of 7, july 1985 high-gain free electron lasers using...

IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-21, NO. 7, JULY 1985 83 1

High-Gain Free Electron Lasers Using Induction Linear Accelerators

T. J. ORZECHOWSKI, E. T. SCHARLEMANN, B. ANDERSON, V. K. NEIL, W. M. FAWLEY, D. PROSNITZ, s. M. YAREMA, MEMBER, IEEE, D. B. HOPKINS, MEMBER, IEEE. A. c . PAUL,

A. M. SESSLER, AND J. S. WURTELE

Abstract-High-power free electron lasers (FEL’s) can be realized using induction linear accelerators as the source of the electron beam. These accelerators are currently capable of producing intense cwrents (102-104 A) at moderately high energy (1-50 MeV). Experiments using a 500 A, 3.3 MeV beam have produced 80 MW of radiation at 34.6 GHz and are in good agreement with theoretical analysis. Future experiments include a high-gain, high-efficiency FEL operating at 10.6 pm using a 50 MeV beam.

I. INTRODUCTION

T HE free electron laser (FEL) [ 11 can produce coherent radiation at wavelengths from the ultraviolet to the mi-

crowave regime. The coherence arises from the trapping and bunching of the electron beam in ponderomotive potential wells generated by the stimulated radiation and the static magnetic (wiggler) field. The output wavelength is determined by a double Doppler shift of the wiggler magnet period. The output power of the laser i s proportional to the amount of electron beam current which can be trapped in the ponderomotive well, and depends on the brightness of the electron beam as well as the size of the ponderomotive well. For a sufficiently bright beam, an appreciable fraction of the beam energy can be converted to coherent radiation.

Induction linacs [2] can produce high-current, high-energy electron beams with pulse durations ranging from tens of nanoseconds to microseconds. Two such machines are currently available at Lawrence Livermore National Laboratory (LLNL). The experimental test accelerator [3] (ETA) produces a 10 kA electron beam with a peak energy of 4.5 MeV and a pulse duration of 30 ns. The advanced test accelerator [4] (ATA) produces a 10 kA electron beam with a peak energy of 50 MeV and a pulse duration of 70 ns. Both of these machines typically run at 1 Hz. The mating of an FEL with such a high-power induction linac can in principle produce very high-power sources of coherent radiation.

Manuscript received January 9, 1985; revised February 15, 1985. This

7405-ENG-48 and DE-AC03-76SF00098, and by the Defense Advanced work was supported by the U.S. Department of Energy under Contracts W-

Research Projects Agency under ARPA Order 4856, Program Code 3B10. T. J. Orzechowski, E. T. Scharlemann, B. Anderson, V. K. Neil, W. M.

Fawley, D. Prosnitz, and S. M. Yarema are with the Lawrence Livermore National Laboratory, University of California, Livermore, CA 94550.

D. B. Hopkins, A . C. Paul, A. M. Sessler, and J. S. Wurtele are with the Lawrence Berkeley Laboratory, Berkeley, CA 94720.

FEL’s have successfully operated at wavelengths in the visible [5] infrared [6]-[9], and millimeter wave regimes [ 101-[14]. The wavelength of the emitted radiation is given by

where X , is the length of the wiggler period and 711 is the parallel energy of the electron beam in units of electron rest mass. Typical wigglers have periods on the order of a few to 10 cm. Thus, production of millimeter wavelength radiation requires only modest beam energies (yIl - 1-5). Electron beams in this energy range are available from a variety of sources. Millimeter wave FEL’s have used beams produced by induction linacs [13], [ 141, Van de Graaff accelerators [ 151, and pulsed diode machines [ 101- [12]. Visible wavelength FEL’s require the high-energy electron beams (Eb > 100 MeV) which are characteristic of storage rings [SI. Infrared lasers can be achieved with intermediate energy electron beams which can be produced by either RF linacs [6]-[9] or induction linacs [16] (Eb - tens of megaelectron volts). The distinct advantage of the induction linac is its high peak power. A drawback of existing induction linacs is that the electron beam emittance tends to be large. The reason is that, up to this time, minimizing beam emittance in these machines has not been a design criterion. Since the laser gain is proportional to the brightness [ 171 (beam current + emittance2), the increase in gain due to the higher current can be nul- lified by the higher emittance unless care is taken to gen- erate a high-quality beam.

In Section I1 of this paper, we describe induction linacs. We present the principles of operation and various physic,s issues associated with this type of accelerator. Beam for- mation is an important item in that it is the limiting factor to high-quality beams. We discuss methods to reduce the beam emittance while maintaining the high beam current.

In Section 111, we present an overview of the theory applicable to FEL’s using induction linacs. In this analysis, the space-charge potential of the beam is ignored with respect to the depth of the ponderomotive well. A two- dimensional code based on a single particle model has been developed, and is being used to analyze present experiments as well as aid in the design of future experi-

0018-9197/85/0700-0831/$01.00 0’ 1985 IEEE

832 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-21, NO. 7, JULY 1985

Accelerator core 7 /Switch

forming network

Fig. 1. Induction accelerator principle

ments. The code is essential in designing and optimizing the longitudinal profile of a tapered wiggler. This type of wiggler, in which either the wiggler period or wiggler field intensity is varied so that the ponderomotive well is always kept in resonance with the (decelerating) beam electrons, underlies all of the high-gain high-extraction efficiency FEL designs.

Detailed results from our millimeter wave FEL experiment on ETA are Rresented in Section IV. This FEL is operated at 34.6 GHz in a single pass amplifier mode. We have measured a gain of 34 dB and an output power of 80 MW. Future experiments include a 10.6 pm laser amplifier using the 50 MeV beam generated by ATA. In Section V, we present the design for the initial experiment in the infrared.

11. INDUCTION LINEAR ACCELERATORS High-voltage, intense electron beams can be produced

using the induction linear accelerator. The present state- of-the-art induction linac is the advanced test accelerator [4] (ATA) at Lawrence Livermore National Laboratory. This accelerator produces 70 ns, 10 kA electron beam pulses at 50 MeV at a rate of 1 Hz. Because the induction linac is a modular device (a fixed amount of energy is added in each section), the final beam energy is limited by the overall length of the device as long as various high- current instabilities are controlled [ 191.

The principle of operation for an induction linac is illustrated in Fig. l . Each induction module can be viewed as a 1:l current transformer. The primary of the transformer is the accelerator power input while the secondary is the beam itself. The core of the transformer surrounds the accelerating column and the change in magnetic flux in this core establishes an axial electric field according to Faraday's law:

where .i? is the induced electric field, d a is an ele_ment of path enclosing the (toroidal) transformer core, B is the (azimuthal) magnetic induction in the core, and dS* is-the no_rmal to the cross-sectional area of the core. Since B = p H , the volts-seconds available to the beam are deter-

::a i i l i i V i 6'8. ? I \ l'% v i t i <, 1 f s

Fig. 2. Induction accelerator module used on ATA.

mined by the permeability, saturation magnetic 'induction, and cross-sectional area of the cores. Typically, high p materials such as ferrite, soft iron, or metallic glass ( p - lo3) are used in the accelerator cores. Each accelerator module of ETA (ATA) is capable of increasing the energy of a 30 ns (70 ns) 10 kA beam by 250 kV.

Fig. 2 shows a cross section of a typical accelerator module. The pulse line driving the primary circuit induces a time-varying toroidal magnetic field in the core. The induced electric field appears across the 2.54 cm gap which is located between adjacent accelerator modules. The electric field distribution in the accelerator module is such that the orbit integral for the particles is constant at any radius. The core in each module is concentric with a focusing so- lenoid which assists in the transport of the beam down the accelerator. The electric field along the accelerator is rep- resented by both the gradient of the scalar potential and time derivative of the vector potential

+ 4 1 aA' c at

E = - V c f , - - - . (3)

Thus, a potential difference is established across the accelerating gap, but both the input and output ends of the accelerator are at ground potential. Between accelerating gaps the potential returns to its initial value, but the elec-

ORZECHOWSKI ez ai.: FEL'S USING INDUCTION LINEAR ACCELERATORS 833

I BEAM

, I Q I ,

FERRITE LOADED ACCELERATOR CAVITY

25 SEC

RAMP FROM - MODULATORS

I WATER WATER BLUMLEIN 25GhV COAXIAL

250hV COAXIAL SPARKGAP

HIGH PRESSURE -

h

Fig. 3. Drive circuit for a single induction module

tric field in this region (between gaps) is zero due to the time rate of change of the vector potential.

The present drive circuit for an ETA/ATA accelerating module is shown in Fig. 3. A capacitor is discharged through a 1O:l voltage transformer which charges a blumlein to 250 kV. The blumlein is discharged through the ferrite loaded accelerator cell with a pressurized gas spark gap switch. The pulse length is determined by the length of the blumlein while the repetition rate is limited by the spark gap. The gas in the spark gap (a mixture of SF6 and N,) becomes contaminated due to gas b reakdoh and electrode material ablation during the discharge. The gas in the spark gap is circulated to remove the debris and, thus, restore the voltage holding capacity of the switch. The present power compression chain can only deliver a short burst ( - 10 pulses) at 1 kHz. 2 s are required between bursts to replenish the primary energy reservoir.

Thus, the average repetition rate of the accelerator is lirn- ited to 5 pulses/s.

The injector provides a 2.5 MeV beam at the accelerator entrance. This beam is generated in a gun which is illustrated in Fig. 4. Ten induction modules are connected in series to produce a potential of 2.5 MV across an anode- cathode gap. The cathode has no axial magnetic field on its surface. As the beam is accelerated between the cathode and anode, it enters an axial magnetic field of several hundred gauss which is used for transport to the accelerator and matching the beam onto the latter's guide field.

Various types of cathodes have been used in the ETA/ ATA guns. Originally, ETA used a hot cathode as the electron source. Since'these cathodes emit with current densities of 10-20 A/cm2, large area cathodes were required to achieve a total current of 10 kA (cathode diameter > 25 cm). These large-area hot cathodes were highly sus-


Fig. 4. 2.5 MeV electron gun used as injector for the ATA.

ceptible to cathode poisoning and proved to be too unre- liable for our use.

Plasma flashboard cathodes [20] have been used exten- sively in both ETA and ATA, and are capable of producing the required current densities ( - 20 A/cm2). These cathodes work as follows: a ground plane is perforated by an array of pins which are isolated from the ground plane by a dielectric insulating material. When a high voltage pulse ( - lo5 V) is applied to the pins, the insulating material between the pins and the ground plane breaks down across its surface producing a tenuous plasma near the flashboard. Several tens of nanoseconds after the igniter pulse is applied, an intermediate grid, located about 2.5 cm from the cathode, is driven to + 100 kV with respect to the cathode and extracts the electrons from the cathode plasma. The gross nonuniformity of the plasma from these cathodes results in beams which have too low a brightness 1211 ( 3 - I /&) for efficient FEL operation at visible and IR wavelengths. The normalized brightness is typically 5 X lo3 A/cm2 * rad’. This type of cathode has been used in the microwave FEL experiment which will be described later in this paper.

Recent experiments with field emission cathodes (.Icath - 100 A/cm2) have shown that an order of magni- tude improvement in brightness can be achieved relative to flashboard cathodes. A normalized brightness of 5 X lo4 A/cm2 rad2 has been achieved on ATA with a field emission cathode [22]. Other experiments [23], [24] have shown that a brightness > lo5 Aicm’ . rad2 can be ob- tained with multi-kiloampere beams. For comparison, a brightness of.106 A/cm2 . rad2 is required for a high-gain, high-efficiency FEL operating in the visible-to-near-IR frequency regime.

111. FEL THEORY In this section, we present an overview of the theoreti-

cal analysis we have used to predict the performance of an induction linac driven FEL and to design our experiments. The analytical and numerical work is based on the single particle equations of motion derived by Kroll, Morton, and Rosenbluth [18] (KMR), and the field equations derived by Colson [25] or Prosnitz, Neil, and Szoke [26]. The particle equations describe the motion of electrons in energy (y) and phase ($) in the ponderomotive potential formed by the wiggler and laser fields. The field equations give the source for the coherent laser field in terms of y and $ of the electrons. The analytical work predicts growth rates for the laser field in the exponential gain regime. We will primarily discuss the growth of microwaves in a waveguide, with particular reference to the electron laser facility (ELF) experiment described below. The linear theory for exponential growth in free-space propagation (including diffraction effects) has been discussed else- where [27].

In what follows, z is the axis of the FEL and of the electron beam propagation. The linear wiggler has a peak magnetic field of &, a period and a total length of L,v. The electromagnetic field has a wavelength X, and a complex electric field amplitude E, = /E,\ eiq. We normalize the wiggler magnetic field using b,v = e Bw/( & mc2) and the electric field with e,7 = eE,/( & mc2). The dimension- less rms vector potentials of the fields are

a,+, E b,Jk,v = bwXw/2n

a,7 = les\ /k,7 = I hS/2n-. (4)

In terms of these parameters, the equations describing

ORZECHOWSKI et al.: FEL’S USING INDUCTION LINEAR ACCELERATORS

the motion in y and + of the jth electron are

835

I I I I

where %, = +j - 4; (5)

where fs is the standard difference of Bessel functions 1251, which represents the decrease in coupling between an electron and the electromagnetic field caused by the electron’s oscillatory longitudinal motion. ,For microwaves in a waveguide, - k, # o,lc; we retain the difference here by defining k , k , + k , - w,/ c.

The equation for the electromagnetic field in a waveguide can be written

where I is the total beam current, and N is the number of electrons in a period of the ponderomotive potential. The transverse dimensions of the waveguide are a and b, and e , is to be considered the complex amplitude of the TE,, mode in the waveguide (the ELF design mode, Section IV). In obtaining (7), we have integrated the field equation over the waveguide, after multiplying by cos (7ry/b) to pick out the TEol mode alone.

Following Bonifacio, Pellegrini, and Narducci [28], we can linearize these equations to examine the regime of exponential growth. The electron beam from an induction linac is nearly monoenergetic, but can have a significant emittance; hence, we will be more concerned with an adequate treatment of emittance than of energy spread. To include emittance effects, we use the important property of the natural focusing of the wiggler, that the averaged square of the perpendicular momentum (wiggler plus betatron motions) of each electron is constant over its betatron orbit. That is,

(y2p: > j = (1 + k2, $j> ( 8) where y g is the maximum vertical extent of an electron’s betatron orbit in a linear wiggler, and a , , is the wiggler vector potential at the midplane.

Therefore, the averaged parallel velocity is also constant and so is the shift of a single electron from precise resonance with the ponderomotive potential. Emittance effects are then well approximated with a single parameter for each electron; e.g., the shift away from resonance. We use

(dbiM) Gain

\\\ 0 I I I 0.0 0.2 0.4 0.6 0.8 1.0

Maxium betatron radius Icml

Fig. 5. Power gain as a function of maximum betatron radius for different beam current as determined by the linear theory. The parameters for the calculation are y = 7.6, B,,, = 4.2 kG, and K, = 0.

which appears in the equilibrium solution for 0, through eJ!eq) = 0 . Jo + ZAkj. (10)

For an electron distribution ,function uniform in y’p, we can write

1 f(Akj) = K, K , - ~ f 2 I Akj < IC, + u / 2 (11)

where K, is the shift from resonance (Ak) at the center of the distribution, and K is the width of the distribution. The linearization procedure then yields a cubic in I’, the complex spatial growth rate of the field (e, oc eirZ)

r3 + 2 r 2 Kc + r [K: + A - K2/4] + ~ k , = o (12)

where

We have set cos (7ryj/b) = 1 for all electrons, and have only retained the variation of a,( y ) off the midplane in (9). We have thereby dropped all but the most important three- dimensional effect, which is the effect of beam emittance on the resonance condition in (9). The quantity Nmodes is the number of waveguide modes to which the electron beam can strongly couple (see the discussion below).

The solutions to (12), expressed in dB m-I for growth in power ( a e:) and at different currents, are plotted in Fig. 5 as a function of beam radius. The steep drop of gain with beam radius is entirely a result of beam emittance effects; i.e., a larger beam radius leads to a larger spread in shifts from resonance in (11). Since we have integrated over the waveguide cross section already, any “fill factor” terms do not contribute to the dependence on radius.

In the oversized waveguide (10 x 3 cm) of the ELF experiment, the TE2, mode has a phase velocity only slightly higher than the TE,, mode; their respective ponderomotive potential wells travel at 0 .932~ (TE.,, mode) and 0 .928~ (TE,, mode) and their resonant 7’s differ by only 2 percent. The electrons can couple nearly as well to the TE,, mode as to the TE,, mode. The TE4, mode has a resonant y above that of the TEol mode by 11 percent, and so does not couple to the electron beam. The TEo3, etc., modes cannot couple to any electron beam (the phase

836 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-21. NO. 7. JELY 1985

velocity of the ponderomotive well associated with these modes is greater than c). The result is that, for the ELF waveguide, only two symmetric waveguide modes can couple to the electron beam, and thus, in (13), Nmodes = 2. This value for Nmodes depends critically on the geometry of the waveguide; in a smaller waveguide only the TEol mode would couple to the electron beam.

The factor Nnrodes appears in (13) because, although we have projected out the TEoi mode on the left-hand side of (7), the full field (TE,, + TE,, . . * modes) affects the particle phase and energy loss on the right-hand side. We are assuming, in lumping the effects of higher modes into the single parameter Nmodes, that the modes couple equally well to the electrons, and that the phase slippage of the higher modes with respect to the TEol mode can be neglected. For ELF parameters, this assumption appears to be a good approximation.

The equations from which this linear theory is derived neglect the effect of space-charge forces. The validity of this approximation is not obvious for the high-current electron beam from an induction linac. Space-charge forces arise from the physical bunching of the electron beam on an RF or optical wavelength. Space-charge forces are predominantly longitudinal, with a sign opposite to the sign of the ponderomotive force; the effect is to reduce the growth rate and delay saturation of the amplifier.

We can estimate the importance of longitudinal space- charge forces by calculating them in the linear theory we have just described. The calculation is self-consistent only if the resulting forces turn out to be negligible compared with the ponderomotive forces:

We first calculate e, as if the space-charge forces were one-dimensional:

- eE, 4lie p e - = ~ = - L i- (15) mc2 mc2 (k,$ + k , )

where p is the bunched charge density, p and ez are both proportional to el(k~%, + k d z - . In terms of e;,

after picking out the + k,)Z - iat Fourier component of p . The electron beam is assumed to have a radius Yb .

Linearizing,

with

iSOj = [2k, + r + Ak;]

from (6) .

The ratio, in inequality (14), can then be written

where r is the growth rate in the absence of space-charge, as determined from (12). It is important to note that no “fill factor” appears for the space-charge forces; i .e. , ez 0: Zlxr;, but Z/(ab/2) enters into le,T(. This difference arises partially because we have used a one-dimensional approximation for l eZ l , but also because the field sources for j eZl and 1 e, I are different. The source for I e,] couples to the vacuum waveguide modes, while the source for !ez ( , because its phase velocity is less than c, does not.

Two-dimensional effects reduce space-charge forces by an amount dependent on (k,s + k,,.)r,,/y. We can estimate the reduction by treating the electron beam as a uniform- density, uniformly bunched cylinder in a cylindrical waveguide of radius b (the short waveguide dimension-still far enough away effectively to be at infinity). Solving the ap- propriate wave equation for E..,

a2EZ 1 a2Ez 41i aJ, a p az2 c2 at2 - c2 at az + 47r - (20)

and imposing E,- = 0 at Y = 03, we obtain a reduction in space-charge forces by a factor

where K , ( x ) is a modified Bessel function. For ELF parameters, with 500 A in a 1-2 cm2 beam, evaluation of these expressions yields !e,( (awfBe,T/y)-’ < 0.2. An effect of this size is marginally significant-it should eventually be included in the linear theory (and simulations) but does not invalidate the theory derived without space charge.

Several other effects not included in the theory or simulations contribute for ELF at the same 10-20 percent level. They are as follows.

i) Large y approximation. The distinction between dyidt and dyldz = (1lP;)dyidt is not preserved in (6 ) , and the Bessel function factor f B is calculated from the large y approximation for the longitudinal motion. These two corrections nearly cancel for ELF.

ii) The transport resonances (see Section IV below) en- countered in the ELF experiment are neglected.

iii) Coherent emission of third harmonics in ELF can be - 10 percent of the power emitted in the fundamental.

These corrections occur in ELF because of the rela- tively low electron energy and the large wiggler amplitude; for future high-energy induction linac driven FEL’s, they should be negligible as far as the FEL theory is concerned. Harmonic emission will always occur in a linear wigger 1251 and will be significant if a , >> 1. Even for ab$ = 1, however, high-power emission in the third or fifth harmonics (even if < 1 percent of the power in the fundamental) can be a serious problem for handling the output laser beam.

In order to study the performance of high-gain FEL am-

ORZECHOWSKI et ul .: FEL'S USING 1NDUCTION LINEAR ACCELERATORS 837

+

PSI (radians)

Fig. 6. The longitudinal ( y $ ) phase space of the electron beam in an FEL, after saturation. Electrons with $ > 0 lose energy to the laser field, and those with $ < 0 gain energy from the field; an excess of electrons with $ < 0 is responsible for the saturation of the amplifier. The three plots in the figure refer to three sets of simulation particles: the third with the smallest emittance (left), largest emittance (right), and the rest (center).

plifiers in detail, we have developed a two-dimensional (r-z) numerical particle simulation code. The code (named FRED) models the interaction of an axisymmetric laser beam with an axisymmetric electron beam in a helical or linear wiggler. A single ponderomotive potential well is followed in z ; thus, no time-dependent phenomena such as sideband instability growth can be studied at present. The laser beam is propagated under the paraxial approximation on a radial grid with -60 grid points between r = 0 and approximately ten times the laser beam waist. The electron beam source for the radiation field is modeled by - 2048 macroparticles which execute full betatron motion in the combined wiggler and external focusing fields (if any). The betatron motion arises from both the finite emittance of the beam and mismatch, if any, at the wiggler entrance. An individual particle's y and $ are advanced with the KMR equations, with y'@: averaged over a wiggle period. We used a predictor-corrector method of the type developed by Gear to advance the field and particle equations simultaneously.

To model ELF, the code operates in x-z space rather than r-z space and assumes a cos (ry/b) dependence in the y-plane. Thus, the TEol, TE,, , TE47, - - modes can be studied simultaneously. Alternatively, the code can op- erate in y z space and study the TEol, TEo3, TE,,, * . e

modes. The code can design its own tapered wiggler by de-

creasing a , with k , held constant. For nonwaveguide FEL's (i.e., 10 pm ATA designs), we taper a , such that a fictitious electron in a fixed circular betatron orbit (at r = rdeSign) remains at a positive $ = $,.. Permitting the value of $, to increase from zero to its final value over about half the synchrotron period increases the final trapping fraction.

The particles are normally loaded in an equilibrium distribution with either a Gaussian or a parabolic profile. The

- 1 $ 0.5

1

0 " ' , , c l , , , , d 0 1 2

2 (meters)

Fig. 7. Radiated power versus wiggler length as determined by two-dimensional simulation. Top curve shows uniform wiggler (note,saturation at 1.75 m); bottom curve corresponds to partially tapered wiggler (laser comes out of saturation). The starting conditions for this particular run do not correspond to the FEL experiment described in Section IV.

latter corresponds to a uniform density in four-dimensional phase space. The distribution is allowed to evolve naturally as the wiggler field is reduced in tapered designs.

FRED produces a set of output files that are then ana- lyzed by a post processor code. Various diagnostics such as laser power, phase front profiles, y-IJ phase space plots, and trapped particle fraction as a function of z have proved extremely useful. The codes are optimized to run on a CRAY-1, and for normal runs use 5 30 s of CPU time.

Fig. 6 and 7 provide examples of output from the code for simulation parameters similar (but not identical) to the parameters of the ELF microwave experiment (Section

838 lEEE JOURNAL OF QUANTUM ELECTRONICS. VOL. QE-21, NO. 7, JULY 1985

Focusing Matchtng 6 KA doublet doublets

To

(A or 6)

Conftguration A Wire mesh ,

Wiggler

e- - / To real t ime position monitor

/

Wire Configuratton B

mesh, Wlggler Mlcrowave

ou tpu t calorimeter or

crystal detectors]

Microwave input

Fig. 8. Schematic of electron laser facility (ELF), Configuration A is used to monitor the electron beam inside the wiggler as well as to measure the small signal gain of the system. Configuration B is the amplifier mode.

IV). Fig. 6 is a y-$ phase-space plot for an amplifier after saturation. Fig. 7(a) is a plot of microwave power versus z for an untapered wiggler; saturation occurs at z = 1.7 m. The phase-space plot of Fig. 6 was made at the end of the run shown in Fig. 7(a). Fig. 7(b) shows what happens to the power when the wiggler is linearly tapered (decreas- ing a,,,) by 10 percent from z = 1.5 m to the end of the wiggler. The power increases past saturation to produce a doubled output power.

IV. ELF: A MICROWAVE FEL We have designed and built an FEL operating in the

microwave regime using the ETA [31]. The purpose of this experiment is to test the physical models used to predict high-gain and high-efficiency FEL operation in the visible spectral region. The experiment, named the electron laser facility (ELF), consists of an amplifier with well-defined initial conditions on the radiation field and the electron beam. Furthermore, the experiment uses no axial guide magnetic field in the wiggler. The presence of this guide field can complicate the electron motion in the wiggler field as well as affect the gain of the laser.

ELF is designed to study the laser gain as a function of radiated frequency, beam current, and emittance, as well as input laser power. The’ experiment also can examine the effect of tapered wiggler magnetic fields, although in what is discussed here, a uniform (untapered) wiggler is em- ployed. A schematic of ELF is shown in Fig. 8. An emittance selector [32] is used to reduce the current and provide a well-characterized electron beam for ELF. Three quadrupole doublets are used to transport the beam to the interaction region (wiggler field). The planar wiggler magnetic field (vertically polarized) is generated by a

pulsed electromagnet. The interaction region consists of a thin-walled stainless steel oversized waveguide, which al- lows for good penetration of the wiggler field. Two different sized waveguides are available: 3 X 10 cm and 3 X 6 cm. The different sizes will enable us to study the effect of filling factor (ratio of e-beam cross section to radiation field cross section). We now describe each of these com- ponents in detail.

The emittance selector consists of 2.54 cm I.D., 2 m long tube immersed in an axial magnetic field. The volume of four-dimensional phase-space, SV,, accepted by the emittance selector is

where B,, is the axial magnetic field in the pipe, and is the radius of the pipe. The accepted four-volume is not precisely ellipsoidal, but the normalized edge emittance e N , defined as if the four-volume were ellipsoidal, is

The edge emittance E is defined to be the area (divided by a) of an ellipse in the two-dimensional (x, x ’ ) or 6, y ’ ) projection of phase-space that encloses the entire electron beam.

Since brightness [21] (density in phase-space) is con- served through the emittance selector, the transmitted current, Itran!,, scales as the square of the ratio of input beam emittance, tin, to transmitted beam emittance, etrans:

This relation holds as long as the phase-space occupied by the input electron beam is uniformly filled.

Fig. 9 shows our measurement of current transmitted through the emittance selector as a function of l?:,$. From (23), one can determine the emittance of the transmitted beam at any Bps. From (23) and (24), we determine the normalized emittance of the ETA beam to be 1.5 ( T ) rad. cm. We typically transmit 10 percent of the incident current through the emittance selector, corresponding to

Beyond the emittance selector, there is no longer an axial magnetic field to help guide the beam. Three quadrupole doublets are used to transport the beam and to match the beam onto equilibrium orbits in the wiggler field. The beam shape at the entrance to the wiggler is approximately circular. Viewing screens can be placed midway between the first two doublets and also between the third doublet and the wiggler, allowing us to examine the beam shape and size. By comparing the beam shape and size with transport code predictions for a given quadrupole transport configuration, we found that the beam emittance is consistent with that expected from the emittance selector.

Between the third doublet and the wiggler, a transition

= 0.47 (x) rad. cm.

ORZECHOWSKI et al.: FEL'S USING INDUCTION LINEAR ACCELERATORS

0.18 3 O ' I

0.14

0.12

~

! 0.3 0.4 0.5 0.6

Fig. 9. Fraction of beam current transmitted through emittance selector as a function of the square of. the magnetic field applied to the device.

,,---( ,_--._, \ x \ ,

Interaction re ton

Wiggler magnet form

Fig. 10. ELF wiggler magnet design showing rectangular solenoids and resulting wiggler field.

is made from elliptical beam tube to rectangular waveguide. At this point, the signal from the local oscillator is injected into the front of the interaction region and co- propagates with the electron beam. The input signal is reflected into the interaction region by a screen placed at 45" to the beam axis (see Fig. 8, configuration B). This screen is transparent to the electron beam and does not affect either its propagation (e.g., induce sausaging) or emittance. Furthermore, this screen blocks any electromagnetic noise generated in ETA from entering the interaction region.

The wiggler magnetic field is generated by two series of rectangular solenoids: one above the interaction region and one belaw. This wiggler design is illustrated in Fig. 10. Adjacent solenoids in the same series are energized in the opposite direction. Corresponding solenoids on the two series are also energized in the opposite direction. The

839

Fig. 11. 1 m section of ELF wiggler (3 m total length). Continuous quadrupoles provide horizontal focusing of the electron beam.

cusp field from the solenoids then forms the wiggler field; the axial component of the wiggler field cancels on the wiggler midplane. The wiggler field is then approximately given by

B , = B,v sin ( k ~ ) cosh (k,,,y)

B, = B, cos (k,z) sinh (k,y) (25)

where y = 0 defines the wiggle plane. The small axial field above and below the wiggler plane provides for vertical focusing of the electron beam. The field created by the wiggler magnets is slightly defocusing in the wiggle plane. In order to -stabilize the electron beam in this dimension, we used horizontally focusing quadrupoles with a gradient of 30 G/cm. This introduces less than 4 percent perturbation to the wiggler field at the edge of the waveguide (x = It5 cm), and is substantially smaller in the electron beam region. A 1 m section of a completely as- sembled wiggler magnet plus quadrupole is shown in Fig. 11.

Each two periods of the wiggler magnet is energized by its own independently controlled power supply. Thus, the profile of the wiggler magnetic field along the beam axis can be tailored to almost any desired shape. The power supply is an ignitron switched capacitor, and the rise time of the current through the wiggler coil is 640 ps. To en- sure that the wiggle axis of the beam coincides with the axis of the wiggler, the first period of wiggler is energized to (0.3BW, - 0.8BW) and the last period is energized to (0.8B,v, - 0.3Bw) where B , is the peak wiggler field inside the uniform wiggler.

For the 34.6 GHz experiment described here, the input signal to the amplifier is provided by a 60 kW pulsed mag- netron (pulse length = 500 ns). The output of the mag- netron is converted from the TElo mode of the fundamental rectangular waveguide to the TE,, mode of the oversized FEL waveguide (interaction region) by means of waveguide tapers. The insertion loss (including mode conversion) of the waveguide tapers and reflecting screen

is 3 dB, leading to 30 kW of microwave power injected into the interaction region.

The beam current into and out of the wiggler is monitored with conventional resistive wall current monitors 1341 built with the dimensions of the oversized waveguide. ELF’S microwave output is monitored with either a com- mercial vacuum laser calorimeter (ADKIN model LC-1, measured absorption = 0.072 for TEol mode at 34.6 GHz), or calibrated crystal detectors preceded by approximately 100 dB of attenuation. The first 46 dB of attenuation was provided by diffraction losses as the microwave beam propagated through air. A large area transmitting horn was required at the output of the FEL waveguide to reduce the electric field at the air-vacuum interface in order to avoid air breakdown. When the calorimeter was used, the time dependence of the microwave pulse could be monitored with a crystal detector which sampled the output radiation through a small aperture in the oversized waveguide.

Initial experiments were unsuccessful because of difficulty in properly matching the electron beam into the wiggler. One difficulty resulted from a large perturbation to the front of the wiggler field due to the ferrite in a current monitor very near the entrance of the wiggler. In addition, the wiggler and vertical betatron motion can couple through the quadrupoles, leading to a resonance which se- verely perturbs the electron orbits and can result in the beam hitting the wall 131). To avoid this instability, the initial vertical displacement of the beam (including beam center and radius) must be kept small (< 1 cm). An axial beam probe 1361 was constructed to monitor the position of the electron beam in the wiggler field. This probe could move through the entire three meters of the interaction region. The probe filled the waveguide (3 X 10 cm), and intercepted the beam with a Ta target (3 mm thick). The resulting X-rays (scattered in the forward direction) were monitored with an NElo8 scintillator and an array of 36 light pipes which were connected to a Reticon camera system. This probe head is illustrated in Fig. 12(a). Using this probe, we could determine the location and approxi- mate size of the electron beam. A video output image is shown in Fig. 12(b). The vertical spacing between light pipes is 5 mm while the horizontal spacing is 9.4 mm. This probe was moved along the interaction region at a rate of 5 mm/s, which gave us the beam position every centimeter in the wiggler (112 Hz operation). Using this system, we could monitor the beam in the wiggler on a real-time ba- sis. When the errors with the wiggler field were corrected and the beam was properly matched in the wiggler, we could get better than 80 percent of the beam through both the beam tube transition (circular to rectangular cross section) and the 3 m wiggler.

After the beam was adequately matched to the equilibrium orbit in the wiggler, the axial probe could be used to monitor the gain of the system in the superradiant mode. This was accomplished as follows. When the axial probe was inserted in the interaction region, the source for the injected microwave signal was replaced with a microwave attenuator and crystal detector. Any microwaves gener-

Lead houslng for

3mm/ / \uy

L F i b e r op t~cs

Scintlllator NE108

(b)

Fig. 12. (a) Schematic of wiggler probe head used to monitor beam position inside wiggler. (b) Typical output signal of probe showing beam in the center of the wiggler.

ated in the interaction region between the wiggler entrance and the location of the axial probe were reflected off the probe face into the microwave detector (note that the crystal is in the fundamental guide (KA band) so only the signal in TE,, mode in the oversized guide is measured). This is illustrated in Fig. 8, configuration B. As the probe is pulled out, the interaction region is length- ened. Fig.13 shows the results of these measurements for a beam energy of 3.6 MeV (y = S.l), beam current of 450 A, and a peak wiggler field of 4.8 kG. The microwave signal grew from noise at a rate of 13.4 dBim. Extrapo- lating this signal back to the wiggler entrance gives an effective input noise signal of 0.35 W. While this noise level is quite small, this is still about an order of magni- tude larger than one would calculate for single particle radiation at this frequency region into the TEol mode [36].

Using the flexibility inherent in our wiggler design, we studied amplifier gain as a function of wiggler magnetic field intensity and as a function of wiggler length. In order to study the amplifier as a function of length, a section of the wiggler of length L, was energized to the desired field B,,,, while the remainder of the 3 m long wiggler was set at 0.7B,$,. This reduced wiggler field should not have con- tributed to the FEL interaction since it was well away from

ORZECHOWSKI et al.: FEL’S USING INDUCTION LINEAR ACCELERATORS 841

1 o4

1 o3

I

u( c

I z 102 2

10

I I

Small signal gain

Effective P,,,,, = 0.35W

z (meters]

Fig. 13. Microwave power reflected off the face of the axial probe as a function of probe position in the wiggler. The slope of the line gives a power gain of 13.4 dB/m. Extrapolating back to zero implies an effective noise (from which the signal grows) of 0.35 W.

resonance, but it provided beam transport through the remainder of the wiggler to the current monitor at the end of the wiggler. We could thus measure the current in the interaction region at all times.

The output power as a function of wiggler field strength is shown in Fig. 14 for L, = 1, 2, and 3 m. The beam energy in these measurements is 3.3 MeV and the beam current is 450 A. Also shown in these curves are the results from the numerical simulation code, FRED, for each of these cases. The amplified signal for L, = 1 m is 1 MW, while for the 3 m long wiggler it is near 80 MW. The measured gain curves for L , = 1 and 2 m are nearly symmetric, while the gain curve for L,“ = 3 m wiggler shows a marked asymmetry: a plateau has developed on the low- frepsncy (high magnetic field) side of the gain curve. As the wiggler length is increased, the peak of the gain curve decreases from 4.28 kG for the L, = 1 m to 3.95 kG for L,v = 3 m.

At the magnetic field strength corresponding to the peak output of the 1 m long wiggler, we examined the amplifi- cation as a function of wiggler length. The results of this experiment are shown in Fig. 15. It is clearly seen that the amplifier goes into saturation at L, = 2.2 m. Beyond this point the output power of the FEL first decreases, then, near L, - 2.6 m, starts to increase again. We attribute this variation in output power beyond saturation to the synchrotron motion of the electrons trapped in the ponderomotive well. Before saturation, the output power as a function of wiggler length shows an exponential gain of approximately 15.6 dB/m. This value agrees well with the small signal gain measurement described above (G = 13.4 dB/m). The gain in the exponential regime scales with

0.9

0.8

I

d 0.4

0.3

0.2

0.1

0 Experlment

0 2-D simulation

3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4 . 5 4 6

B, IkiloGaussI

Fig. 14. Measured and calculated gain curves (P, versus B,) for a 1, 2, and 3 m long uniform wiggler.

B,/y3” and this value is similar in both experiments (0.21 versus 0.20). (The gain, for a high emittance beam, does not depend on B,ly3” or B,213y. The important scaling parameter, though, is the ratio of which is nearly identical for the two cases.)

The dashed curve in Fig. 15 shows the result of the numerical simulation for this experiment. The analytical theory and two-dimensional code used to analyze FEL performance have been described in a previous section. In attempting to model the experimental results, all but one important experimental parameter is known. This un- known parameter is the extent to which the electron beam is mismatched into the wiggler. If we model the mismatch

842 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-21. NO. 7, JULY 1985

0.8

0.7

0.6

a 0.5 4-

5 mz 0.4

- X

La 0.3

0.2

0.1

I / / ; Experiment ~

I 1 2 3

0 2-D simulation

Z (meters)

Fig. 15. Microwave power emitted as a function of wiggler length. Note that the FEL goes into saturation at 2.2 m (experimental).

as a sausaging oscillation of the electron beam in the wiggler, then a single value for the maximum beam radius (rb = 0.8 cm) is adequate for both the linear theory and for the numerical simulations to model the observed exponential gain and saturated output power. With the ex- ception of the L, = 1 m gain curve, the predictions from both the simulation and the linear theory (exponential gain) agree both in shape and in amplitude to within 25 percent of the experimental results. In particular, the code cor- rectly predicts the variation of output power with wiggler length beyond saturation and the asymmetry in the 3 m gain curve. The discrepancy between the measured and calculated 1 m gain curve is probably a result of small signal measurements as well as the difficulty in calculating small extraction levels in the presence of numerical noise; the difference between measured and calculated power at the peak of the 1 m gain curve corresponds to a 10 percent discrepancy in exponential growth rate.

V. 10.6 pm EXPERIMENT An FEL experiment is now being designed for the 50

MeV, 10 kA advanced test accelerator. The object of the experiment is to test models which predict that both high gain and efficient energy extraction can be achieved in an optical FEL power amplifier. Operation in both the exponential gain regime and trapped-electron, saturated-amplifier regime will be studied.

The experiment will be composed of a conventional 10.6 pm laser oscillator and an FEL power amplifier. Our baseline experimental parameters are listed in Table I. The wiggler will be a “hybrid-hybrid”- with both SmCo and electromagnets exciting specially geometrically tailored polefaces. We plan to do initial experiments with a 5 m wiggler and low power laser source. This configuration will be used to measure small signal exponential gain and verify the performance of both beam transport and wiggler systems. Wiggler accuracy will also be checked by measuring the spontaneous radiation spectrum as the wig-

TABLE I BASELINE ATA/FEL EXPERIMENTAL PARAMETERS

Energy 50 MeV

Wavelength 10.6 mlcrons

Wiggler Per iod 8 cm

Wiggler Peak F i e l d 2.3 kG

Normal ized Edge Emi t tance 0.14 rad-cm

E l e c t r o n Beam I n i t i a l Radius 0.45 cm

Inpu t Lase r Beam Waist 0.36 cm

Output Laser Beam Waist 0.64 cm

Wiggler Length 25 m

gler is trimmed with electromagnets. We expect exponential gains in excess of 10 in an untapered wiggler.

Experiments will then proceed with a longer wiggler and high-power laser source. This will permit an investigation of tapered wiggler operation. These experiments are designed to work at normalized edge emittances of 0.1-0.2 rad - cm. The amount of current passed through the wiggler”wil1 depend on the brightness achieved with ATA. We expect large signal gains in excess of 5 with extraction efficiencies of - 10 percent. Improved brightness (as has been demonstrated with new injectors) [21]- [24] should greatly enhance the FEL’s performance. Of particular interest in these experiments are the effects of refractive index guiding in a wiggler many Rayleigh ranges long [27].

VI. CONCLUSION High-current electron beams from induction linear ac-

celerators are presently being used in high-power FEL experiments. A microwave FEL has successfully operated with 80 MW of output radiation (34.6 GHz) using a 500 A, 3.3 MeV electron beam produced by the ETA. A 10.6 pm FEL is being designed and will use the 50 MeV beam from the ATA. This device is scheduled for completion in mid-1986.

The microwave experiments are adequately modeled using a two-dimensional FEL code: FRED. The exponential gain regime can be explained by a model based on the linearized equations of motion in y-$ space. Both the code and the analytic model neglect space charge. Even at the long wavelengths in the microwave region, this is allow- able when the finite transverse dimensions are properly accounted for (X, - rb).

ACKNOWLEDGMENT We wish to thank the members of the Beam Research

Group at LLNL for the support in conducting the experiment as well as for helpful comments, suggestions, and explanations on various aspects of induction accelerators and relativistic electron beam physics.

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ORZECHOWSKI et a l . : FEL’S USING INDUCTION LINEAR ACCELERATORS

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7 2 (61) 3 = - @*Y2SV,

where 6I is the current enclosed by the four-volume SV, in transverse phase space, @ = u/c. and y is the Lorentz factor of the electron beam. This definition differs from the definition of normalized brightness

843

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B. Anderson, photograph and biography not available at the time of publication.

V. K. Neil, photograph and biography not available at the time of publication.


W. M. Fawley, photograph and biography not available at the time of pub- D. B. Hnpkins (S’56-M’59), photograph and biography not available at the lication. time of publication.

D. Prosnitz, photograph and biography not available at the time of publication. A. C. Paul, photograph and biography not available at the time of publi-

cation.

A. M. Sessler, photograph and biography not available at the time of publication.

J. S. Wurtele, photograph and biography not available at the time of publication.

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