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, e-beam current, gain and efficiency) are reviewed; design tradeoffs are described. The study includes consideration of typical requirements of power beaming to a high altitude platform such as atmospheric absorption versus frequency and transmitting and receiving antenna requirements. A conceptual design of a compact, moderate voltage (0.5-3 MeV), high current (1- 10 Amp) EA-FEM operating in the mm-wavelength band is presented as an efficient power source for space beaming. The FEM design parameters are presented based on analytical and numerical models. Expected performance parameters of an FEL (gain, energy conversion efficiency, average power) are discussed as related to the proposed application.
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.
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 T2 we calculate the classical radiant intensity from the optical gratings due to this process. Sample numerical calculations based on a ruby grating result in substantial radiation levels.
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.
Duke University, Durham, NC 27514, USA
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 N short bunches of electrons propagating through the undulator. The coherence of the synchrotron radiation emitted from the bunched beam grows with the number N of the e-beam pulses entering the interaction region. When N grows to infinity, the radiation becomes perfectly coherent at all harmonic frequencies of the pulse injection (bunching) frequency.
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 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.
Department of Chemistry, Weizmann Institute, Rehovot, Israel
Faculty of Engineering - Physical Electronics,
Tel-Aviv University, Ramat-Aviv 69978, Israel.
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 (10-7 Hz) for cw FEL's with parameters similar to those of the FEL experiment of Elias, et al.
Abstract We report the observation of synchronous energy exchange between nonrelativistic electrons and the ponderomotive (beat) force of two counterpropagating, intense, pulse CO2 laser beams, operating at different frequencies in a stimulated Compton-scattering scheme. The interaction takes place in the nonlinear (trapping) regime, and its physics is the same as in laser accelerators and efficiency-enhanced free-electron lasers with long wigglers. Two different mechanisms of enhanced energy transfer were observed - electron trapping and phase-area displacement.
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., 60, 1279 (1970)] was analyzed and shown to be too small to account for the measured radiation. The experiment and Van den Berg's theory predict stronger emission at azimuthal angles off the plane perpendicular to the gratings. This observation leads to conclusions regarding the design of optical cavities for Smith-Purcell fee-electron lasers and orotron millimeter-wavelength-radiation tube devices.
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 CO2 laser and the signal wave is the radiation of a high-power pulsed dye laser. We propose to use a hollow dielectric waveguide in order to overcome the pump wave diffraction and obtain a long interaction length.
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 ~0 in all bremsstrahlung FEL's, in comparison to Cerenkov-Smith-Purcell FEL's. Some expressions which were derived earlier for the magnetic bremsstrahlung FEL, like the expression from gain in the low-gain regime with the space charge effect correction and the low-gain regime with the space charge effect correction and the low-gain expression for efficiency, are shown to be special cases of more general expression.
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