linac technology for free-electron lasers

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LINAC TECHNOLOGY FOR FREE-ELECTRONLASERS

R. Cooper, P. Morton, P. Wilson, D. Keefe, A. Faltens

To cite this version:R. Cooper, P. Morton, P. Wilson, D. Keefe, A. Faltens. LINAC TECHNOLOGY FORFREE-ELECTRON LASERS. Journal de Physique Colloques, 1983, 44 (C1), pp.C1-185-C1-200.�10.1051/jphyscol:1983118�. �jpa-00222547�

https://hal.archives-ouvertes.fr/jpa-00222547

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JOURNAL DE PHYSIQUE

Colloque CI, suppldment au no2, Tome 44, fe'vrier 1983 page CI-185

LINAC TECHNOLOGY FOR FREE-ELECTRON LASERS

R.K. cooper', P.L. ort ton', P.B. ~ilson+** ,D. ~eefe++ and A. ~altens++*

Los AZamos National Laboratory, Los Almos, NM 87545, U.S.A. tanfo ford Linear Accelerator Center, Stanford, CA 94305, U.S.A. ++Lawrence Berkeley Laboratory, BerkeZey, CA 94720, U.S.A.

R6sumQ- On passe en revue la technologie des acc616rateurs lingaires de puis- sance QlevQe destin6s aux lasers h dlectrons libres.

Abstract- Electron linear accelerator technology for high-power, short-wavelength f ree-electron lasers is reviewed.

I. INTRODUCTION

The first successful free-electron laser (FEL) experiment^'-^ used linear accelerators as their source of high-energy electrons. Perceived limitations in linac performance have led experimenters to propose free-electron lasers using electron beams in storage rings6 and even in betatrons and synchrotron^.^ Experiments have been proposed that use low-voltage high-current beams8 to explore free-electron laser interaction in the collective or Raman regime. The purpose of this paper is to concentrate on the properties of high-energy electron linear accelerators for use in free-electron lasers operating principally in the Compton regime. To fix our focus somewhat, we shall consider electron energies in the 20- to 200-MeV range and consider requirements for high-power free-electron lasers operating in the 0.5- to 10-urn range. Thus we will not discuss Cockroft-Walton type accelerators nor pulsed-diode machines.

We present first a little motivational analysis that will introduce the two principal types of linacs and indicate the utility of both for free-electron laser work. At the same time we hope to point out that the accelerator and its design is an integral part of the free-electron laser system, and not just a given entity around which laser designs must be based. We direct our preliminary remarks toward high-power free-electron laser amplifiers and oscillators and deduce some desirable characteristics of the linacs that deliver electron beams for these devices.

For a high-power amplifier (that is, a high-gain single-pass system) to work, we must have a high-power electron beam. Since the individual electron energy is fixed by the wiggler design and operating optical wavelength, this means that we are interested in high beam currents. The length of the electron beam bunch is only constrained by the requirement that the electron beam-optical beam slippage be small compared to the electron beam length, that is, Re-bUnch~>A,Nw, where A, is the optical wavelength, and Nw is the number of periods in the wiggler. High

*Work performed under the auspices of the US Department of Energy with the support of the Air Force Office of Scientific Research, the Defense Advanced Research Projects Agency, and the Naval Air Systems Command.

**This work supported by the US Department of Energy, Contract No. DE-AC03-76SF005 15.

***This work was supported by the US Department of Energy under Contract No. OE-AC03-76SF00098.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983118

http://www.edpsciences.org

http://dx.doi.org/10.1051/jphyscol:1983118

CI-186 JOURNAL DE PHYSIQUE

e f f i c i e n c y e x t r a c t i o n o f the e lec t ron energy i n t h e s i n g l e pass o f t h e a m p l i f i e r d i c t a t e s t h a t we operate i n t h e nonl inear regime, t h a t t h e w igg le r be tapered, and t h a t i n i t i a l o p t i c a l f i e l d amplitudes should be h igh t o t r a p t h e maximum number o f electrons. The r e p e t i t i o n r a t e o f t h e l i n a c i s determined by the a p p l i c a t i o n and may n o t necessar i ly be p a r t i c u ' l a r l y h igh ( f o r example, i n heavy i o n f u s i o n app l i ca t ions the rep r a t e may be a few her tz ) .

For an o s c i l l a t o r appl icat ion, we need no t r e q u i r e la rge gains because s ince the photons i n the system pass through t h e wiggler reg ion many t imes and can i n t e r a c t w i t h many e l e c t r o n pulses. The ga in need on ly be s u f f i c i e n t t o overcome c a v i t y losses and t o prov ide whatever energy i s coupled out o f t h e o s c i l l a t o r system. The r e p e t i t i o n frequency o f t h e e l e c t r o n bean pulses i s , however, determined i n t h i s mode o f operat ion by t h e round- t r ip t ime o f t h e o p t i c a l pu lse i n t h e o p t i c a l resonator; t h a t i s , f o r t y p i c a l l abora to ry dimensions we are t a l k i n g about some 10 's t o 100's o f nanoseconds between e l e c t r o n pulses. Thus we are t a l k i n g about pu lse rep- e t i t i o n frequencies f rom 10 t o 100 MHz o r higher. Again, t h e e lec t ron bunch leng th must be >>XsNw ( f o r example, a 100-period w igg le r w i t h As = 1 um imp l ies

= 0.1 mm).

For tuna te ly f o r our f i e l d o f endeavor, both t h e h igh peak-current requirement o f t h e amp1 i f i e r and t h e h igh pu lse - repe t i t i on frequency requirement o f t h e osc i 1 l a t o r can be met by present-day l i n a c technology, although no t necessar i ly by t h e same machine. As we s h a l l subsequently descr ibe i n more d e t a i l , both t h e induc t ion l i n a c and t h e rf l i n a c appear t o have s i g n i f i c a n t r o l e s t o p l a y i n high-power free- e lec t ron l a s e r technology. A .Few quick s t a t i s t i c s here may be i n order t o o r i e n t t h e reader t o t h e c h a r a c t e r i s t i c s o f these two r a t h e r d i f f e r e n t types o f l i n e a r accelerator. The most advanced induc t ion l i n a c a t the present t ime i s near ing com- p l e t i o n o f cons t ruc t ion near Livermore, Ca l i fo rn ia . It i s the Advanced Test Accel- e r a t o r (ATA)' const ructed by t h e Lawrence Livermore Nat ional Laboratory. The ATA w i l l have a 50-MeV e lec t ron energy, a 70-ns, 10-kA e l e c t r o n pulse w i t h a 1-kHz r e p r a t e f o r shor t bursts, w i t h an o v e r a l l 5-Hz average rep ra te . Thus the peak power o f t h e ATA beam w i l l be 500 GW; t h e short- term average power can be as h igh as 35 MW, wh i le the long-term average i s 175 kW.

The most advanced rf e l e c t r o n l i n a c a t present i s t h e Stanford two-mile accelerator a t t h e Stanford L inear Accelerator Center (SLAC). The SLAC machine i s capable o f accelerat ing t o 20 GeV a 100-mA beam o f 1.5-us dura t ion a t a r e p e t i t i o n r a t e o f 360 Hz. Each 20-GeV micropulse conta ins 5x109 e lec t rons and has a 3-ps durat ion. Thus the peak power (de l i ve red by a micropulse) i s 5 TW, t h e average power i n t h e 1.5-ps pulse i s 2 GW, and t h e 'long-term average power i n t h e SLAC beam can be as h igh as 1 MW.

While most e lec t ron rf l inacs use a t r a v e l l i n g wave accelerat ing s t r u c t u r e (see Sec. I 1 1 below) such as t h a t o f t h e SLAC accelerator, an a t t r a c t i v e a l t e r n a t i v e f o r high-power cw operat ion l i e s i n a high-impedance standing-wave s t r u c t u r e o f t h e type used a t the high-energy end o f a proton l i n a c such as t h e Los Alamos Meson Physics F a c i l i t y (LAMPF) accelerator. This machine prov ides an average cur ren t o f 1 mA a t a k i n e t i c energy o f 800 MeV. At t h e end o f t h e l i nac , a micropulse approximate ly 20 ps i n dura t ion conta ins 5 x 1 0 ~ p a r t i c l e s , f o r a peak cur ren t o f t h e order o f 40 A, w i t h a 201.25-MHz r e p e t i t i o n frequency. During t h e t ime t h e machine i s accelerat ing, nominal ly 6% o f t h e time, t h e average cur ren t i s 16 mA, and the long-term average cur ren t i s 1 mA. Thus t h e LAMPF peak beam power i s 32 GW, t he short- term averaqe power i s 12.8 MW, and t h e long-term average i s 800 kW.

11. INDUCTION LINACS

An induc t ion l i n a c cons is ts o f an i n j e c t o r and a se r ies o f accelerat ion modules each o f which presents a r e l a t i v e l y constant, e s s e n t i a l l y e l e c t r o s t a t i c , acceler- a t i n g voltage t o t h e beam. This voltage i s u s u a l l y maintained across t h e accelera- t i n g gap f o r some few nanoseconds (depending on t h e geometry) wi thout the use o f

magnetic materials, some hundred or so nanoseconds using ferrite cores, and some few microseconds using ferromagnetic or metglas cores. The use of the various core materials is dictated primarily by cost and space considerations. Each module is energized in time so that it has achieved its desired voltage before the arrival of the beam. Figure 1 (from Ref. 9) shows a conceptual development of the accelerator module idea. Figure 2 shows a more or less realistic induction-linac acceleration- module design. The "voltage" V : l ~ d z across the accelerating gap can be maintained for a time T = A@/V where A@ is the magnetic flux change achievable in the core. For a magnetic core material this flux change is (Bsaturation + Bremanant ) x core area. For an air core th?s-ti6e-isuzallyreiated to the time required for an electromagnetic wave to make a trip from the feed point to the module wall and back to the gap.

For the high currents and high peak powers (for example, the 2.5-GW power per ATA module delivered to the beam) used in past and present induction-linac designs, pulsed-power technology has been used to provide both the high voltage and high currents usually used. A typical charging circuit will use a modest (30-kV) resonant charging circuit that will in turn be used in a resonant charging transformer circuit to charge a Blumlein line typically to a few hundred kV. The Blumlein line, when a high voltage switch (typically a spark gap) is closed, will deliver a constant voltage pulse to a properly matched load for a time equal to twice the time it takes an electromagnetic wave to travel the length of the line. For long pulses, in order to keep the Blumlein line dimensions reasonable the line may be filled with a dielectric, such as water. For even longer pulses (in the usec range) the Blumlein pulse-forming line would be replaced by a lumped-element pulse forming network (PFN).

A somewhat simplified analysis (from Ref. 10) of the action of the induction-linac module, fed by a transmission line of characteristic impedance Zo, uses the concept of a gap impedance, Zg, which for high frequencies is given by9

Zg = 60 g/a ohms , (1 1

where g is the gap length and a is the gap radius. The voltage across the gap will result from three terms: the incident voltage from the feed line v:, the voltage

reflected from the gap, Vi = V+(Z - Zo)/(Zg + I,), and the voltage wave generated 0 9

by the beam current Vb = I (Z Z )/(Z +Z ) since the beam "sees" the gap impedance b.570 g 0

paralleled by the transmission-line impedance. The efficiency of the induction- linac module can be defined as the ratio of the power delivered to the beam to the power delivered to a matched load. This efficiency is

When maximized, this efficiency is

C1-188 JOURNAL DE PHYSIQUE

which can be made close to unity by choosing Zo<<Z The achievement of such a g'

high efficiency, however, would require a precise matching of the voltage and current waveforms, and a specific design value of the beam current.

A somewhat different sort of induction linac embodied in the RADLAC design" is shown in Fig. 3. After the central radial conductor has been charged, half the double gap is shorted by a coaxial array of spark gaps, so that a net voltage is seen across the gap. This voltage is constant until the wave generated by the shorting action of the spark gaps reaches the unshorted gap (the cavity is tapered to maintain a constant impedance). In the absence of dissipation in the cavity, the net voltage across the double gap is as shown in Fig. 4.

Present day technology permits an average accelerating gradient of approximately 1 MV/m (RADLAC = 3MV/m), with a repetition rate approaching 1 kHz. Table I, taken from Ref. 9, gives parameters for most of the induction linacs built to date. At high repetition rates, switch lifetime becomes a problem. With some care, an energy spread AE/E of 0.1% can be achieved readily. Reference 10 gives switch characteristics, and Ref. 9 is a good review of induction-linac technology, including information on the effects of various core materials. Reference 12 discusses high beam-current accelerator research.

111. RF LINACS

The number of rf electron linacs in the world is of the order of 1000 (Ref. 13), and they are as diverse as their applications, which range from medical therapy to industrial radiography to nuclear physics. 6. ~ o e w ' ~ has given a comprehensive review of these machines. The basic principle of operation is simply that an electron should be acted upon by an electromagnetic wave that, on average, presents a constant phase to the electron. If one considers confining the electromagnetic wave to the interior of a waveguide, then a modification of the waveguide must for be made to lower the phase velocity of the wave, since vphase - > c in an empty

waveguide of uniform cross section. In many rf electron' linacs, this modification takes the form of loading with disks; that is, the disk-loaded waveguide supports electromagnetic waves with vphaSe (c that can be used to accelerate electrons.

An alternative approach to acceleration is to arrange for a series of resonant cav- ities energized with rf power and properly phased so that a given electron is acted upon by the same value of electric field in each cavity it transits. A linac con- structed this way is referred to as a standing wave linac, and this is the accelerator approach upon which we shall concentrate in this paper.

By far the most popular standing wave accelerating structure in electron linacs is the side-coupled structure invented at Los Alamos.14 This structure is a development resulting from the observation that a chain of coupled resonators having a n/2 phase shift per cell is relatively insensitive to tuning errors. In such a structure every other cavity is unexcited, thereby contributing not at all to acceleration and cutting the average accelerating gradient in half. The average gradient can be increased by reducing the length of the unexcited cells (the bi- periodic system) or better yet, moving these unexcited cells off to the side (the side-coupled structure). Figures 5 and 6 (from Ref. 15) shows the conceptual development just outlined and a cutaway view of a typical side-coupled structure.

A figure of merit often defined for a linac structure is known as the (uncorrected) shunt impedance per unit length

z E u ohms per unit length ,

where Ez i s t h e a x i a l e l e c t r i c f i e l d d i s t r i b u t i o n a t peak f i e l d s , L i s the

leng th o f one per iod o f the s t ructure, and P/L i s t h e power per u n i t length d iss ipa ted i n t h e s t r u c t u r e wal ls. C lear l y t h i s impedance parameter i s a measure o f the a b i l i t y o f a s t r u c t u r e t o prov ide an accelerat ing f i e l d f o r a g iven power d iss ipa t ion . An e lec t ron cross ing a c a v i t y w i t h f i e l d given by E ~ ( Z ) cos wt w i l l ga in an energy

W = l EZ(z) cos 4 dz -g/2

i f the f i e l d i s a t maximum s t reng th when the e l e c t r o n i s i n the center o f t h e c a v i t y (z=O). I n t h i s expression, g i s the accelerat ing gap length and v i s t h e e l e c t r o n speed. If EZ i s independent o f z, as i n a n'lOIO mode o f a p i l l b o x

c a v i t y neglect ing the bore hole, t h i s energy ga in i s

2 s i n 2 W = Ez w = EzgT 9 -

v

namely t h e "gap vo l tage" EZg times t h e t r a n s i t - t i m e f a c t o r T E sin(wg/2v)/(wg/2v). More general ly, the t r a n s i t - t i m e f a c t o r may be def ined as16

o r w i t h more e laborate expressions i f transverse e f f e c t s are included.

The occurrence o f the t r a n s i t - t i m e f a c t o r i n t h e expression f o r energy ga in makes t h e more meaningful d e f i n i t i o n o f shunt impedance per u n i t length

Designers o f accelerator s t ruc tu res have been working f o r many years t o increase the shunt impedance as much as possible. Various coupl ing schemes have received t h e o r e t i c a l and experimental treatment, and t h i s i s an area o f ac t i ve i n t e r e s t a t present. Table I 1 reproduced from Ref. 17 should g i v e an idea o f t h e nature o f t h i s e f f o r t .

Other parameters used t o character ize a given accelerat ing s t ruc tu re are the q u a l i t y f a c t o r Q o f a c e l l , and ZSh/Q, where Q E LW/P w i t h W t h e energy s tored i n the resonator and P the average energy d iss ipated. For a p i l l b o x cav i t y , w i l s o n L 6 g ives t h e f o l l o w i n g r e l a t i o n s :

G * T ~ ZSh/Q= , and

JOURNAL DE PHYSIQUE

where R s = (wpo/2a)1/2 = nZ0(6/X) i s the surface res is tance

(Zo = impedance of f ree space = 377 Q, a = c o n d u c t i v i t y o f c a v i t y w a l l s and

X = 2nc/w). The q u a n t i t i e s G1 and G2 are func t ions o f t h e geometry

(pol i s the f i r s t r o o t o f Jo(x) = 0 ) :

G2 = 4:0 = 967 ohms , and

where L i s the leng th o f the p i l l b o x cav i ty , and b i s the rad ius.

F i n a l l y , the resonator f i l l i n g time, Tf, which measures how r a p i d l y f i e l d s b u i l d up i n t ime when the d r i v i n g vo l tage i s applied, i s

where QL i s the loaded Q o f t h e resonator, and 8 i s t h e c a v i t y coupl ing

constant16 (usua l l y ;2: 1).

Table I11 from Ref. 18 gives the frequency dependence o f various parameters charac- t e r i z i n g rf l i n e a r accelerators, and the normal preference i n frequency f o r those parameters.

I V . LIMITATIONS

The energy spread t h a t can be achieved i n an rf e l e c t r o n l i n a c i s l i m i t e d by the v a r i a t i o n i n rf acce le ra t ing f i e l d along the leng th of the bunch, and by s ing le - bunch beam loading. For a Gaussian bunch o f rms length aZ, r i d i n g on t h e c r e s t o f an rf wave w i t h wavelength X, t h e f i r s t e f f e c t gives

The second e f f e c t , which depends on the charge per bunch, i s due t o the wake poten- t i a l produced a t t h e t a i l o f t h e bunch by charge a t t h e f r o n t o f t h e bunch. The r e l a t i v e energy spread due t o t h i s e f f e c t i s

where Ea i s the accelerat ing gradient, and k l i s a s t r u c t u r e constant given by

Here w i s the energy s tored per u n i t length, and r/Q i s t h e Zsh/Q per u n i t length. ,. Note t h a t kl scales as wL. For t h e SLAC disk-loaded st ructure, kl " 20 R/ps a t

2856 MHz. F i n a l l y , B(o) i n Eq. (17) i s a f u n c t i o n o f bunch leng th t h a t can be computed i f the l o n g i t u d i n a l wake p o t e n t i a l i s known f o r a g iven s t r u c t u r e ( the l o n g i t u d i n a l wake p o t e n t i a l i s simply t h e p o t e n t i a l as a f u n c t i o n o f d is tance f o l l o w i n g a u n i t p o i n t charge passing along t h e a x i s o f t h e s t ruc tu re ) . For t h e SLAC st ructure, B(az) i s 6.0 f o r uz = 0 and 3.0 f o r a, = 1 mn.

By ad jus t ing t h e phase of t h e center o f the bunch t o r i d e an appropr ia te d is tance ahead o f t h e c r e s t o f t h e rf accelerat ing wave, t h e r i s i n g slope o f t h i s wave can p a r t i a l l y compensate f o r t h e decelerat ing wake p o t e n t i a l . By t h i s means the energy spread given by Eq. (17) can be reduced by perhaps a f a c t o r o f 5, bu t w i t h some loss i n t h e mean energy of t h e bunch.

The transverse emittance (see Appendix) o f an rf l i n a c beam i s l i m i t e d by cumula- t i v e beam breakup and by single-bunch emittance growth. Cumulative beam breakup i s a complex phenomenon i n which o f f - a x i s bunches a t t h e f r o n t o f a long t r a i n o f bunches i n t e r a c t w i t h t h e ( u s u a l l y ) lowest frequency d i p o l e mode i n the s t r u c t u r e t o produce a d e f l e c t i o n away from the ax is f o r the f o l l o w i n g bunches. S i g n i f i c a n t emittance growth can be expected when t h e quan t i t y1 '

becomes comparable t o un i t y . Here I. i s the average cur ren t dur ing t h e bunch t r a i n , V ' i s t h e accelerat ing gradient, z i s t h e accelerator length, c t i s the leng th o f the bunch t r a i n , Xb i s t h e wavelength o f t h e breakup mode, and r l /Q i s t h e average t ransverse shunt impedance per u n i t length o f t h e s t ructure. For breakup i n the constant gradient SLAC st ructure, Xb 1.4 X and rl/Q " 130 R/m. For a uni form (not constant g rad ien t ) disk-loaded s t ruc tu re ,

S ing le bunch emittance growth i s again due t o t h e t ransverse f o r c e produced by o f f - ax is charges a t t h e f r o n t o f the bunch ac t ing t o d e f l e c t t h e t a i l o f t h e bunch. If a bunch i s undergoing be ta t ron o s c i l l a t i o n s w i t h a wavelength XB, t h e amplitude o f t h e o s c i l l a t i o n s a t the t a i l o f t h e bunch w i l l be greater than t h a t a t the head o f t h e bunch by t h e r a t i o

where q i s the t o t a l bunch charge, z i s t h e length o f the accelerator, Vo i s the average energy and wl(2uz) i s the t ransverse d i p o l e wake p o t e n t i a l a t 20,. D e t a i l s o f t h e d i p o l e wake are g iven i n Ref. 15. As an example, f o r t h e SLAC d i s k -


loaded s t r u c t u r e wk = 3 x 1015 v/cm2 a t 20, = 2 mm. Note t h a t the amplitude o f the d i p o l e wake per u n i t length o f s t ruc tu re va r ies as w3 a t t ime t z w-l.

Induc t ion l i n a c s a lso s u f f e r from the beam breakup i n s t a b i l i t y . Although the induc t ion - l i nac s t r u c t u r e i s no t i n t e n t i o n a l l y resonant, the re e x i s t TMln,-like resonances i n p r a c t i c a l s t ruc tu res t h a t can d e f l e c t t h e beam from i t s des i red a x i a l pos i t i on . While the t ransverse shunt impedance f o r these modes can be d e l i b e r a t e l y lowered, t h e h igh cur ren ts ytnployed make t h e beam breakup i n s t a b i l i t y a troublesome fea tu re o f l i n a c operat ion.

The energy spread i n an induc t ion l i n a c a r i ses p r i n c i p a l l y from two sources: t ime v a r i a t i o n o f the gap vo l tage and t h e beam p o t e n t i a l . Present day p r a c t i c e w i l l permi t Ay/y from the former source t o be r e a d i l y adjusted t o about 0.1%. The Ay/y due t o the beam p o t e n t i a l (Ref. 20) has the value 301/RyEo f o r a uniform-density beam o f cu r ren t I and p a r t i c l e - r e s t energy Eo i n e l e c t r o n v o l t s . For shor t t ranspor t distances w i t h laminar f low, i t i s poss ib le t h a t t h e space- charge p o t e n t i a l cou ld be counteracted a t the source end w i t h a segmented cathode w i t h a r a d i a l p o t e n t i a l va r ia t ion , o r ( f o r an equ ipo ten t ia l source) by d i v i d i n g t h e beam a t the load end among several e l e c t r o s t a t i c a l l y shielded channels o r by neu- t r a l i z i n g t h e space charge w i t h o ther charged p a r t i c l e s . For long t ranspor t systems w i t h considerable betat ron o s c i l l a t i o n motion, the f i r s t two schemes are impract ica l , and a Ay/y o f t h e order o f t h a t c i t e d above may be considered t o be a p roper ty o f the beam.

V. APPLICATIONS TO THE FEL

Regardless o f whether we have an induc t ion l i n a c o r an rf l i n a c as our source o f high-energy e lec t rons t o d r i v e an FEL amp l i f i e r , e f f i c i e n t conversion o f t h e beam energy t o r a d i a t i o n requ i res t h a t both the energy spread Ay/y and the beam emittance be small. For good e f f i c i e n c y we want the q u a n t i t y

t h a t i s , t h e bucket he ight should be a t l e a s t o f the order o f the energy spread. I n t h i s r e l a t i o n a, and as are t h e usual electromagnetic vector p o t e n t i a l s o f t h e w igg le r and o p t i c a l f i e l d s , respect ive ly , m u l t i p l i e d by e/moc (MKS u n i t s ) . Thus f o r good e f f i c i e n c y o f operat ion i n an amp l i f i e r , the inpu t l a s e r i n t e n s i t y

0

requ i red (= a:) w i l l be p ropor t iona l t o t h e f o u r t h power o f the energy spread;

t h a t i s ,

I i n p u t laser " ( A Y / Y ) ~ .

For o s c i l l a t o r operat ion t h i s same dependence on energy spread r e l a t e s t o the c i r - c u l a t i n g i n t e n s i t y i n t h e o p t i c a l resonator.

The e l e c t r o n beam q u a l i t y as measured by i t s emittance (see Appendix) p lays an important r o l e i n t h e t rapp ing process. It can be shown t h a t the (unnormalized) emittance g ives r i s e t o a minimum e f f e c t i v e energy spread

so t h a t the o p t i c a l i n t e n s i t i e s o f the a m p l i f i e r i n p u t laser and the o s c i l l a t o r c i r c u l a t i n g beam may depend s t rong ly on the emittance.

Both induc t ion l i n a c s and rf l i n a c s a t present s a t i s f y the Lawson-Penner sca l ing law, nE = 50 n 1 1 / ~ / ~ ~ . It does n o t seem unreasonable a t t h i s time, the re being apparent ly no fundamental l i m i t o ther than t h e cathode emission l i m i t , t o expect t h a t w i t h c a r e f u l research and development t h i s emittance can be improved by an order o f magnitude o r so.

Emi t tance

The concept o f emittance provides one measure o f accelerator beam qua l i t y . I n t ransverse phase space (x-x ' o r y-y ' where t h e pr ime ind ica tes d e r i v a t i v e w i t h respect t o d is tance along t h e beam propagation d i r e c t i o n ) t h e beam occupies a c e r t a i n area. This area, d iv ided by n, i s c a l l e d t h e emittance, denoted by t h e symbol E. The f a c t o r n r e s u l t s from t h e p r a c t i c e o f c i rcumscr ib ing t h e actual phase-space area, which may look l i k e a bow t i e o r an S-shaped f i g u r e o r something more complex, w i t h an e l l i p s e . I f t h e e l l i p s e i s upr ight , as i t w i l l be a t a beam wa is t o r ant iwais t , t h e phase-space area w i l l be g iven by ~ X ~ X ' ~ , where xo and x a o are the e l l i p s e semiaxes. I f the transverse fo rces ac t ing on t h e i n d i v i d u a l p a r t i - c l e s i n t h e beam are a l l l i near , then, i n the absence o f accelerat ion, t h e emittance can be shown t o be a constant o f t h e motion. I f t h e beam i s accelerat ing. then the emittance decreases by t h e f a c t o r By; t h a t i s , the normalized emittance

= phase space area n n BY

i s constant.

I n e l e c t r o n l i n a c s one source o f emittance i s t h e thermal motion o f the e lec t rons i n t h e cathode. A f i n i t e cathode temperature g ives r i s e t o a d i s t r i b u t i o n o f e l e c t r o n energies t ransverse t o t h e d i r e c t i o n o f emission. The emittance r e s u l t i n g from t h i s thermal d i s t r i b u t i o n o f e l e c t r o n v e l o c i t i e s i s g iven by (Ref. 20, p. 221)

where R i s t h e cathode radius.

The cur ren t drawn from the cathode w i l l be p ropor t iona l t o the cathode area, t h a t i s . 11/2 a R. Using a cathode cur ren t dens i t y 10 ~ / c m 2 and a cathode temperature g i v i n g kT = 0.1 eV, we can w r i t e Eq. (A.2) as

Any g r i d present w i l l d i s t o r t e lec t ron t r a j e c t o r i e s , g i v i n g transverse motion t h a t serves t o increase the emittance. Any nonl inear fo rces r e s u l t i n g from focusing and e x t r a c t i o n elements, f rom space-charge f i e l d s , and from the accelerat ing f i e l d s , may a lso cause t h e emittance t o increase.

An e m p i r i c a l l y determined law r e l a t i n g emittance t o average cur ren t i n e lec t ron l i n a c s s ta tes t h a t t h e emittance s a t i s f i e s


This relationship is widely known as the Lawson-Penner scaling law and holds, within factors of 2 or 3, for a large number of electron linacs. Emittances obeying this law are well over an order of magnitude greater than the emittance due to the cathode alone, indicating that careful attention to details in electron gun design and the design of focusing and accelerating systems may bear fruit in terms of significant reduction of emittance.

ACCELERATION SHORT CIRCUIT GAP /

ELECTRON

- 7 INPUT VOLTAGE

ACCELERATION GAP

FERRlTEllRON TAPE

INPUT VOLTAGE 7%. ('l.L'̂.

Fig. 1. Conceptual model of an induction module.

I I

Coaxial Blumleln tor rhort pul898 Lumped element PFN for long pulrrr

Fig. 2. Induction acceleration cavity and voltage generator.

RADIAL PULSE LINE

MARX GENERATOR

SF6 SWITCH

Fig. 3. RADLAC: radial line geometry.

Fig. 4 . Unshorted gap voltage vs t ime.

JOURNAL DE PtlYSIQUE

F ig . 5. The n/2-mode operation o f a resonant c a v i t y chain.

BEAM --- CHANNEL

CAVITY

COUKING CAVITY

F ig . 6. The side-coupled c a v i t y chain. The accelerat ing c a v i t i e s a re shaped f o r maximum shunt impedance, and the coupling c a v i t i e s a re staggered t o reduce asymmetries introduced by the s lo ts .

TABLE I

HIGH CURRENT LINEAR INDUCTION ACCELERATORS

Accelerator IER-2 Design ETAIATA FXR LIU 10 RADLAC I n j e c t o r Study

Prototype

Locat ion Dubna NBS LLNL LLNL USSR Sandi a

Year B u i l t , 1971 1971 ETA 1981 1975 1980 Proposed, o r f u l l op. 81 Pub1 ished ATA schd. 82

P a r t i c l e

K i n e t i c Energy

Beam Current

Pulse

Rep Rate (PPS)

Number of Switch Modules

Core Type

Switch

Module Vo l t

Core V o l t

Accel Length

e

30MeV

250A

500ns

50

1500

Ni-Fe Tape

Thyratron

250kV

22kV

210m

e

1 OOMeV

2kA

~ P S

1

2 50

Fe Tape

Spark Gap

400kV

40kV

250m

e

5/50MeV

lOkA

30ns170ns

5 1000 Burst

10/200

F e r r i t e

Spark Gap

250kV

10153m

e

20MeV

4kA

60n s

1 /3

54

F e r r i t e

Spark Gap

400kV

40m

e

13.5MeV

50kA

20-40ns

24

Water

Spark Gap

500kV

e

9MeV

25kA

15ns

4

O i 1

Spark Gap

1.75MV

3m

JOURNAL DE PHYSIQUE

TABLE I1

Structure

RF LINEAR ACCELERATOR STRUCTURES ( 1.35 GHz, B=l )

Disk and Side On-axis Ring Coaxial washer coupled coupled coupled coupled

Coupling (%) 50 5 l l b 18 12b

Outer radius (cm) 16.8 9.0a 9.0 14.7 12.9

Cooling difficult medium easy medium easy difficulty difficulty

Ease of manufacturing difficult difficult easy medium easy dffficulty

Material cost (% of total structure cost) 2.5 2 2 5.7 4.5

Vacuum conduction high fair 1 ow fair low

Direct beam excitation of higher order axially symmetric modes in accelerating (A) and coupling (C) cells unknown A only A and C A only A only

Direct beam excitation of beam break-up (BBU) unknown A only A and C A only A only modes (not calculable)

BBU mode propagation unknown unknown between unknown no neighboring propagat ion cell s

a ~ o e s not include side couplers.

b~ould be 1 arger.

TABLE I11

Parameter

FREQUENCY DEPENDENCE OF PRINCIPAL MACHINE PARAMETERS

Frequency Frequency preference dependence High Low Notes

Shunt impedance per u n i t l eng th ( r ) f 1 / 2 X a

RF loss f a c t o r (4 ) f -1/2 X a

F i l l i n g t ime ( t ~ ) f-3/2 X a, b

To ta l RF peak power f -1/2 X a, b, c

RF feed i n t e r v a l (L) f -3/2 X a, b

No. o f RF feeds f3 /2 X a, b, d

RF peak power per feed f - 2

RF energy s tored i n accelerator f-2

Beam loading (-dV/di) f1/2

Peak beam cur ren t a t maximum conversion e f f i c i e n c y f-1/2

Diameter o f beam aper ture f - 1

Maximum RF power ava i lab le f rom s i n g l e source f - 2

Maximum permiss ib le e l e c t r i c f i e l d s t reng th f 1/2

Re1 a t i ve frequency and dimen- s iona l to lerances f 1/2

Absolute wavelength and dimen- s iona l to lerances f -1/2

Power d i s s i p a t i o n c a p a b i l i t y of accelerator s t r u c t u r e f - 1

Notes: a. For d i r e c t sca l ing o f modular dimensions o f accelerator s t ructure. b. For same RF a t tenua t ion i n accelerator sec t ion between feeds. c. For f i x e d e l e c t r o n energy and t o t a l length. d. For f i x e d t o t a l length. e. When l i m i t e d by cathode emission. f. When l i m i t e d by beam loading. g. Approximate; empir ica l .

C1-200 JOURNAL DE PHYSIOUE

REFERENCES

1. R.M. P h i l l i p s , IRE Trans. E lect ron Devices, Vol. ED-7, pp. 231-241, Oct. 1960.

2. L.R. El ias, W.M. Fairbank, J.M.J. Madey, G.J. Ramian, H.A. Schwettman, and T.I. Smith, Phys. Rev. Le t t . 36, 717 (1976).

3. D.A.G. Deacon, L.R. E l ias, J.M.J. Madey, H.A. Schwettman, and T.I. Smith, Phys. Rev. L e t t . 38, 8921 (1977).

4. W.E. Stein, C.A. Brau, B.E. Newnam, R.W. Warren, J. Winston, and L.M. Young, Proc. 1981 L inear Accelerator Conf., Los Alamos Nat ional Lab LA-9234-C, p. 219.

5. J.M. Slater, J. Adamski, D.C. Quinley, T.L. Churchi l l , L.Y. Nelson, and R.E. Center, t o be publ ished i n IEEE J. o f Quantum Elect ron ics, Feb. 1983.

6. D.A.G. Deacon, "Theory o f t h e isochronous storage r i n g laser," Ph.D. d isser ta t ion , Stanford Univ., Stanford, CA, June 1979.

7. C.A. Brau, N.A. Kurn i t , and R.K. Cooper, U.S. Patent App l i ca t ion S e r i a l No. 342,682, Jan. 26, 1982.

8. L.R. E l i a s and G. Ramian, Physics o f Quantum Elect ron ics, Vol. 9, p. 577, Addison-Wesley ( 1982).

9. A. Fal tens and D. Keefe, Proc. o f t h e 1981 L inear Accelerator Conf., Los Alamos Nat ional Lab LA-9234-C, p. 205.

10. A. Faltens and D. Keefe, Proc. X I n t e r n a t i o n a l Conf. on High Energy Accelerators, Vol. I, p. 358, Pro tv ino (1977).

11. R.B. M i l l e r , K.R. Prestwich, J.W. Poukey, B.G. Epstein, J.R. Freeman, A.W. Sharpe, W.R. Tucker, and S.L. Shope, J. App. Phys, 52, 81184 (1981).

12. D. Keefe, P a r t i c l e Accelerators, Vol. 11, p. 187 (1981).

13. G.A. Loew, Proc. o f the 1976 Proton L inear Accelerator Conf., Chalk R ive r Nuclear Laborator ies AECL-5677.

14. E.A. Knapp, B.C. Knapp, and J.M. Potter, Rev. Sci. I n s t r . 39, p. 979 (1968).

15. E.A. Knapp, Ch. C . l . 1 ~ i n L inear Accelerators P. Lapos to l le and A. Septier, eds. (North Holland, Amsterdam, 1970).

16. P.B. Wilson, SLAC-PUB-2884, p. 8 (February 1982) ( a l s o Physics o f High Energy P a r t i c l e Accelerators, p. 458, AIP Conference Proc. No. 87 (1982)).

17. J.-P. Labr ie and J. McKeown, Nucl. Ins t . and Meth., 193, p. 437 (1982).

18. R.B. Neal, Ed., The Stanford Two-Mile Accelerator.

19. G. J. Caporaso, K.W. Struve, UCID-19402, Lawrence Livermore ~ a b o r a i o r y , Jan. 1982.

20. J.D. Lawson, The Physics o f Charged P a r t i c l e Beams, Clarendon Press, Oxford (1978), p . 127.

linac technology for free-electron lasers

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