* B. Levush, T.M. Antonsen, V.L. Granatstein,*
*Institute for Plasma Research,*
*University of Maryland, College Park, MD 20742, USA*

** Abstract **Experiments on the radiation build-up process
obtained using a prebunched e-beam free-electron maser at Tel-Aviv University
(TAU) are compared to results of theoretical studies carried out at TAU
and at the University of Maryland (UMD).

Two computer codes were developed and employed for simulation of FEM operation. A non-linear three-dimensional 'amplifier', code based on a coupled-mode approach was employed for calculations of small-signal gain,

extraction efficiency and saturation power. This code (FEM3D) allows simulation of FEL operation taking into account space- charge effects.

The power evolution of several longitudinal modes was also studied numerically using a one dimensional, multifrequency simulation code MALTID; it was also observed in initial experiments.

Numerical calculations of extraction efficiency for the TAU-FEM were made for all resonator eigen-frequencies lying under the FEM net gain curve. It was found that for a constant set of parameters the maximum efficiency is obtained at an eigen-frequency, which differs from the maximum gain frequency. Prebunching of the e-beam provides a unique opportunity to choose any desired oscillator eigen-frequency and thus to select the highest efficiency mode. This makes it possible to obtain efficiency enhancement of the oscillator by a factor of about two.

** Abstract** A theoretical and numerical
investigation of the effects of azimuthal and radial spreads of canonical
momentum on an electron beam focused by a magnetic lens in the presence
of space-charge forces is presented. The particles are inserted with an
initial Gaussian distribution in the transverse space and in the momentum
coordinates or with a uniform initial current distribution. The particle
trajectory equation is derived for parameters of an arbitrary applied fields
configuration with cylindrical symmetry, and a nonvanishing initial canonical
momentum. In the absence of an initial momentum spread particles launched
above a critical radial distance from the axis exhibit a phase-space tearing
effect in the electron distribution. The inclusion of initial canonical
momentum spread in the model allows for skewed trajectories with strong
centrifugal force which prevents the appearance and overshadows the effect
of strong space-charge forces near the axis which are responsible for the
phase-space tearing effect.

* Abstract *We report a first demonstration
of single-mode selection in a free-electron maser (FEM) using electron
beam prebunching at or near the natural oscillation frequencies of the
resonator. The FEM oscillation frequency can be selectively locked to each
eigenfrequency of the resonant waveguide cavity within the frequency band
of the FEM net gain. the electron beam is prebunched at a frequency close
to an eigenfrequency of the cavity, the oscillation buildup process is
sped up and the radiation buildup time is shortened significantly. Measurements
are in good agreement with collective (Raman) free-electron laser theory.

** Abstract** A comparative analysis of wave profile modification
effects in Raman free-electron lasers is presented. The analysis is based
on a 3D theoretical model that is valid in both Raman and Compton regimes.
We study two companion effects, the optical guiding and the excitation
of space-charge waves with transverse field components. Both effects are
compared through exemplary parameters based on previous free-electron laser
experiments. We conclude that transverse field profile modification due
to space-charge waves may be significant in comparison to the optical guiding
effect.

* Abstract *Theoretical investigations of waveguides for
FEL operating at submillimeter wavelengths were made. Several types of
overmoded waveguides, i.e. rectangular, circular, parallel curved plates
waveguide and metal-dielectric waveguide, were studied in order to achieve
the best gain/loss ratio in FEL operation.

Gain calculations were made in the low gain regime. Waveguide ohmic losses were calculated taking into account the anomalous skin effect and the influence of surface roughness.

Numerical calculations made for the parameters of the Israeli tandem electrostatic FEL show that a parallel curved plates waveguide and a metal-dielectric waveguide provide good gain/loss ratios up to frequencies of the order of 1,000 GHz (while conventional rectangular and circular waveguides do not).

** Abstract **The Electrostatic-Accelerator Free-Electron Laser
(EA-FEL) operating at mm wavelength is considered as a source for energy
transfer through the atmosphere to a high altitude platform. The
high average power and high efficiency attainable from appropriately designed
EA-FEL make it a suitable candidate as an efficient source of mm- waves
for power beaming from a ground station. Various aspects of the FEL as
a high power oscillator (operating voltage,

** Abstract **The design and measurements of a resonator operating
near 100 GHz and intended for use in a Tandem FEL are presented. The designed
resonator employs two parallel curved plates as a waveguide. In FEL operation
the mode is excited. The resonator employs two wave splitters as reflectors.
The wave splitters are segments of an overmoded rectangular waveguide which
is connected at one end to the waveguide as described above, and is shorted
at the other end by a metal plate with an aperture in the center for e-beam
passage.

Gain calculations were made in the low gain regime. At the operating frequency the curvature of the plates and the gap size were chosen so as to maximize the gain..

A multimode analysis of the wave splitter was made. Calculations show, that the optimal splitter width and length allow achievement of very low diffraction losses at the aperture (~2%). This means that the aperture can be made sufficiently large to allow efficient beam entrance into the resonator without degrading its Q-factor. A resonator prototype was constructed and its performance was evaluated experimentally.

** Abstract **In this work spontaneous emission is investigated
in a waveguide free-electron maser, taking into account previously untreated
interaction effects in the vicinity of the waveguide cutoff frequency.
Our study is based on the exact waveguide excitation equations, formulated
in the frequency domain for a single electron moving in a planar magnetostatic
wiggler. An analytical solution of the amplitude of the excited waveguide
mode in the frequency domain was obtained using the Green technique and
allows us to calculate the spectral density of the radiated power and the
time-dependent radiated field with good accuracy using a numerical inverse
Fourier transform. The obtained solution shows that for TE-modes the spectral
density of the radiated energy tends to infinity at the cutoff frequency
of a lossless waveguide. The character of this singularity is, however,
such that the total radiated energy is finite. The radiated electromagnetic
field in the time domain has the form of very long (of the order of tens
of characteristic times on the scale of , where is the wiggler length and
c is the speed of light) pulse, lagging behind the electron, at the carrier
of cutoff frequency, in addition to two finite wave packets, corresponding
to the two synchronism frequencies. The results of a numerical calculation
of the radiated energy spectral density and of the radiated electromagnetic
field in the time domain are presented.

** Abstract** The possibility of use of a TEM transmission
line in free-electron masers (FEM) is discussed. It is shown that at the
centimeter and long millimeter wavelengths such transmission lines allow
one to combine the advantages of an open cavity and a waveguide based resonator.
A particular case of a FEM based on the use of a shielded two-wire transmission
line is investigated theoretically.

The mathematical approach which allows one to calculate transmission line parameters of importance to the FEM application is developed. It is based on use of the integral equation technique and on a new representation of the Green function of the internal region of a circle, which was obtained in this paper. Numerical analysis of effective mode area, wave impedance and attenuation constant was made for the odd TEM mode, which is excited in FEM operation.

As an example the FEM under research at Tel-Aviv University was considered. The frequency dependence of gain for a FEM operating in the linear regime was calculated. The obtained gain value is much higher than the ohmic losses in the transmission line which shows the possibility of employing the TEM transmission line in this FEM.

*F.V. Hartemann, G.P. Le Sage, and N.C. Luhmann, Jr.,*
*Department of Electrical Engineering, University of
California,*
*Los Angeles, CA 90024, USA,*

*R.S.Zhang and C. Pellegrini,*
*Department of Physics, University of California,*
*Los Angeles, CA 90024, USA.*

** Abstract** The coherent synchrotron radiation process in
a waveguide is theoretically investigated. A single, short bunch propagating
through a wiggler is considered. In a waveguide, two very distinct regimes
are possible. At grazing, where the beam velocity matches the wave group
velocity, the bunch emits a single, ultrashort chirped pulse whose duration
is determined by the interaction bandwidth and the waveguide dispersion.
Away from grazing, where slippage dominates, two distinct pulses are radiated
at the Doppler upshifted and downshifted frequencies. Both the time and
frequency domain expressions for the radiation characteristics are derived.

*A. Yariv,*
*Applied Physics Dept., California Institute of Technology,*
*Pasadena, CA 91125, USA*

** Abstract **An alternative mechanism for Smith-Purcell radiation
is proposed. This mechanism may have relevance to recent reports of higher
radiation power. The electron beam excites resonant transition of atomic
quantum levels in the optical grating material by the fields of the traversing
electrons. The dipole moments of all the atoms which are excited by the
same electron radiate in phase with each other and produce "super-radiant
radiation". To calculate the radiant intensity due to this process we first
calculate the dipole moments of the atoms excited by the classical electrical
field of the traversing electron. Assuming that the dipole oscillations
are dominated by a collision time T

** Abstract** This paper introduces a development of a normalized
axial velocity distribution function and a susceptibility term for an electron
beam in a planar wiggler FEL. The model includes the independent contributions
of the energy spread and the angular spread, the emittance and the betatron
motion, to the axial velocity distribution function.

In the case of an emittance dominated spread, the resulting distribution function is a skewed, asymmetrical function. The e-beam susceptibility is described in this case by the first derivative of the complex error function (the plasma dispersion function), convolved with a decaying exponent.

The "exact" distribution function and the susceptibility integral that are represented in this paper may be used in any linear, kinetic FEL model to improve its accuracy in cases where the angular spread, the emittance or the betatron motion, are dominant spread sources.

** Abstract** Three-dimensional models which describe the electron
beam transport and electro- magnetic (EM) interaction in a Free-Electron
laser (FEL) are presented. The models are based on single particle force
equations, and take into account emittance and space-charge effects in
the e-beam, and transverse spatial variation in the radiation field. In
the e-beam transport problem, a cylindrically symmetrical transverse density
distribution is assumed, having an arbitrary azimuthal and radial angular
spread. The particle trajectories are obtained by solving numerically the
equation of motion for a general electric and magnetic field in the presence
of space-charge forces. The parameters of the particles in the beam are
then displayed in real space and phase space. In the FEL model, the total
electromagnetic field (including the RF space-charge field) is expanded
in terms of normal modes of the waveguide (including the cut-off modes).
The field interaction with the e-beam is described by the force equation
for electrons and a set of EM excitation equations for the waveguide modes.
The model takes into account 3-D effects of the radiation and space-charge
fields, and thus provides a complete description of the FEL interaction
for any kind of symmetry of the e-beam and of the waveguide cross-section.
The equations are solved numerically to simulate FEL operation in the nonlinear
Compton or Raman regimes.

*P.G. O'Shea,*
*Duke University, Durham, NC 27514, USA*

*V.L. Granatstein,*

University of Maryland, College Park, MD 20742, USA

** Abstract **Advanced concepts of electrostatic accelerator
free-electron lasers (EA-FELs) are discussed. The capabilities of electrostatic
accelerators to produce continuous high energy electron-beams enable construction
of efficient FELs, for generation of high average power of radiation at
a wide range of the electromagnetic spectrum. Employing RF linacs for charging
electrostatic accelerators provides transport of larger e-beam currents,
and correspondingly producing even higher power. The unique features of
EA-FELs make them excellent sources for applications, which require high-power
radiation.

** Abstract **We derive the conditions for establishment of
a transverse supermode in a free- electron laser oscillator, and demonstrate
the evolvement of a supermode by means of a three-dimensional nonlinear
code. Both the analytical formulation and the numerical code are based
on coupled-mode theory.

The oscillator supermode is a combination of transverse modes that keeps its field profile at any point along the oscillator intact after each round-trip, and therefore it is the steady-state result of the oscillation buildup process. In the FEL, as in any laser, the oscillator supermode is identical with the amplifier supermode only if the feedback process is entirely non-dispersive. If this is not the case, the steady-state supermode field profile varies along the oscillator axis.

The simulations demonstrate that the transverse supermode evolution process is primarily a linear regime process and can be proceeded or even completed before saturation.

** Abstract** A three dimensional study of transverse mode
evolution in a free-electron laser (FEL) oscillator is presented. The total
electromagnetic field circulating in the resonator is represented as a
superposition of transverse mode of the cavity. Coupled mode theory is
employed to derive a generalized 3-D steady-state oscillation criterion,
from which the oscillator supermode can be found analytically in the linear
gain approximation.

The oscillator supermode, which is the eigenmode solution of the oscillator at steady-state, keeps its transverse profile and polarization after each round-trip. Relations between the oscillator supermode and the amplifier supermode are discussed. It is shown that they are identical only when the feedback process is entirely non-dispersive and non-discriminating.

We employ a 3-D non-linear simulation code based on the same transverse mode expansion to demonstrate the evolvement of transverse modes in the oscillator towards formation of a supermode in a simple example. The simulation shows that the steady-state result of the oscillation buildup simulation is identical to the supermode predicted by the analytical approach.

** Abstract **Evolution of the time domain fields and the spectral
power of super-radiant radiation in a free-electron laser oscillator (e-beam
pulses shorter than a wavelength) are investigated. We consider a finite
train of

When the super-radiant emission takes place inside a resonator, the
coherency of the emitted radiation is enhanced. Under the condition of
mode-locking, the fields add in phase and the spectral energy distribution
becomes narrow. When the finesse *F *of the resonator is small *F
< N*, the spectral width of the out-coupled radiation emitted from
the resonator is limited by *N*, and in the opposite case *F > N*,
it will be limited by* F*. If the number of pulses *N* grows
to infinity, the out-coupled radiation reaches a steady state of perfect
coherence with reduced harmonic contents (determined by the Finesse of
the resonator). There is no threshold for emission of this kind of coherent
radiation.

** Abstract **An alternative approach for the analysis of the
electromagnetic field and plasma wave propagation in a waveguide filled
with an electron (e) beam is presented. The analysis is based on a formal
exact expansion of the total electromagnetic field in terms of waveguide
modes. We subsequently use linear fluid plasma equations and electromagnetic
coupled-mode theory to find the dispersion relation for the eigen-modes
of the beam (plasma) loaded waveguide. The proposed method enables one
to solve for the Langmuir space-charge waves in an e-beam with an arbitrary
transverse geometry and density distribution, moving along any uniform-cross-section
waveguide at constant average velocity. The use of the method is demonstrated
by presenting a calculation of the dispersion curve and the plasma frequency
reduction factor of plasma modes in a practical case of a circular beam
drifting along a rectangular waveguide.

** Abstract** We compute the small signal gain curve and various
gain parameters by solving numerically the generalized gain-dispersion
equation of free-electron lasers (FEL), which characterizes the conventional
magnetic bremsstrahlung FEL, as well as large number of other FEL devices.
The model includes high gain, collective, and axial velocity spread effects,
and some waveguide effects. The FEL gain regimes are investigated and presented
in terms of only three universal FEL characteristic parameters. The approximative
analytic gain expressions are compared to the numerical computation results,
and the approximation error is computed and displayed. In the intermediate
regimes (high-low gain, tenuous- collective beam, cold-warm beam), the
gain parameters are given in terms of useful curves, and a heuristic approximative
formula is suggested for estimating the axial velocity spread gain reduction
factor in all gain regimes. We also define and compute gain bandwidth and
beam quality acceptance parameters in all gain regimes.

** Abstract **The field of radiation emission from electron
beams is reviewed with special reference to work related to free-electron
lasers. Different schemes of interaction in periodic structures, electromagnetic
slow-wave structures, and in transverse confining force are distinguished.
Various effects and devices such as traveling wave amplifiers, Smith-Purcell
radiators, Cerenkov and bremsstrahlung-free electron lasers, cyclotron
resonance masers, coherent bremsstrahlung and channeling radiation are
discussed and the differences and relations among them are explained. A
simple comprehensive model is developed to describe electron-beam interaction
with an electromagnetic waved in periodic electromagnetic structures. The
model is general enough to describe both collective and single-electron
modes of interaction and quantum mechanical, classical and Fermi degenerate
regimes. Simplified expressions are developed for the gain by stimulated
emission of radiation and for gain conditions of the Smith-Purcell-Cerenkov
type free-electron lasers under conditions of very thin electron beams
and infinite interaction length.

*G.Kurizki,*
*Department of Chemistry, Weizmann Institute, Rehovot,
Israel*

*S. Ruschin,*
*Faculty of Engineering - Physical Electronics,*
*Tel-Aviv University, Ramat-Aviv 69978, Israel.*

*A.Yariv,*
*Sackler Institute of Advanced Study, Tel-Aviv University,
Tel-Aviv 69978, Israel and*
*California Institute of Technology, Pasadena, CA 91125,
USA*

** Abstract** This article presents a unified formulation and
review of an extensive class of radiation effects and devices based on
free or quasifree electrons. The effects and devices reviewed include slow-wave
radiators [such as Cerenkov, Smith-Purcell, and TWT (traveling-wave tube)
effects and devices], periodic bremsstrahlung radiators [such as undulator
radiation, magnetic bremsstrahlung FEL's (free-electron lasers), and coherent
bremsstrahlung in the crystal lattice], and transverse-binding radiators
[such as the CRM (cyclotron resonance maser) and channeling radiation].
Starting from a general quantum-electrodynamic model, both quantum and
classical effects and operating regimes of these radiation devices are
described. The article provides a unified physical description of the interaction
kinematics, and presents equations for the characterization of spontaneous
and stimulated radiative emission in these various effects and devices.
Universal relations between the spontaneous and stimulated emission parameters
are revealed and shown to be related (in the quantum limit) to Einstein
relations for atomic radiators and (in the classical limit) to the relations
derived by Madey for magnetic bremsstrahlung FEL for on-axis radiative
emission. Examples for the application of the formulation are given, estimating
the feasibility of channeling radiation x-ray laser and optical regime
Smith-Purcell FEL, and deriving the gain equations of magnetic bremsstrahlung
FEL and CRM for arbitrary electron propagation direction, structure (wiggler)
axis, and radiative emission angle.

** Abstract **The problem of fundamental laser line broadening
due to random spontaneous emission of radiation and amplification of thermal
radiation noise is analyzed in terms of a classical fluctuating field phasor
model. We derive a general expression for the intrinsic linewidth, given
in terms of the spectral power of the radiation noise source, which can
be classical or quantum mechanical in nature. In the case of a two-level
atomic laser, we recover by the use of Einstein relations, the traditional
linewidth formula of the Schalow Townes form. In the case of the free-electron
laser (FEL), using the explicit expression for the spontaneous emission,
we present calculation of the laser linewidth by purely classical methods.
The result agrees with the one obtained in the framework of a quantum-mechanical
model. By using "extended Einstein relations" which are applicable to classical
radiators, we show that a Schalow-Townes-type formula can also be obtained
for the FEL. The theory predicts extremely narrow intrinsic linewidth (10

** Abstract** We report the observation of synchronous energy
exchange between nonrelativistic electrons and the ponderomotive (beat)
force of two counterpropagating, intense, pulse CO

** Abstract **Parametric instabilities in the interaction between
a cold-electron beam, a static electromagnetic pump, and a scattered (signal)
electromagnetic wave are studied. The interaction schemes are classified
according to the mutual sense of propagation of the waves and the beam.
The unified analysis yields the known convective and absolute slow-plasma-wave
instabilities [forward- and backward-wave free-electron lasers (FEL)].
In addition, we identify the possibility of convective and absolute fast-plasma-wave
instabilities. Analysis and numerical computation of gain and oscillation
in both known and new instability mechanisms are performed in the framework
of a general model beyond the range of previously reported studies. A general
approximate threshold condition expression for all the possible absolute
instabilities is given. All of these instabilities may appear in practical
schemes like FEL oscillators as parasitic effects. Their relative importance
is considered by means of numerical examples.

** Abstract** In this analytical study, we examine the radiation
power generated at the output of a prebunched free electron laser in the
low and high gain regimes, including space charge effects. The output radiation
results from three different processes: pure free electron radiation emission,
pure prebunching (super-radiant) emission and stimulated prebunched beam
emission. We also explore the Manley-Rowe relations which correspond to
the parametric processes in FEL devices, including all the elementary quantum
excitations of the system: wiggler and signal photons and slow and fast
plasmons. The analysis is based on a one-dimensional fluid plasma equations
model, in the small signal regime, and it applies to various kinds of FEL
mechanisms.

** Abstract** The power radiation pattern of Smith-Purcell
radiation is measured at various latitudes and azimuth angles relative
to the electron beam. The experimental data are used to evaluate the various
models and the physical mechanisms previously suggested to describe Smith-Purcell
radiation. Good agreement is observed between the experimental data and
the theoretical curves derived from Van den Berg's analysis [J. Opt. Soc.
Am. 63, 1588 (1973)]. The radiation mechanism proposed by Salisbury [J.
Opt. Soc. Am.,

** Abstract** An experimental study of a two-stage millimeter-wave
source in which the same intense relativistic electron beam first produces
powerful (500-MW) radiation at 12.5 GHz and then uses that radiation as
a "pump" for a free-electron-laser interaction at frequency f >140 GHz
is described. Implication for two-stage free-electron-laser experiments
with reduced electron energy requirements are discussed.

*C.M. Tang, and P. Sprangle,*
*Naval Research Laboratory, Plasma Physics Division,
Washinton, DC 20375, USA*

** Abstract** We examine the feasibility of high power generation
of visible radiation by a process of applying an axial accelerating electric
field on electrons trapped in the ponderomotive potential of a Compton
scattering free electron laser. We consider a scheme where the pump (wiggler)
field is produced by a high-power pulsed CO

** Abstract **This paper discusses in
a comparative way the main operating parameters of various free-electron
lasers (FEL's), providing a useful tool for laser design and a comparative
evaluation of the various lasers. We show that the various kinds
of FEL's satisfy the same gain-dispersion relation and differ only in a
single coupling parameter .
The different gain regimes which are common to all FEL's are delineated.
We find the small signal gain in all the gain regimes (warm and cold beam,
low- or high-gain, single electron, collective or strong coupling interaction).
The laser gain parameter, radiation extraction efficiency, maximum power
generation, and spectral width are given and compared in the various kinds
of FEL's and gain regimes. The maximum power generation of all FEL's
(except Compton-Raman scattering) is shown to be limited by an interaction
region width parameter. This parameter and, consequently, the laser
power are larger in the highly relativistic limit by a factor ~

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