INDEX. Abstracts of articles,

Transcription

1 Abstracts of articles, Accelerator(s) electrostatic, see Electrostatic accelerators examples of, induction, 607 QIUCSB DC, 606 for single-pass FELs, , 695 two categories of, 648 ACO storage ring, 344, 353, 698 ADONE storage ring, 344, 353, 481 angular distribution measurements in, 485 FEL Experiment with, intensity distribution of peak wavelength in, ADONE wiggler magnet parameters of, spontaneous radiation from, 698 Alfven current, 648 Amplification experiment, at Frascati National Laboratory, 497, see also Free electron laser amplification Average energy loss, see also Energy loss vs. initial electron energy, 258 vs. initial radius, 255 vs. initial slant angle, 257, 261 vs. initial transverse velocity, 256, 260 vs. injection radius, 259 Axial distance, vs. normalized radiation amplitude, Axial velocity shear, and transverse spatial gradients in wiggler field, 233 Backscattering process, kinematics of, 562, see also Raman backs ca t te ring Ballistic regime, electron beam energy and, Bambini-Renieri-Stenholm one-electron Hamiltonian, 122 Beam emittance, 341 Beam waist oscillations, for relativistic electron beam, 318 Bell Laboratories tunable FEL, 536 Bending magnets, in storage ring layout, , 483, see also Magnet Betatron motion amplitude variation, in synchrotron emission process, 354 Betatron oscillations, transverse, 415 Betratron phase advanced turn, 431 Betatron tune, for LEDA-Fl, Block equations, for electron distribution, Block vector, 141, 165 Bremsstrahlung FELS analysis of,

2 686 Bremsstrahlung FELS (continued) basic difference from Cerenkov- Smith-Purcell FELs, 2 coupling coefficient for, 33 coupling parameter for, 31 electromagnetic eigenmodes in, 9 electrostatic, 37 magnetic, see Magnetic bremsstrahlung FEL as special case of Compton-Raman scattering, 2 susceptibility function for, 35 in unified theory, 685 Bucket effective height, 255, capture energy spread an4, 259 vs. electron energy spread, 267 Bucket energy, diabatic decrease in, 265 Bunched beam, see also Electron bunches spontaneous radiation by, stimulated emission by, coherent emission from, Bunched input distribution, 468 Buncher, see Electron buncher Bunching coefficients, 580 Bunch length, defined, Bunch lengthening, for ADONE, Canonical momentum components, 37 Catalac, in racetrack energy' recovery system, 278 Cavity length shortening, power output and, 183 Cavity resonator, amplification of, 534 Cerenkov-Smith~Purce11 FEL, see also Smith-Purcell FEL analysis of, coupling coefficient for, 33 coupling parameter for, 30 Cerenkov-Smith-Purcell FEL, ( continued) difference with bremsstrahlung FEL, 2 electromagnetic eigenmodes in, 9 gain parameter for, 61 unified theory of, 685 Chao-Gareyte model, 492 Characteristic coefficient, 338 Classical equations of motion, CNEN Frascati Center, FEL-microtron activity at, Coherence brightening, 182 Coherent radiation sources, earliest, 190 Coherent scattering, Coherent states, Coherent X-ray generation, optical klystron for, Cold beam gain regime, efficiency at, Cold beam high gain collective regime, Cold beam high gain-strong couping regime, Cold beam low gain regime, 45, 79 Cold electron beam, electrostatic dispersion relation for, 543 Collective interaction lasers, basic processes in, Collective variable, defined, 161 Columhia-NRL FEL, 132, 525 efficiency of, 535 layout of, 533 Columbia University, Pulserad 220 facility at, 536 Common gain-dispersion relation, 38 Compton-Raman FEL, 17 coupling parameters for, 31, 36 electron beam pumping in, 36 gain parameter for, 61

3 687 Compton-Raman FEL, (continued) interaction width limitation in, 78 quiver momentum amplitude for, 37 Compton-Raman scattering, see azso Raman Scattering bremsstrahlung FEL and, 2 TEM wave and, 10 unified theory of, 685 Compton scattering, stimulated, Constant parameter wiggler, Converter, electron beam as, 572 Coupling coefficient, 357, 363, 383 Coupling constants, as strong signal regime, 161 Coupling width, expression for, Courant-Snyder invariant, 340 Courant-Snyder theory, 607 Crossed polarizers, separation of input beam and input emission by, 271 Cut-off frequency correction, 545 Cyclotron mode, 524 e.b., see Electron beam; Electron bunches Efficiency, interaction length and, 70 Efficiency coefficient, for various gain regimes, 64 Efficiency enhancement, by electron beam re-acceleration, variable wiggler method of, 554 Electromagnetic mode, fields of, Electromagnetic power output, as function of helical magnetic field, 549 Electromagnetic pump wave, 514, 517 Electron beam ballistic regime and, in foilless-diode geometry, high quality requirement for, periodic focusing of, 233 relativistic nature of, 3-4 schematic of, 231 transverse dimensional effects and, Electron beam average velocity, 574 Electron beam collector, for UCSB Damping constant, 349 Damping partition numbers, 349 FEL, Daresbury Laboratory Science Electron beam cross section, in- Research Council, crease in, 72 Detuning parameter, gain and, Electron beam distribution, 213 Diffusion coefficient, 351 Electron beam dynamics, in drift Dispersion functions, in storage space ring, 425 Electron beam emittance, 213, 601 Dispersion relation Electron beam energy, output freformal derivation in, quency and, 544 normalization of, Electron beam energy spread, Distribution function, source of, transformation to (EBS)b sys- Electron beam lifetimes, in LELA tem, 594 experiment, 494 Doppler-shifted laser frequency, Electron beam parameters, in FEL microtron activity, 300- Drift space, electron beam dynam- 301 ics in, Electron beam prebunching, 551 Dump chicane, in racetrack energy recovery system, 278 Electron beam re-acceleration, efficiency enhancement by,

4 688 Electron beam requirements, , Electron beam rest frame, simulated scattering in, 503 Electron beam system, improvement, 268 Electron beam transport channel, achromatic, 362 Electron buncher beam dynamics in, as converter, Electron bunches, see also Electron bunching in FEL theory, formation of, 177 Gaussian distribution for, interaction with laser and wiggler field, 143 lethargic delay and, overlapping between laser and, 388 radio frequency accelerating system and, 216 in stronger fields, 198 Electron bunching coherent emission in, Monte Carlo simulation of, in relativistic klystron, 558 spontaneous radiation and, Electron bunch length, Electron distribution, dense or cold, 502 Electron distribution function evolution of, 100 transformation to (EBS)b system, 594 Electron energy, defined, 600 Electron energy loss, see also Energy loss average, see Average energy loss three-dimensional calculation in variable-parameter FEL, , 686 Electron energy spread, Electron energy transfer, to radiation field, 99 Electron-field coherent states, defined, 134 Electron motion, design code equations for, 276 Electron phase-space evolution, , see also Phase space Electron phase space trajectories, 253, 468 Electrons bunch of, see Electron bunches equations of motion for, Electron storage rings, see Storage rings Electron trajectory nominal, 428 phase space, 253, 468 random spread of, 528 Electron velocity spread, limitations on, Electrostatic accelerator FEL, electron beam requirements for, with energy recovery, with no energy recovery, two-stage FELs using, , Electrostatic bremsstrahlung FEL, quiver momentum amplitude for, 37, see also Bremsstrahlung FEL Electrostatic dispersion relation, 27-48, 543 Electrostatic generator, 606 Emittance growth, for off-axis initial motion, 429 Energy evolution equation, derivation of, 446 Energy loss average, see Average energy loss vs. initial electron energy, 254, 258 vs. initial radius, 255 vs. initial slant angle, 257, 261 vs. initial transverse velocity, 256, 260

5 Energy loss (continued) vs. injection radius, 259 Energy-phase bucket, electron capture in, 250, see also Bucket effective height Energy sustainer, schematic of, 470 Equations of motion classical, for electrons, linearized, modifications to, in storage ring laser, 470 in wiggler field, Exact trajectories, Expanded gain, normal regime and, , see also Gain; Gain-expanded FEL Fabry-Perot resonator, 3, 531 Far infrared frequencies, metal mesh filters for, , 693 Far infrared generation, FEL components for, 312 Fast rotating vectors, vs. slow coefficients, 193 Fast running phase, , 370 FEL, see Free electron laser FELIX experimental facility, , 698 beam transport system of, l components of, design philosophy of, diagnostics of, 291 electron linac for, 290 electron source for, experimental program of, as far infrared source for research, 293 gain optimization for, laser system for, 291 main parameters of, output power and tuning for, 289 periodic magnet for, ELIX Experimental facility, (continued) purpose of, FEL-ndcrotron activity, at CNEN Frascati center, FELIX optical klystron, 292 Field modulus, time evoluoion and, l35 Filling factor, 192 Finite beam energy spread, gain and, 526 Finite transverse dimensions, of radiation and electron beam, 230 Flouquet-Bloch mode, in C-S-P FEL, 9 Flouquet mode, orthonormalization of, 13 Flouquet theorem, 12 Foilless-diode geometry, electron beam and, Fokker-Planck equation, 351, 370 Fokker-Planck formalism, 366, 390 Four-element metal mesh filter, for far infrared, Frascati microtron, Frascati National Laboratory, FEL activity in, Free electron laser, see also Laser accelerator fundamentals for, advantages of, 91 analysis of, applications of, 541, 702 bremsstrahlung, see Bremsstrahlung FELs Cerenkov-Smith-Purcell, see Cerenkov-Smith Purcell FEL characterization of in different regimes, 541 classical equations for, 123 classical theories of, 93 classical trajectories of, 121- l37, 689 coherent states in, , 689 Co lumbia-nrl, 132 component wave numbers for, 8

6 690 Free Electron Laser (continued) conceptual design of, configuration of, 231 vs. conventional lasers, 178 coupling parameters for, cross-section diagrams of, 74 differences from conventional lasers, , see also Laser dispersion diagrams for, 6 dispersion gain relation in, distributed feedback in, 535 efficiency of, 65-67, 378, 389, 403, , 535, 617 efficiency enhancement for, , , 692 electromagnetic wave-electron beam interaction, 11 electrostatic accumulation in, electron dispersion relation for, 543 electron beam parameters in, electron beam requirements for, 604 energy transfer in, 91 exact dynamics of, for far infrared, , 693 first successful operation of, 189, 295 frequency vs. beam voltage for, 546 gain function in, gain parameter for, Hamilton picture of, high-gain millimeter and submillimeter, 501 infrared and ultraviolet, , 311, 319, 542, 693 injection-mode locked, 270 intense-beam, 514 interaction range in, interaction schemes in, 5-6 kinematics of, 11 laser action in, LELA parameters for, lethargy effect in, , 218, 383, 393 Free Electron Laser (continued) low beam energy experiment with, 691 low gain regime in, many-particle theory of, 121 multimode analysis of, GH~ experiment in, 548 nonlinear theory of, , one-dimensional model equations for, operating conditions for, operating principles of, 92-94, 190, 264, 311, 597 optical technology of, 695 parameters of, 250, 332, 615 periodic segments for, in photochemistry, physics of, practical problems of, 366~ 367 pulse propagation and laser technology in, radiation condition for, 5-10 Raman regime in, 50-52, 518 relativistic electron beam, schematic of, 92, 139, 269 single-particle equations of motion for, single-pass vs. conventional, 243 small signal regime in, spectral width of, Stokes diagrams for, 506 storage ring operation of, , 488~489, 686, 688 storage ring parameters for, submillimeter, swept-gain, 178 system of equations describing, 109 theory of, D effects in, transverse gradient in, 689 tunable, 536 two-stage, 516, 518 types of, 2

7 691 Free Electron Lasers (continued) unified linear formulation of, 1-84 uniform waveguide in, 15 USCB model, variable wiggler form efficiency enhancement of, Vlasov equation for, wave and particle dynamics for, , 685 wiggler magnetic field. in, 93, see also Wiggler; Wiggler magnetic field Free electron laser action, as stimulated Compton backscattering or magnetic bremsstrahlung, 190 Free electron laser amplification, principle of, Free electron laser amplifier efficiency of, 378, 535 high gain, 688 schematic representation of, 4 Free electron laser amplifier regime, Free electron laser beam, spacetime structure of, 106 Free electron laser cavity, with intracavity filter, Free electron laser components, for far infrared generation, 312 Free electron laser experiment, in ADONE, GHz, 548 Redondo Beach, Free electron laser gain regimes, 43-59, Free electron laser interaction, physical mechanism associated with, 542 Free electron laser microtron device characteristics of, 298,303 experimental layout for, 302 laser beam characteristics for, Free Electron laser microtron device (continued) wiggler and transport channel performance in, Free electron laser noise, 367 Free electron laser operation, see Free electron laser, operating principles of as second-order phase transition, 201 Free electron laser operator, in storage ring, Free electron laser oscillator, laser beam parameters and, numerical results for threshold regime in, operation of, 192 in optimum operating regime for, steady state equations for, in storage ring, , 403 threshold regime in, Free electron laser parameters, 250, 332, 615 Free electron laser power, Free electron laser program, ultimate goal of, 263 Free electron laser theory in multimode regime, 687 multimode small analysis of single-pass operation, 694 Vlasov-Maxwell description of, Free electron laser waveguide structure, electromagnetic modes excitation in, Functional cancellation, of transverse excitation, Function X, laser power density e-beam width, and laser frequency in, Fusion, FEL uses for, 699 Gain, detuning parameter and, Gain coefficient ratio, 384 Gain curve function, for maxwellian distribution, 56

8 692 Gain curves, Gain expanded FEL, cancellation of transverse excitation in, electron dynamics and characteristic regimes in, gain curves in, Gain-expanded wiggler, 295, see also Wiggler Gain expansion electron energy and transverse position in, 425 high-energy extraction regime and, undulator for, with zero vertical dispersion, Gain expansion mechanisms, 77 Gain expansion technique, 413 Gain experiment, at Los Alamos Scientific Laboratory Gain function, , 648 Gain parameter, electron beam energy and, 62 Generating function, for magnet structure, 455 Group slippage, between electron and photon bunches, 382 Hamiltonian in FEL theory, physical meaning of, 145 Harmonic number of rf system, 345 Hartree approximation, 161 Heisenberg equations of motion, 123 High-energy extraction regime, High-field wiggler, , see also Wiggler High gain collective regime, stimulated scattering in, 517 High quality accelerators, requirements for, , see also Accelerator(s) Hole burning effect, in gain curve of warm beam FEL, 71 Induced emission, laser beam amplification and, Induction accelerator, 607 INFN, see Frascati National Laboratory Infrared free electron laser, , 673, 693 Infrared generation, with FEL, 542 Infrared multiphoton dissociation, isotope selective, Injection chicane, in racetrack energy recovery system, 278 Injection energy coordinate, vs. l-aser energy loss reduction, 476 Intense-beam free-electron lasers, 514 Interaction range, Interaction variable, advantage of, 125 defined, 124 time history of, 149, 165 Interaction width limitation, 78 Intracavity filter, for far infrared, Intracavity optical amplitude, enlargement of, 199 Isochronous storage ring laser, , 697 operational characteristics of, threshold condition for, 479 Isomagnetic machines, equation for, 352 Isotope selective infrared multiphoton dissociation, Isotope separation, of sulfur and carbon, 676 ith interaction variable, 152 ith laser mode pseudo Rabi frequency of, 150 time dependence of, 148 variation of action in, 151 ith laser mode frequency, 150, 162, 368 ith laser mode wavenumber, 368

9 Kapitza injection, in IDicrotron, 298 Large coupling width regime, 381 Laser, see also Free electron laser collective interaction, infrared and ultraviolet, 673 performance data for, 675 radiation features of, 669 tunable high-efficiency, 263, 672 Laser efficiency , see also Free electron laser, efficiency of Laser energy loss reduction, vs. injection energy coordinate, 476 Laser frequency Doppler-shifted, stabilization of, 534 Laser lethargy, , 218, 313, 393 Laser modes, evolution equations for, Laser optical waves, waveform for, Laser power density, at FEL interaction starting time, 387 Laser signal power density, 267 LASL, see Los Alamos Scientific Laboratory LEDA-F1, F2 machine, betatron tune for, damping in, longitudinal motion in, off-energy transverse motion for, optical functions for, 340 o and o. Eo parameters for. 353, 364 transverse beam dimensions for, Ledatron, 3 LELA experiment, , 699, see also ADONE; Frascati National Laboratory optical parameters in, Lethargy effect, , 218, 383, 393 Linac accelerator, 279, Linear system, vs. storage ring system, 469 Livermore induction accelerator, 607 LNF, see Frascati National Laboratory Longitudinal magnetic bremsstrahlung FEL, gain parameter of, 61, see also Bremsstrahlung FEL Longitudinal motion, in LEDA Fl, F2 experiments, Long-pulse FEL, laser signals from, 537 Lorentz force, in bremsstrahlung FEL, 34 Lorentz force equation, 13, 193 Lorentz theorem, Los Alamos Scientific Laboratory FEL development program at, , 694 racetrack experiment at, Magnet constant-field, 461 excitation-cancelling vs. nonexcitation cancelling, 460 functional cancellation, 461 periodic, Magnetic bremsstrahlung FEL, see also Bremsstrahlung FELs coupling parameters for, 31 gain dispersion relation for, 36 Lorentz force in, 34 low-gain regime for, 49 quiver momentum amplitude for, 37 unified theory of, 685 VLASOV equation linear response theories for, 34 Magnetic field, periodic, 425 Magnetoresonant superradiant signal. 532

10 694 Magnetostatic wiggler, 514 Magnetic period, deviation of, 456 Many-particle theory, 121 Marx-Bank energy store, 527 Maximum power generation, interaction range and, Melekin injection, in microtron, 298 Metal mesh filter for far-infrared frequencies, four-element, Metal mesh grid, two-dimensional, 313 Microtron, see also Free-electron laser-microtron device as accelerator for single-pass FEL, characteristics of, 298 in CNEN Frascati center, layout of, 297 operating principle of, 296 particle injection in, Microtron-FEL characteristics, Microtron source, development of, 536 Microwave power, as function of beam energy, 553 Mode competition and cooperation, 71 Momentum compaction, 347 Momentum conservation diagrams, Monoenergetic electron beam, transverse motion for, 336 Motion in vertical plane, Multimode FEL theory, , see also Free electron laser theory Multimode small signal regime, Multiphoton mass spectrometry, ultraviolet-laser-induced, Multiple-scaling perturbation theory, 177 Nonmonochromatic electron beam, gain for, 105 Off-axis motion, 429, Off-energy transverse motion, in LEDA-Fl, F2, On-axis initial motion, One-dimensional model, equations for, One-particle theory, 132 Optical bucket, electron tripping in, 243 Optical cavity parameters, in LELA experiment, 498 Optical functions, in LEDA-Fl and F2, 340 Optical klystron for coherent X-ray generation, , 690 idealized, 560 in LELA xperiment, 499 Optical parameters, in LELA experiment, Optical power density, parameters for, 463 Optical pulse intensity, for Stanford pulse resonator, 184 Optical pulse spectrum, for Stanford FEL, 185 Optical system, improvement in, Optical trap electron trajectories in, 474 existence of, momentum compaction in, 474 size of, 473 Optical wave evolution, Optimum operating regime, of FEL oscillator in SR, Orotron, 3 Oscillator emission, as function of position of movable short, 550 Oscillator experiment at Frascati National Laboratory, in Los Alamos Scientific Laboratory, 279 Oscillator operation, principle of, 191

11 Output frequency vs. beam energy, 544 Raman REL efficiency as function of, 511 Output scattered wave, growth rate of, Parallel beam energy spread, 526 Particle dynamics, Pendulum analogy, , failure of, 128 Pendulum approximation, Pendulum equation as electron equation of motion, 470 electron evolution and, 197 quasi form of, 416 Pendulum-like trajectories, 130 Pendulum phase-space, Pendulum potential, self-cons isten t, 197 Pendulum magnet, , 696 Periodic magnet, see also Magnet construction features of, lineshape of, magnetic field calculations for, performance limitations of, with transverse gradient, 425 wiggler, 274, see also Wiggler magnet Phase contributions, 155 Phase equation, derivation of, Phase evolution equation, 438 construction of, 452 for constant period magnet, 453 Phase-matching condition, 6 Phase-matching diagrams, Phase shift, particle trajectories as function of, 478 Phase space electron motion in, 607 of simple pendulum, 193 Phase-space bucket parameters, 252 Phase-space diagrams, Phase-space electron trajectories, 98, 468 Phase-space evolution, Phase-space trajectories, 468 Photochemistry, FEL applications in, Photoionization mass spectrometry, experimental arrangement for, 679 Plasma dispersion function, 40 Polac, in racetrack energy recovery system, 278 Power output, cavity length shortening and, 183 Power-tuning curves, pulse propagation and, 182 Prebunched electron, microwave emission from, 552 PRF, see Pseudo-radiation field Pseudo-harmonic motion, for LEDA Fl, 229 Pseudo Rabi frequency, of ith mode, 150 Pseudo-radiation field, 140, 359 Pulse calculations, basic equations for, 181 Pulsed free-electron laser, physics of, , see also Free-electron laser Pulse energy, renormalization of, 180 Pulse propagation laser lethargy and, schematic diagram of, 176 Pulserad 220 facility, Columbia University, 536 Pump amplitude maximum gain vs. density for, superradiant power spectral width and, 532 superradiant stimulated Raman backscattering and, 530 Pump waves, 514, 517 Quasi-Bloch equations, 181 Quasi-pendulum equation, 416, see also Pendulum equation Quiver momentum amplitude, 37

12 696 Racetrack energy recovery system, at Los Alamos Scientific Laboratory, 278 Radiation amplitude, vs. axial distance, Radiation beam schematic of, 231 transverse dimensional effects in, Radiation field design code equations for, 276 evolution of, , Radiation storage, in Stanford laser, Radiative power, equation for, 72 Radiative trapping trajectories, Raman backscattering stimulated, , 693 superradiant stimulated, 530 Raman high-gain collective regime, 50-52, 508 Raman regime REL efficiency as function of output frequency, 511 with quasi-optical cavity, 518 two-stage, 519 Raman scattering, insulated, Ramdom-phase approximation, criteria for, 432 Recirculated electron-beam machines, 696 Relativistic electrons, beam waist oscillations for, 318 Relativistic klystron, electron bunching in, , see azso Optical klystron Repetitive pulsing, 536 Resonant electron energy, 96 Resonant frequency, equations for, 169 Resonator length, in Stanford laser, rf acceptance, in LELA experiment, Robinson's theorem, 349 Scattered field, expression for, 564 Scattering coherent, kinematics of, 567 Raman, SCS, see Stimulated Compton Scattering Short-pulse evolution, Single-particle dynamics, in FEL storage ring, Single-particle equations of motion, Single-pass FEL analysis of, vs. conventional FEL, 243 Slow-running phase, 163 Slowly varying equations, 193 Slowly varying phase, 164 SM, see Super mode Small coupling width regime, 381 Small signal analysis, Small signal analysis, multimode, 688 Small signal gain, in LELA experiment, 490 Small signal regime, 97-99, Smi th-purcell FEL, see azso Cerenkov-Smith-Purcell FEL analysis of, coupling coefficient for, 33 coupling parameter for, 30 gain parameter for, 61 Space charge effect, 47 Space charge wave idler, 524 SPEAR storage ring, 344, 354 Spectrum measurements, in forward direction, 482 Spontaneous optical klystron, 572, see azso Optical klystron Spontaneous radiation, from wiggler magnet, Spon taneous synchron tron radiation emission, in wiggler magnet, SR, see Storage ring

13 Stanford pulsed FEL, radiation storage in, resonator length in, Stanford superconduc ting linac, 295 Stanford University, first FEL operation at, 295 Stimulated Compton scattering, 140, Stimulated Raman backscattering, FEL based on, , 693 Stimulated Raman FEL, defined, 523 Stimulated Raman regime, 51 Stimulated synchrotron radiation emission, in wiggler magnet, Stokes diagram, for free electron laser, 506 Storage rings, , 160 ADONE, see ADONE storage ring bending magnets in, 483 FEL amplifier regime in, FEL efficiency in, 389 FEL operation in, FEL oscillator in, isochronous, see Isochronous storage ring laser laser insertion and, layout of, operation of, , 688 particle motion analysis in, 432 rf cavity in, 431 single-particle dynamics in, transverse position of electrons in, 425 Storage ring based system advantages of, 467 vs. linear system, 469 Storage ring LEDA-Fl, layout of, , see also LEDA Fl, F2 Storage ring parameters, 332, Strong pump regime, 508 Strong singal regime, Strong wiggler regime, Sulfur, isotope separation for, 676 Superconducting linac, 605 Super modes, as eigenfunctions of integral equations, 212, Superradiant experiments, Superradiant power spectrum, Susceptibility function, for bremsstrahlung FEL, 35, 38 Swept-gain laser, 178 Synchronous phases, for LEDA-Fl, F2, Synchrohron emission process, betatron motion amplitude variation in, 354 Synchrotron motion recurrence equations, 350, 369 Synchrotron radiation damping due to, 427 transverse motion damping and, 431 Synchrotron radiation emission, in wiggler magnet, Synchrotron radiation excitation, Synchrotron radiation loss, electron energy and, 117 Thermal spread parameter, normalized, Three-dimensional calculation, of electron energy loss in variable-parameter FEL, Three-dimensional effects in FEL wiggler field, 230 illustration of, Three-wave resonance bandwidth, 525 ThLeshold cavity loss, 394 Threshold regime, of FEL oscillator in SR, Threshold value, 391 Time history, of interaction variables, 149

14 698 Total radiation field, evolution of, Touschek effect, 494 Transformation equation, properties of, Transport channel performance, in FEL-microtron device, Transverse beam dimension, for LEDA-Fl, F2, Transverse beam emittance, 603 Transverse dimensional effects, and nonlinear theory of FEL, Transverse electromagnetic wave, in bremsstrahlung FEL, 9-10 Transverse electron coordinates, 232 Transverse electron current, equation for, 108 Transverse electron velocity, vs. wave amplitude growth rate, 510 Transverse electrostatic bremsstrahlung FEL, transverse electron beam and, 35 Transverse excitation cancellation of, computation of, 430 nature and description of, Transverse gradient, higherorder effects and, 414 Transverse magnetic bremsstrahlung, gain parameters for, 61 Transverse modulating FELS, electron mechanical momentum distribution for, Transverse optical klystron defined, 572 layout of, Transverse betatron oscillations, Transverse wave, cyclotron mode as, 524 Trapped electron energy, diabatic decrease in, 265 Tunable FEL, Bell Laboratories, 536 Tunable laser, high-efficiency, 263, 672 Twiss coefficients, 341, 362, 372 Two-stage free electron lasers, TWT amplifiers, 15, 20, see also Smith-Purcell FELS Ubitron, 3, 529 Ultraviolet FEL, Ultraviolet laser-induced multiphoton mass spectrometry, Undulator longitudinally varying period, tapered, 612 technical problems in construction of, types of, variable period, Undulator field, 598 Undulator parameters, Undulatrons flat, helical, permanent-magnet, technical problems in construction of, 696 Uniform distribution, filamentation and, 468 Uniform input distribution, 468 University of California at Santa Barbara FEL, , 694 conceptual layout of, design of, design parameters for, 326 electron beam collector for, future applications for, program objectives in, 328 Vacuum chamber apertures, in LELA experiment, 495

15 Vacuum phase slippage, between electrons and laser field, 382 Variable parameter FEL, threedimensional calculation of electron energy loss in, Variable wiggler, 269, 295, see also Wiggler FEL efficiency enhancement with, , 554 field at symmetry axis of, 272 parameters for, 269 pulse length in, 273 theory of, Vlasov equation, basic FEL properties and, 140 linear response theories and, 34 solution of, 101 Vlasov-Maxwell equations, perturbative solution of, 1l0-1l1 Warm beam-high gain regime, Warm beam-low gain regime, 57-59, 79 efficiency at, Wave amplitude growth rate, vs. transverse electron velocity, 510 Wave and particle dynamics, Waveguide structure, electromagnetic modes excitation in, Weiszacker-Williams approximation, 140, 166 Wernholm injection, in microtron, 297 Wiggler axially variable, 114 bunched electron beam in, 697 coherent bunched electron beam and, constant-parameter, defined, gain-expanded, 295 helical, Wiggler (continued) high-field, linearly polarized, 142 magnetostatic, 514 net dispersion of, 414 normalized energy vs. distance along, with parameters varying along axis, Hl-1l5 permanent magnet, 274 potential well in, 114 in racetrack energy recovery system, 278 radial varying field flat, 607 sinusoidal, special high-field, 371 tapered, 614, 699 technical problems in construction of, , 696 variable, , , , 554 variable parameter, , 209, 295 Wiggler coherent beam, 481 Wiggler design, at Los Alamos Scientific Laboratory, Wiggler exit, electron bunching at, , 116 Wiggler field, amplitude tapering in, 264 bunching of electrons at, electron trajectory and, 95 equations of motion in, , 414 FEL interaction and, 147 function of, 93 linearly polarized, 231 schematic of, 231 strong, transverse dimensional effects and, transverse electron velocity and, 505 transverse spatial gradients in, 233 Weiszacker-Williams approximation in, 140, 166 Wiggler magnet

16 700 Wiggler magnet (continued) Wriggler parameters, for variable wiggler, , focusing properties of, 405~ , 295 Kx and Ky parameters for, 338 Wiggler performance, in FELmicrotron device, 301- off-energy closed orbit in, in pulsed free-electron laser, Wiggler photons, scattering of, spontaneous radiation from, spontaneous synchrotron radiation emission in, 358- J64 stimulated synchrotron radiation emission in, storage ring layout and, synchrotron power radiation in, 350 Wiggler wavelength vs. effective perpendicular energy spread, 266 in pulsed FEL, 176