Low-gain Regime Research Articles

The 3-D FEL pulse propagation equation: An analytical treatment in the low-gain and small-signal regime

In this paper we show that the transverse mode evolution of a FEL operating with short pulses can be treated, in the small-signal and low-gain regime, using a relatively simple mathematical technique leading to a potentially fast numerical algorithm. We also point out that analytical solutions can be obtained for the cases where the slippage length is small compared to the longitudinal bunch length.

Low-voltage high-gain resonant-cavity avalanche photodiode

For p-i-n photodiodes and avalanche photodiodes (APDs) in the low-gain regime, there is a performance tradeoff between the transit-time contribution to the bandwidth and the quantum efficiency. A new photodetector structure is demonstrated that alleviates limitations imposed by this tradeoff. This structure utilizes a thin ( approximately=900 AA) depleted absorbing layer to reduce the transit time and achieve avalanche gain at low bias voltage (V/sub b/ approximately=9 V). The external quantum efficiency has been enhanced ( eta /sub e/>49%) by incorporating the structure into a resonant cavity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The effects of field errors on low-gain free-electron lasers

The effects of random wiggler magnetic field errors on low-gain free-electron lasers (FELs) are examined analytically and numerically through the use of ensemble averaging techniques. Wiggler field errors perturb the electron beam as it propagates and lead to a random walk of the beam centroid, variations in the axial beam energy, and deviations in the relative phase of the electrons in the ponderomotive wave. The random walk of the beam centroid and the consequent variations in the axial beam energy are discussed. The deviations in the relative phase resulting from the field errors are examined. The effect of the field errors on the FEL gain in the low-gain regime is determined. The benefits of beam steering are analyzed, and addition methods for reducing the detrimental effects of field errors are discussed. >

The relationship between optical guiding and the relative phase in free-electron lasers

The relative phase in this case is defined as the shift in the wavenumber from the vacuum value integrated over the interaction length. The relative phase is studied from the standpoint of the linear stability analysis in both the high- and low-gain regimes, and the qualitative implications in each of these regimes of the relative phase on the refractive guiding of the signal are identical. Specifically, the relative phase is found to be negative at the low-frequency end of the gain band. The relative phase increases with increasing frequency over this band until it turns positive at a frequency approximately 10% below the frequency of peak gain. Thus optical guiding is indicated over a large portion, but not all, of the gain band. The specific example of interest involves the low-gain regime prior to saturation. In this case, it is shown that the analytic result is in substantial agreement with the calculation of the relative phase. >

Vlasov theory of wiggler field errors and radiation growth in a free-electron laser.

The intrinsic field errors of realistic wiggler structures degrade the quality of the electron beam as it propagates through the structure. In the following, we investigate the impact of the degraded-quality electron beam on the rate of conversion of beam energy into electromagnetic field energy. Specifically, we apply the linearized Vlasov theory to evaluate the expressions for free-electron-laser (FEL) gain in the low-gain regime and the growth rate in the high-gain regime. The analysis is both theoretical and computational and yields qualitative and quantitative agreement on the dominant physical processes. In addition, several figures of merit are identified that delineate conditions under which field errors have a negligible effect on the FEL growth rate.

Electron-beam propagation through a magnetic wiggler with random field errors

The effects of random field errors on the propagation of a relativistic electron beam through a wiggler magnet are analyzed both theoretically and numerically. Both helical and planar wiggler configurations are studied, with and without the effects of transverse focusing forces. Theoretical expressions are derived for the random electron motion for (i) individual realizations of field errors and for (ii) ensembles of statistically identical wigglers. These results are then confirmed through three-dimensional particle simulations of electron-beam transport including the effects of finite emittance. In addition to producing a random walk of the beam centroid, the field errors lead to significant variations in the parallel beam energy. Asymptotically, the variance of the parallel beam energy scales as z1/2, where z is the axial propagation distance. Although transverse beam focusing reduces the asymptotic scaling of the rms centroid displacement from z3/2 to z1/2, transverse focusing is not effective in reducing the parallel energy variation (the variance of the parallel beam energy is only reduced by a factor of √2). Statistically, the variance of the parallel beam energy may be interpreted as an effective parallel energy spread due to field errors. In order to maintain the wave–particle resonance in small-signal free-electron lasers, it is desirable for this effective energy spread to be small compared to the intrinsic efficiency. As an example, in the low-gain regime (assuming a helical wiggler in the strong-wiggler limit), this requirement implies that the normalized rms field error must satisfy δB̂rms&amp;lt;1/(2πN3/2), where N is the number of wiggler periods.

Measurement of homogeneously broadened spectra of spontaneous emission and small-signal gain in a low-energy, waveguide-mode free-electron laser

The spontaneous emission spectrum and the small-signal gain have been measured in a low-energy, waveguide-mode free-electron laser. Measurements are carried out at microwave frequencies (25–40 GHz) in an X-band rectangular waveguide with a low-energy (450–600 keV, γ∼2), low-current (∼1.5 A), low-energy spread (ΔE/E≪10−4) relativistic photoelectron beam. The measured spontaneous emission spectrum agrees well with the homogeneously broadened spectrum of the TE10 waveguide mode. The measured small-signal gain spectrum is in good agreement with the theoretical prediction calculated under the assumption of operation in the low-gain Compton regime.

Spontaneous emission and small-signal gain of a low-.GAMMA., waveguide-mode free-electron laser operating in the low-gain Compton regime.

Fundamental operation characteristics (a spontaneous emission spectrum and a smallsignal gain) of a low-γ, waveguide-mode free-electron laser have been measured by using a good quality relativistic photo-electron beam. Measurements are carried out at microwave frequencies (25-40 GHz) in an X-band rectangular waveguide with a low energy (450-650 keV, γ-2), low current (-1.5 A), low energy spread (ΔE/E′0-4) relativistic photoelectron beam. The spontaneous emission spectrum measured agrees well with the homogeneously broadened spectrum of a TE10 waveguide mode. The small-signal gain spectrum measured is in good agreement with theoretical prediction calculated by assuming the operation in the low-gain Compton regime.

On the amplification mechanism of the ion-channel laser

The amplification mechanism of the ion-channel laser (ICL) in the low-gain regime is studied. In this concept, a relativistic electron beam is injected into a plasma whose density is comparable to or lower than the beam's density. The head of the electron beam pushes out the plasma electrons, leaving an ion channel. The ion-focusing force causes the electrons to oscillate (betatron oscillations) about the axis and plays a role similar to the magnetic field in a cyclotron autoresonance maser (CARM). Radiation can be produced with wave frequencies from microwaves to X-rays depending on the beam energy and plasma density: omega approximately 2 gamma /sup 3/2/ omega /sub pe/, where gamma is the Lorentz factor of the beam and omega /sub pe/ is the plasma frequency. Transverse (relativistic) bunching and axial (conventional) bunching are the amplification mechanisms in ICLs; only the latter effect operates in free-electron lasers. The competition of these two bunching mechanisms depends on beam velocity nu /sub 0z/; their dependences on nu /sub 0z/ cancel for the cyclotron autoresonance masers. A linear theory is developed to study the physical mechanisms, and a PIC (particle-in-cell) simulation code is used to verify the theory. The mechanism is examined as a possible explanation for experimentally observed millimeter radiation from relativistic electron beams interacting with plasmas. >

An analytical calculation for the laser gain in a long pulse free-electron laser

For a long pulse free-electron laser (FEL) in the low gain regime, an approximate expression is given to describe the optical field gain from the small signal to the weak saturation. The result is shown to agree with those from a 1-D computer simulation.

Mode competition and suppression in free electron laser oscillators

The stability of single-mode operation of free electron laser (FEL) oscillators is investigated. Two models of an untapered FEL oscillator are considered. The first model is called the klystron model. In the klystron model the FEL interaction occurs at two points: a prebunching point and an energy extraction point. In this model the nonlinear electron dynamics are solvable exactly, leading to a complex delay equation for the wave fields. The stability of single-mode operation can then be determined easily as a function of a single-pass gain, energy mismatch–frequency, and the difference between the group velocity of the radiation and the beam velocity. The second, more realistic model has a distributed interaction region of finite length: Stability of single-mode operation in this device must be determined numerically. The results of the models in the low gain regime are compared and the parameter regimes where stable single-mode operation is possible are determined. It is found that the time to reach a single-mode state can be extremely long.

Regions of stability of FEL oscillators

The stability of single mode operation of FEL oscillators is investigated. We consider two models of an untapered FEL oscillator. The first model is called the klystron model. In it the FEL interaction occurs at two points: a prebunching point and an energy extraction point. In this model the nonlinear electron dynamics are solvable exactly leading to a complex delay equation for the wave fields. The stability of single mode operation can then be determined easily as a function of single pass gain, energy mismatch frequency, and the difference between the group velocity of the radiation and the beam velocity. The second, more realistic model has a distributed interaction region of finite length. Stability of single mode operation in this device must be determined numerically. The results of the models in low gain regime will be compared and the parameter regimes where stable single mode operation is possible will be determined.

A linear three-dimensional model for free electron laser amplifiers

This paper introduces a generalized, linear, three-dimensional model of the FEL amplifier. This 3-D model that is represented by a matrix gain-dispersion equation is valid in the various FEL gain regimes; the low and high gain regimes and the space-charge dominated regimes. It includes electron-beam longitudinal velocity spread effects that are caused by energy spread, transverse emittance and betatron motion. The model provides solutions for the EM-wave amplitude and phase profiles for any initial transverse profiles of the electron beam and of the EM wave, given at the entrance to the interaction region. The matrix gain-dispersion equation consists of angular spectrum components and therefore it is applicable for free-space FEL schemes and for rectangular waveguide schemes as well. Different linear three-dimensional effects, such as optical guiding, gain focusing, reduction of space-charge effects, bending of the radiation beam, off axis-gain, etc., are all inherently included in the presented model. Figurative results, derived according to the parameter sets of two representative high-gain FELs, are demonstrated.

A review of the theory of pulse propagation in the long bunch low gain regime

In this paper we review the theory of pulse propagation in the free electron laser using an analytical method valid for FELs driven by radiofrequency (rf) accelerators with rms bunch length large compared to the slippage distance. We obtain analytical expressions for the relevant supermodes both in the spatial and in the frequency domain. We show that the FEL supermodes form a bi-orthogonal basis. We also derive simple expressions for quantities of practical interest such as, for example, the width of the cavity detuning curve.

Response of transient stimulated Raman scattering to a pulse train

Analytic solutions to the problem of the response of stimulated Raman scattering (SRS) in the low-gain regime to an optical pulse train of short pulses are obtained. Solutions cover the cases of propagation in uniform and certain nonuniform media for arbitrary pulse repetition rates. The solutions describe memory effects in the SRS response to such currently available sources as radio-frequency free-electron lasers and mode-locked devices.

High-speed InP/InGaAsP/InGaAs avalanche photodiodes grown by chemical beam epitaxy

High-performance InP/InGaAsP/InGaAs avalanche photodiodes (APDs) grown by chemical beam epitaxy are described. These APDs exhibit low dark current (less than 50 nA at 90% of breakdown), good external quantum efficiency (greater than 90% at a wavelength of 1.3 mu m), and high avalanche gain ( approximately=40). In the low-gain regime, bandwidths as high as 8 GHz have been achieved. At higher gains, a gain-bandwidth-limited response is observed; the gain-bandwidth product is 70 GHz. >

The linear theory of the circular free-electron laser

A small signal theory of a free-electron laser (FEL) with a rotating electron beam in a uniform axial magnetic field and in an azimuthal wiggler field (the ‘‘circular’’ FEL) is developed. The analysis includes the low and high gain regimes and the influence of longitudinal space-charge forces. It is found that the circular FEL instability has two regimes: a strong pump regime and a negative mass dominated regime. The negative mass regime replaces the weak pump (Raman) regime found for the usual FEL geometry in which the electron beam propagates in the axial direction (the ‘‘linear’’ FEL). The dispersion relation is evaluated, and the resulting growth rates are compared with those of the linear FEL. For a cold beam, at fixed output frequency, the growth rate in the strong pump regime is larger, by a factor of γ2/3, in the circular FEL. The negative mass instability is shown to increase the growth rate and modify the bandwidth of the circular FEL in the strong pump regime. However, the circular FEL performance is found to be more sensitive to the energy spread than the linear FEL.

Analytical treatment of free-electron laser in the long-pulse limit.

We discuss a method to obtain analytical solutions of the evolution equation of the optical signal in long-pulse free-electron-laser oscillators in the low-gain and small-signal regime. Supermodes are identified with the eigenstates, harmonic-oscillator orthonormal functions, of a non-Hermitian Hamiltonian. Inhomogeneous broadening effects due to energy spread and emittance are included. The space-time characteristics of the laser field are obtained with a significant reduction in the computer time.

Free-electron-laser radiation induced by a periodic dielectric medium.

Stimulated emission by an unaccelerated electron beam propagating through a periodically modulated dielectric is studied. The laser gain in the low-gain regime is calculated for the case of a cold, tenuous electron beam by applying the Einstein-coefficient technique in the classical limit \ensuremath{\Elzxh}\ensuremath{\rightarrow}0. In the high-gain, strong-pump regime equations for the evolution of the electron beam dynamics and of the radiation are developed using a self-consistent, one-dimensional model for the interaction. Analytic calculations of the small-signal gain, and numerical computations of the nonlinear saturation characteristics, are presented.

Microtemporal and spectral structure of storage ring free-electron lasers

The microtemporal and spectral structure of free-electron lasers has been analyzed in the low gain, low field, and small slippage regime. Analytical expressions of the longitudinal eigenmode (super-modes) is derived for various configurations including the undulator, the optical klystron, and an intracavity dispersive element. Longitudinal and spectral narrowing of the laser pulse is predicted down to a limit set by the Fourier transform. On storage ring, it is found that early saturation prevents the laser from reaching this limit, in good agreement with results from the Orsay experiment. The insertion of a Fabry-Perot etalon in the cavity should make possible a relative linewidth on the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> .