 MWatt.

Super ACO i s a s y n c h r o t r o n r a d i a t i o n d e d i c a t e d 800 MeV s t o r a g e r i n g c u r r e n t l y u n d e r c o n s t r u c t i o n a t Orsay. I t w i l l b e a c h i e v e d i n 1986. I n t h a t r i n g t h e anomalous bunch l e n g t h e n i n g h a s been minimized. A l s o , t h e e l e c t r o n d e n s i t y w i l l b e r a t h e r h i g h ,

i n p a r t i c u l a r when u s i n g a 500 MHz RF c a v i t y ( 1 2 0 t h harmonic o f t h e r i n g f r e q u e n c y ) . S t r a i g h t s e c t i o n s 3m l o n g w i l l be a v a i l a b l e f o r t h e u n d u l a t o r and t h e f r e e e l e c t r o n l a s e r , o r f o r f r e q u e n c y m u l t i p l i c a t i o n e x p e r i m e n t s .

Although super-ACO working e n e r g y w i l l be 800 MeV, t h e machine h a s been d e s i - gned i n o r d e r t o b e a b l e t o r u n a t l o w e r e n e r g i e s . We have c a l c u l a t e d t h e number of p r o t o n s produced a t 400 MeV (where t h e e n e r g y s p r e a d oy/y i s o n l y 2.5 l o T 4 ) by t a k i n g r e a s o n a b l e f i g u r e s f o r t h e p a r a m e t e r s ( p , = 1 . 3 1012 e l / c m 3 , i = 7 mAlbunch,

a1 = 0 . 7 cm). F i g u r e 5 shows t h e r e s u l t s o b t a i n e d f o r a n u n d u l a t o r o p t i m i z e d f o r FEL s t u d i e s r a t h e r t h a n f o r t h i s e x p e r i m e n t . However, oge c a n s e e t h a t t y p i c a l l y lo1'

p h o t o n s / p u l s e c a n be o b t a i n e d down t o a t l e a s t 500 A , c o r r e s p o n d i n g t o c o h e r e n t peak powers c l o s e t o 1 KWatt. These h i g h peak powers s h o u l d a l l o w m u l t i p h o t o n e x c i t a t i o n and n o n - l i n e a r p r o c e s s e s s t u d i e s i n t h e V . U . V . s p e c t r a l r a n g e . T h e r e f o r e t h i s t e c h n i - que w i l l open a new f i e l d o f i n v e s t i g a t i o n i n s o l i d s t a t e and m o l e c u l a r p h y s i c s .

JOURNAL DE PHYSIQUE

Number of coherent photons

t

-

$ /

i

I A7 T;' 6- ..*-

9

/ 0% /

1 T*/* Nd= 5 0

I

1 10 100 P laser lM Watt)

Fig. 5 - Expected number of photons on t h e r i n g Super ACO on v a r i o u s harmonics of a pump l a s e r a t 226 nm.

I V . THE FREE ELECTRON LASER

A f r e e e l e c t r o n l a s e r on a s t o r a g e r i n g i s , i n p r i n c i p l e , a simple d e v i c e . I t i s made w i t h an u n d u l a t o r and an o p t i c a l c a v i t y ( s e e F i g . 1 ) .

How t h e system works ? I t i s o u t o f t h e scope of t h i s paper t o g i v e a d e t a i l - ed d e s c r i p t i o n of t h e F.E.L. / % / . We w i l l j u s t summarize t h e important parameters.

- When an e l e c t r o n t r a v e l s i n a s t o r a g e r i n g it has only a l o n g i t u d i n a l velo- c i t y : t h e n it cannot couple t o an e l e c t r o m a g n e t i c f i e l d . ( w h i c h i s t r a n s v e r s e ) . The purpose of t h e u n d u l a t o r i s t o c r e a t e a t r a n s v e r s e v e l o c i t y of t h e e l e c t r o n allowing coupling t o t h e t r a n s v e r s e e l e c t r i c f i e l d ( t r a n s f e r of k i n e t i c energy of t h e e l e c t r o n beam t o t h e photon). A c c e l e r a t i o n of t h e e l e c t r o n beav i s made a t t h e expense of t h e e l e c t r o m a g n e t i c f i e l d .

- The f i r s t l a s e r o s c i l l a t i o n has been o b t a i n e d a t Orsay i n June 1983 /8/

showing t h e f e a s i b i l i t y of t h e experiment. The emission was o b t a i n e d around 6508 A a n d ' a l l o w e d a very d e t a i l e d s t u d y of t h e mechanism of t h e l a s e r . The main problems can be summarized a s f o l l o w s :

- t h e s m a l l s i g n a l g a i n p e r pass G i s a ~ N ~ I ~ / C ~ / ~

where I i s t h e peak c u r r e n t , X t h e t r a n s v e r s e dimension of t h e beam. This shows immediaeelg why on A . C . O . it i s o n l y p o s s i b l e t o have a l a s e r i n t h e range

4000-6000 A due t o t h e f a c t t h a t t h e g a i n v a r i e s a s t h e cube o f t h e number of p e r i o d s . The g a i n o p t i m i z a t i o n demands l o n g u n d u l a t o r ( 3 t o 5 meters i n s t e a d o f 1 . 2 m on A . C . 0 . )

.

We a r e p r e s e n t l y b u i l d i n g a n o p t i c a l k l y s t r o n f o r s u p e r A.C.O. The main cha- r a c t e r i s t i c s a r e given i n Table I . The lower l i m i t of t h e expected wavelength range i s determined mainly by t h e m i r r o r r e f l e c t i v i t y which drops r a p i d l y below 120 nm.

The o u t p u t power o f t h e l a s e r i s l i m i t e d t o few % of t h e synchrotron power e m i t t e d a l l around t h e r i n g . Then f o r s u p e r A . C . O . t h e expected power should be of t h e o r d e r of few w a t t s i n t h e v i s i b l e and t h e u l t r a v i o l e t .

a ) Super ACO e l e c t r o n beam c h a r a c t e r i s t i c s a t 400 MeV

- E m i t t a n c e E z 2.8 mrad

- Energy s p r e a d : 2 . 6 10- 4

- I

P 50 A

- RF f r e q . 500 MHz

- I n j e c t i o n ^t

- Bunch l e n g t h 2 . 7 mm

b ) O p t i c a l k l y s t r o n

- Length 3.3 m

10 cm

15 ( p e r u n d u l a t o r ) 0 t o 300

- Expected wave- l e n g t h r a n g e - Gain a t X=150 nm :

- Maximum K 6

I s h o u l d mention t h a t a 1 G e V s t o r a g e r i n g s p e c i a l l y d e s i g n e d f o r f r e e e l e c - t r o n l a s e r ( w i t h 25 m e t e r s u n d u l a t o r ) h a s been p r o p o s e d by J . Madey /9/ and it i s u n d e r c o n s t r u c t i o n now a t S t a n f o r d . I n t h a t c a s e , r a t h e r h i g h g a i n s h o u l d be o b t a i n e d

ACKNOWLEDGEMENTS

A l l t h e e x p e r i m e n t s d e s c r i b e d h e r e have been done a t Orsay. I would l i k e t o thank t h e p e o p l e i n v o l v e d : B a z i n , B e r g h e r , B i l l a r d o n , Elleaume, G i r a r d , L a p i e r r e , O r t e g a , Velghe and a l s o t h e S t a n f o r d group i n t h e b e g i n n i n g o f t h e F.E.L. e x p e r i m e n t (Madey, Deacon, Robinson).

REFERENCES

/1/ "Rapport d e P r o s p e c t i v e Super-ACO", LURE i n t e r n a l r e p o r t , Orsay, 10 A p r i l 1981 / 7 / European S y ~ ~ r h r c t r o n Rad. F a c i l i t y , Supplement I I , E d i t o r s D . J . THOMPSON and

M.W. POOLE, ESF, S t r a s b o u r g , May 1979, p . 54.

/ 3 / J . WEBSTER, "Cathode-ray bunching", J. Appl. Phys.

10,

P r i n c e t o n N.J. ( 1 9 5 0 ) .

Ci-162 J O U R N A L DE PHYSIQUE

/ 4 / P.L. CSONKA, "Enhancement o f s y n c h r o t r o n r a d i a t i o n by beam m o d u l a t i o n " , P a r t i c l e A c c e l . 8 , 225 ( 1 9 7 8 ) .

N.A. VINOKUROV a 6 d A . N . SKRINSKII, " L i m i t i n g power o f a n o p t i c a l k l y s t r o n on a l i n e a r e l e c t r o n a c c e l e r a t o r " , P r e p r i n t IMP 78-88, N o v o s s i b i r s k ( 1 9 7 8 ) . / 5 / P. ELLEAUME,"Storage r i n g PEL t h e o r y " , P r o c . o f t h e 1984 f r e e e l e c t r o n

l a s e r c o n f e r e n c e , September 3-7 ( 1 9 8 4 ) , t o b e p u b l i s h e d . / 6 / P. ELLEAUME, O p t i c a l k l y s t r o n s , J . P h y s i q u e % , ( 1 9 8 3 ) C l - 3 3 3 - 3 5 2 .

R. COISSON a n d F. d e MARTINI, F r e e e l e c t r o n c o h e r e n t r e l a t i v i s t i c s c a t t e r e r f o r U.V. g e n e r a t i o n , Phys. o f Q u a n t . E l e c t r .

2,

M . BERGHER, M . VELGHE, Y . PETROFF,"Optical f r e q u e n c y m u l t i p l i c a t i o n by a n o p t i c a l k l y s t r o n on t h e A . C . O . s t o r a g e r i n g " ,

Phys. Rev. L e t t . 5 3 , 2405 ( 1 9 8 4 ) .

J . M . ORTEGA, B . G ~ R D , Y . LAPIERRE, C . BAZIN, M . BILLARDON, P . ELLEAUME, M . BERGHER, M . VELGHE, Y . PETROFF,to b e p u b l i s h e d .

/ 8 / M . BILLARDON, P. ELLEAUME, J . M . ORTEGA, C . B A Z I N , M . BERGHER, M . VELGHE, Y . PETROFF, D. DEACON, K.E. ROBINSON and J.M.J. MADEY,

P h y s . Rev. L e t t .

51,

191 J.M.J. MADEY, AIP Conf. P r o c e e d i n g s "Free E l e c t r o n G e n e r a t i o n o f Extreme U l t r a v i o l e t C o h e r e n t R a d i a t i o n " Brookhaven 1 9 8 3 , p . 1 2 ,

Ed. b y J.M.J. MADEY a n d C . PELLEGRINI.