The evolution of a long pulse (pulse length much greater than the slippage distance) in a tapered wiggler free-electron laser is studied by numerical solution of the 1-D theoretical model for a realistic set of magnet, electron beam, and optical resonator parameter values. Single-pass gain curves are calculated for low and high light intensity. We find that an initial, low-amplitude, incoherent pulse grows into a coherent pulse whose growth rate agrees with the calculated small signal gain. The transient evolution of coherent pulses is calculated for several different cavity length detunings, and a quasi steady-state desynchronism curve is given. The frequency changing behavior of the optical pulse is shown to occur through sideband generation associated with synchrotron oscillations. Pulse evolution with an ideal intracavity high-pass optical filter is calculated.

The evolution of the two-dimensional radiation pulse in the free electron laser (FEL) oscillator is analyzed in association with electron pulses with arbitrary radial and axial profiles. In the FEL interaction region, the transverse variation of the wave equation is evaluated analytically, while the axial and the temporal variations are evaluated numerically. In free space, the radiation pulse is decomposed into Gaussian resonator modes and propagated analytically. Numerical results in the small electron beam radius limit, i.e., the radius of the electron beam much smaller than the minimum waist of the resonator mode, are presented.

The operation of a Free Electron Laser (FEL) in an oscillator mode using a variable parameter wiggler has been investigated by a combination of theoretical analysis and numerical simulation. The linear eigenmode analysis leading to a calculation of the linear gain per pass has been carried out for both ultra-short and finite length micropulses. The effects of sideband growth and suppression are studied using a simulation code. Stable large amplitude pulse propagation is achieved by passing the pulse through a band-pass filter to attenuate sideband modes above and below the main pulse frequency. A minimum current criterion is derived which must be satisfied to ensure both linear gain and stable pulse propagation.

A continuously tunable alexandrite laser source for injection into a high power visible FEL is designed to promote high efficiency performance without the need for complex wiggler design. The Kroll-Morton-Rosenbluth one-dimentional equations of motion are used to estimate the injection power requirements for both a RF LINAC FEL oscillator and an Induction LINAC FEL amplifier. Subject to this analysis, alexandrite laser performance characteristics are determined in order to deliver the peak powers required for immediate gain saturation of the FEL. Extension of the alexandrite tuning range via non-linear optics is proposed to permit eventual semi-continuous laser injected FEL operation from the UV to the near-IR.

Electron-beam energy spectral measurements were made on a tapered-wiggler free-electron laser amplifier. A 10 MeV electron beam from a traveling-wave linear accelerator interacted in a tapered-wiggler with an intense 10.6pm CO2 laser beam. The electron spectra show a 4 percent net energy loss and a 9 percent peak loss. Measurements of electron energy spectra, extraction efficiency as a function of electron-beam energy, and extraction efficiency as a function of optical power are presented and are consistent with theoretically predicted performance.

A high power visible wavelength free electron laser oscillator experiment has been proposed by the Mathematical Sciences/Boeing team. The experiment is an extension of the infrared amplifier experiments described at this conference.1 The oscillator design is a high extraction, single pass experiment using a SmCo5 permanent magnet tapered wiggler, the electron beam is provided by a RF linac. This paper outlines the accelerator requirements and describes progress in development of a high current injector for the accelerator.

A high-gain FEL experiment using the 10 kA, 4.5 MeV Experimental Test Accelerator (ETA) is described.

Metal mirrors will probably be required to realize the full broad-band tuning capability of the FEL oscillator. In this paper we analyze the operation of an acousto-optic output coupler for such cavities.

Simple scaling laws for free-electron laser oscillator mirror alignment tolerances are given based on geometric optics. The effect of geometric walk-off and diffractive scraping are discussed. In cavities that are nearly concentric, the effect of diffraction can relax the alignment tolerances.

A general approach to optimization of the free-electron laser interaction is used to develop the scaling of emittance and energy spread requirements for tapered wigglers optimized for highest optical gain at fixed e-beam energy extraction. The required e-beam properties are found to be quite stringent at visible wavelengths. The applicability of various methods of emittance acceptance enhancement is examined. One very promising option is a magnet canting scheme for providing two plane focusing in planar wigglers. Two-plane focusing relaxes the severe emittance requirement resulting from the need to maintain spatial overlap between the optical beam and the free-expanding e-beam. In addition, options for adjusting various system parameters for enhanced emittance acceptance, at reduced gain per unit current, are explored. Comparison of e-beam quality requirements and state-of-the-art linac capabilities shows that tapered-wiggler oscillator experiments are feasible at visible wavelengths.

A careful analysis of the second harmonic generation conversion efficiency for a medium power infrared free electron laser (FEL) has been carried out. Thermal effects, linewidth effects and dispersion in the nonlinear crystal have been taken into account. Some simple approximate relations have been derived to provide estimates of the conversion efficiency attainable when using high power, high repetition rate picosecond pulses produced by a linac-driven FEL.

We describe a variable emittance filter designed for the Electron Laser Facility (ELF). The filter attenuates the 4.5 MeV, 6 kA Experimental Test Accelerator (ETA) beam, permit-ting electrons only which fall within a given region of phase space (r, dr/dz) to pass. Initial experimental results are presented.

Measurements of the optical beam quality of the 3.2 micron output of the Stanford Super-conducting FEL are reported. Profiles of the far field focus are presented in both time average and single shot cases. The results differ by less than 10% from the predictions for an ideal Gaussian beam. Also presented are measurements of the near field profile and the Rayleigh range.

Optical gain has been detected at 10.6 μm during the recent tapered-wiggler free-electron laser amplifier experiment at Los Alamos. In addition, it was possible to measure separately the coherent spontaneous emission at the fundamental and at the second-hand third-harmonic wavelengths. Separation of the stimulated gain and coherent spontaneous emission from each other and from the high-power (gigawatt) CO2 laser radiation was possible by use of polarization analysis and passive frequency filtering in hot CO2 gas. The magnitude of the optical gain signals near resonance was consistent with the theoretically predicted gain of about 1%. Optical measurements as a function of several parameters of the electron beam (energy and current) and the CO2 laser (power) provided further supporting evidence for our identifications.

Plans have been made to modify the Los Almos free-electron laser amplifier experiment to allow its use as an oscillator at 10.6 microns. Several major changes were required, all of which have now been completed. The necessity for these changes is discussed as are the details of their fulfillment. In some cases we have progressed to the point where we can report on the performance of the new systems. The present status is described.

A beam recovery efficiency of 99.4% has been demonstrated with a 2.5 MeV, 1.2 ampere electrostatic accelerator electron beam system developed at UCSB to drive single-stage and two-stage free-electron lasers. Beam quality tests carried out at 10 keV and 2.5 MeV show that the measured transverse beam emittance agrees well with the theoretical limit imposed by the electron transverse thermal velocity distrubution generated by a thermoionic electron gun cathode and it is better than a factor of ten below that calculated from the Lawson-Penner relation. Also, a description of the UCSB FIR oscillator experiment is presented.

A high-efficiency, free electron laser, oscillator experiment is being conducted at Los Alamos National Laboratory. A buncher system has been designed to deliver 30-ps, 5-nC electron bunches to a 20-MeV standing-wave linac at the 60th subharmonic of the 1300-MHz accelerator frequency. The first 108.3-MHz buncher cavity accepts a 5-ns, 5-A peak current pulse from a triode gun. Following a 120-cm drift space, a second 108.3-MHz cavity is used, primarily to enhance the bunching of the trailing half of the bunch. A 1300-MHz cavity with 20-cm drift spaces before and after the cavity completes the beamline compo-nents. The bunching process continues into the linac's first three accelerating cells. Two thin iron-shielded lenses and several large-diameter solenoids provide axial magnetic fields for radial focusing.

Electron beam diagnostics for the Los Alamos free-electron laser oscillator experiment have been designed to measure the time dependence of the electron energy distribution with time intervals ranging from 30 ps to 200 ps. The electron beam consists of macropulses that have a 100 us duration and a 1 Hz repetition rate. Each macropulse consists of a series of micropulses that have 1,30 ps duration, %50 A peak current, and 1,50 ns separation. The primary purposes of the electron beam diagnostics is twofold: (1) optimization of the bunching system to provide a maximum peak current in the micropulses and (2) measurement of the time dependence of the electron energy distribution during build-up of the photon field in the oscillator. Because the exact time of build-up is uncertain, provisions have been made to allow the observation window to be varied from 10 to 100 us and to be delayed by times up to 100 us.

In addition to the usual circularly symmetric TM010 mode used to accelerate particles in an rf linac, there is a large number of modes with cos 4) or sin (0 dependence, for example the TMlxx modes. These latter modes possess a uniform magnetic (dipole) field near the axis of symmetry and therefore can deflect the beam away from the axis. Any portion of an accelerated beam that is off-axis will drive these modes, so that subsequent portions of the beam will be deflected. This deflected beam will then resonantly drive the same modes in downstream cavities, so that still later portions of the beam will be more severely deflected, and so on. In this paper I report the results of numerical simulations of this so-called cumulative beam-breakup instability. The simulation assumes that only the TMlio mode acts to deflect the beam, and further assumes that this mode does not couple from one accelerating cavity to the next.*

A description of the UCSB wiggler is presented along with results of theoretical and computer analyses of its electron beam transport properties. Measurements of the magnetic fields and their deviations from ideal are described. Some observations of actual beam behavior are described, and finally, expected improvements in magnetic field uniformity, beam diagnostics, and beam transport modeling are discussed.

Described is a forthcoming TRW/Stanford experiment to observe oscillation with a tapered wiggler. The laser will produce high efficiency (>1%) and short wavelength (1.6 1.1m). Adjustable tapering in the wiggler will allow data to be collected from a variety of tapers.

A review of the two-stage free electron laser (FEL) research program at KMS Fusion, Inc. is presented. The work includes cavity and wiggler magnet design, a study of methods for minimizing electron energy spread at high first stage intensity, and calculations of second stage gain. A quasioptical cavity is proposed to contain the first-stage long-wavelength radiation while permitting transmission of second-stage short-wavelength radiation. A permanent magnet helical wiggler will be used to produce the long-wavelength radiation. At high first stage intensities (- 108 W/cm2) the energy spread produced in the wiggler will be 10% . For the experiment being proposed the beam line and electron collector must be modified to accept this spread. Companion papers in this volume give additional details of the cavity design and minimization of energy spread.

We discuss the main limitations of a single pass FEL device within the framework of the Lawson-Penner law. We show that very good performances can be obtained, in principle. Finally we point out that under suitable conditions the short wavelenght region (namely, visible and UV) may be covered by an FEL operating with a low energy electron beam machine.

Phase space displacement is investigated as a method of reducing energy spread in free electron lasers producing long-wavelength radiation (- 1 mm) at high laser intensity (- 107- 'OR W/cm2). The technique is described and compared with the more conventional tapered wiggler that traps electrons in decelerating phase space buckets. A band model is developed to describe the movement of electrons around the phase space buckets and estimate the resulting energy spread. The energy spread obtained from the band model is compared with that obtained from a multiparticle computer simulation. Laser gain obtained by bucket capture is found to be comparable to gain obtained by phase space displacement at high intensities but energy spread is a factor of a few lower.

The small-signal gain spectrum of high-gain free electron lasers has been studied analytically. The parametric dependencies of peak gain value, optimum detuning and gain width are presented. The criteria for experimental considerations are given.

The results of a two-dimensional simulation of a high-gain free electron laser (FEL) amplifier is presented. The simulation solves the inhomogeneous paraxial wave equation. The source term is radially resolved and is obtained by tracking the interaction of the laser field with localized macroparticles.

The performance of a low gain, free-electron laser (FEL) operating in the Compton regime is evaluated in the presence of e-beam displacements in planes parallel or perpendicular to the FEL linearly polarized wiggler magnetic field. In this fully coupled, nonlinear formalism, the gain is described by a 3-D extension of the Kroll-Morton-Rosenbluth (KMR) equations and evaluated by using optical fields that are propagated numerically between sections of the wiggler (and the oscillator) using the Gardner-Fresnel-Kirchhoff (GFK) algorithm. The oscil-lator extraction efficiency, optical gain, and the 3-D transverse mode and gain distributions are computed in the absence of slippage between the optical and e-beam pulses, using standard iterative techniques for obtaining resonator solutions. The influence of local off-axis magnetic fields and betatron oscillations on individual particles is included in the gain computations.

The Kroll-Morton-Rosenbluth equations of motion for electrons in a linearly polarized, tapered wiggler are utilized to describe gain in free-electron laser amplifiers. The three-dimensional amplifier model includes the effects of density variation in the electron beam, off-axis variations in the wiggler magnetic field, and betatron oscillations. The input electromagnetic field is injected and subsequently propagated within the wiggler by computing the Fresnel-Kirchhoff diffraction integral using the Gardner-Fresnel-Kirchhoff algorithm. The injected optical beam used in evaluating amplifier performance is initially a Gaussian which in general may be astigmatic. The importance of the above effects on extraction effi-ciency is computed both with rigorous three-dimensional electromagnetic wave propagation and a Gaussian treatment of the field.

First we present approximate analytical solutions to the wave equation inside an over-moded metallic rectangular waveguide. The cold eigenmodes are expressed in terms of cylindrical Gaussian-Hermite functions times trigonometric functions to insure the boundary conditions. Next, we discuss a numerical three-dimensional calculation for a Free Electron Laser (FEL) amplifier which is based on the Lienard-Wiechert solution of the Maxwell's equations cast in an integral form. This approach is readily and efficiently extended to include the effects of the metallic boundaries of the waveguide by means of the method of "image currents". Finally, the radiation field in the cavity emitted by the electrons in the presence of the combined fields of a co-propagating eigenmode wave plus a linearly polarized magnetic undulator is expanded in terms of cavity eigenmodes. This expansion allows us to compute the gain per resonator mode.

A quasioptical cavity consisting of a cylindrical, metallic, overmoded, TF01 wavequide between two spherical end mirrors will be used to contain long-wavelength (- 1 mm) pump radiation in a two-stage PFL. The major loss mechanism is found to be mode conversion. Two different modified cavities are shown to suffer negligible mode conversion, and two more possible approaches, with low mode conversion and additional advantages, are discussed.

Axisymmetric cw multi-pass diffractive numerical calculations for the free-electron laser (FEL) are presented. The output is extracted around the edge of one mirror in a symmetric resonator of low Fresnel number. Excellent beam quality and small mode area inside the wiggler are obtained when the resonator is in a negative-branch unstable configuration. We suggest the use of a deformable mirror for gain-switching a tapered-wiggler FEL.

We derive the most general equations of motion for the electrons and the electromagnetic field in a free electron laser including the effects of diffraction and pulse propagation. The field evolution is expressed in terms of the amplitudes and phases of a complete set of transverse modes. The analytic solution is given in the small signal regime, where the theory is shown to be in excellent agreement with a recent experiment at Orsay.

A storage ring free-electron laser oscillator has been operated at a visible wavelength A = 6500 A .

Recent results on optical gain measurements on the ADONE FEL are reported and discussed. In addition, the results of a computer analysis of the Rayleigh length which optimizes the extraction of energy from the ADONE beam are discussed together their implications on the configuration of the optical cavity to be used for the FEL oscillator. These simulations have been based on a suitable extension of the Madey's theorem and on a representation of the electron work against the field of a gaussian beam by means of the far field radiated by the single electron. In turn, the accuracy of the calculated far field has been tested by comparison with the measured patterns of the spontaneous radiation.

The small-signal gain per pass of a free electron laser is analysed by taking into account the divergence of the light beam and the finite cross-section of the e-beam.The ana-lysis is based on a suitable extension of Madey's theorem.

The optical modes in a free-electron laser are examined by following the evolution of the optical field envelope self-consistently over many passes. After normal saturation in strong optical fields, the oscillation of trapped electrons causes the laser to become unstable and create sidebands. In some cases the mixing of modes is highly non-linear, and the optical field spectrum becomes broadband and chaotic.

A unified classical stochastic treatment of spontaneous and stimulated emission in a free-electron-laser oscillator is presented. The theory accounts for photon noise phenomenologically and includes also the effects of electron shot noise. Computer simulation results for the time evolution of the laser field, from incoherent spontaneous emission to coherent stimulated emission and eventual saturation, are reported for a one-dimensional model of the Stanford free-electron-laser oscillator.

Recent results on the photon statistics of the free-electron laser regarding start-up, amplification and steady state operation are summarized. The underlying theoretical model is based on the fully quantized Bambini-Renieri Hamiltonian.

We have developed a model for computer simulation of shot noise and quantum field fluctuations in order to study the effect of noise on the startup and saturated operation of a free electron laser. The model is described and some results relevant to the Stanford 3 μm laser are presented.

Free electron laser experiments and other high power radiation sources are very demanding of beam quality for good efficiency at short wavelength. The approach to obtaining high current bright beams is examined. We conclude that very bright beams require high current density cathodes and strong magnetic fields. A new definition of beam brightness for field immersed diodes is suggested by the data. We find that perturbations on the electron beam are enhanced as a result of beam density.

A 2-μsec-duration electron beam from an induction linac is used to drive a free electron laser (FEL). Beam generation and transport are critical problem areas which have been addressed. Radiation from various wigglers has been analyzed, and both cyclotron and FEL modes are present if an axial guide field is used. Experiments with a helical wiggler and no guide field have been very successful in eliminating cyclotron emission and maximizing FEL radiation. Power levels in excess of 1 MW with corresponding efficiencies of > 1% have been observed in super-radiant experiments.

The nonlinear efficiency of magnetized free electron lasers versus axial magnetic field has been investigated through particle simulations. The presence of the axial magnetic field in a free electron laser around gyroresonance is observed to introduce a strong long wavelength Raman backscattering instability which itself gives rise to electron trapping and caused the desired short wavelength radiation to saturate earlier than an unmagnetized free electron laser. The results of single mode particle simulations show that the nonlinear efficiency of a cyclotron maser operated in the auto resonance regime can reach 25% with beam energy = 1 Mev, beam current = lkA, and β, = 1/y. The output radiation frequency scale with beam energy according to γ2ΩO and the process converts both the longitudinal and transverse components of beam energy into radiation.

It has been suggested that for a given output wavelength, electron energy requirements could be greatly reduced in a two stage FEL. The principal of a two-stage device has been demonstrated in an experiment where the same intense relativistic election beam first produces 500 MW of 12.5 GHz radiation through a backward-wave-oscillatior (BWO) process, and then uses the BWO radiation as a wiggler for an FEL operating at --200 GHz. Improvements in the initial experimental configuration which will optimize the 200 GHz emission are described.

Frequency-resolved measurements of emission from a superradiant millimeter-wave free-electron laser using an intense relativistic electron beam have demonstrated high power, good efficiency, high gain, and broad gain bandwidth, and broad tunability, all in good agreement with theoretical predictions for operation in the collective regime.

A test-model free-electron laser, FEL, has been operated at voltages from 120 to 280 kV. The laser has a 2-cm wiggler period and utilizes a linearly polarized wiggler. The resonator is composed of a 1.75-cm-dia circular waveguide coupled to 8.89-cm-dia spherical mirrors. The beam current is about 15 A and the FEL operates at near threshold. The theoretical gain exceeds the measured cavity losses (10 to 30 percent per pass) only for the higher Q modes. The most intense emission occurs at frequencies near the waveguide cutoff of 10.2 GHz, where we estimate the emitted power to be saturated at 10 to 100 kW. Signals have been observed to last for over 10 ps. This lower frequency mode, (which we presume is the backward TE11 FEL wave), dominates. Radiation is reproducibly observed to appear during periods when the voltage corresponds qualitatively to resonator modes; with each mode usually occurring twice during the pulse, e.g. during the rise and fall of the voltage. The rate of change of the voltage affects the gain under these circumstances and the signal is quenched if the change exceeds about 4% per ps. Harmonic frequencies are also observed at frequencies near to, but not on, the forward-wave branch of the FEL-dispersion curve. The intensity of the third harmonic (31 GHz) is on the order of 44 W.

The nonlinear evolution of Raman free-electron lasers in the presence of an axial guide-field is investigated numerically in an amplifier configuration. The nonlinear currents which mediate the interaction are computed by means of an average over particle phases, and the inclusion of fluctuating space-charge fields in the formulation permits the investigation of both the stimulated Raman and Compton scattering regimes. Initial conditions are chosen to describe the injection of a monoenergetic beam into the interaction region composed of a uniform axial guide field and a helical wiggler field which increases adiabatically to a constant level. After an initial transient phase, the results show a region of exponential growth of the radiation field which is in excellent agreement with linear theory. Saturation occurs by means of particle trapping. The efficiency of the interaction has been studied for a wide range of axial guide fields, and substantial enhancements have been found relative to the zero-guide-field limit.

A fully self-consistent theory of the free-electron laser is derived in the collective regime which includes all transverse variations in the wiggler field as well as the effects of a finite waveguide geometry. A set of coupled differential equations is found which describes an arbitrary radial beam profile, and a dispersion equation is obtained under the assumption of a thin monoenergetic beam which is solved numerically for the growth rates of the TE11 and TM11 modes in a cylindrical waveguide.

Expressions for operating wavelength, gain, and schematic designs for Compton regime Cerenkov lasers are presented. Conditions required for operation at infrared and visible wavelengths are established and proof of principle experiments are discussed.

We describe a non-interactive Thqmson-Backscattering experiment to determine the parallel-energy spread of a 1 KA/cm2, 600 KV beam. Principles of the experiment, optics, complicating factors (e.g. X-rays, background light), Diode and TEA laser performance, and preliminary single-channel scattering data are discussed. A momentum-spread of (Δγ/γ)1/2% is consistent with the data.

This paper considers the possible amplification in dielectric media of x-ray and vacuum ultraviolet radiation by electron beams. The medium can be a uniform dielectric resulting in stimulated Cherenkov radiation or a periodic, inhomogenious dielectric resulting in stimulated transition radiation. Two distinct geometries for resonators are considered. In one case, a simple confocal resonator is placed at an oblique-angle to the electron beam. In the other, a conical mirror is used to reflect the entire radiation cone back onto the electron beam. The small signal gain for a short interaction length is found for both these cases to vary linearly with frequency resulting in higher gain for shorter wavelengths.

We present an overview of the regimes in which operation of an x-ray free-electron laser (FEL) may be feasible, including discussion of static and electromagnetic wigglers, quantum recoil, high-gain operation, mass-shift broadening, and electron beam quality.

We present a comprehensive, quantum mechanical treatment of the spontaneous radiation emitted by a relativistic charged particle traversing a crystal in the systematic reflections geometry. Unlike previous models, this one includes the full three-dimensional periodicity of the crystal potential and is valid for all regimes of particle motion. The emission frequencies are shown to be determined by a combination of two mechanisms: momentum transfer to the lattice and interband or intraband transitions in the potential that is perpendicular to the plane of the channel. Those frequencies that rely on momentum transfer are determined by the period of the potential either in the atomic planes that define the channel or perpendicular to them. Both mechanisms are shown to be important in describing the spectrum of the emitted radiation.

We describe a research program for investigation of stimulated Compton (Thompson) scattering. The present development of an experimental system based on two high power pulsed TEA CO2 lasers and a non-relativistic beam is described. Results of theoretical analysis of the system are reported, including development of Manley-Rowe relations, conditions for backward wave oscillation and simulation of electron dynamics in a multitude of ponderomotive potential fields generated by multi-mode pump and signal waves. In conclusion a vaguard design concept of trapped electron pulsed two stage FEL system is proposed for consideration in outer space applications.

The dispersive free-electron laser (dispersive FEL) is a normal free-electron laser (FEL) with a dispersive magnetic field, similar to that of the optical klystron (OK), superimposed on some of the undulator magnets. Small signal gain, electron energy acceptance bandwidth and saturation efficiency of the normal FEL, OK and dispersive FEL are compared. It is found that for a given electron energy acceptance the dispersive FEL has about a factor of two higher gain than the OK. For a given length, and some non-negligible intrinsic cavity loss, the dispersive FEL has higher saturated output power than the normal FEL. For storage ring operation, where the intrinsic energy bandwidth is small and the length is limited, the dispersive FEL has higher gain than either the conventional FEL or the optical klystron.

Gas loading of a free-electron laser modifies the phase-matching condition while the small-signal gain expression remains the same. This permits a wider parameter space than the vacuum FEL, which is particularly advantageous at shorter wavelength operation. Scattering of the electrons by the gas limits the interaction length, but available gains are still high enough to allow oscillation build-up. For example, a 0.5μm wavelength helical wiggler FEL pumped by a 100 MeV electron beam is restricted to a length of 40 cm with a small signal gain of 361, and reaches saturation in less than a microsecond.