C. James Elliott

Conceptual designs of a 50 nm FEL oscillator and a 20–40 nm SASE amplifier☆

Abstract This paper consists of two parts; (1) the conceptual design, and optical performance characteristics, of a grazing angle of incidence ring resonator utilizing multifaceted metal mirrors for use with a 50 nm rf linac driven XUV FEL oscillator, and (2) electron beam and wiggler requirements for a self-amplified spontaneous emission (SASE) amplifier to produce high power in the 20–40 nm wavelength range. The basis for these studies is the 3- d FEL simulation code FELEX which, in part (1), is used to derive tolerances on mirror figure and thermal distortion, alignment sensitivity, and alternative output coupling methods. In part (2), the sensitivity of the output characteristics of an XUV FEL SASE amplifier to wiggler field errors is also studied.

Harmonic power implications on free electron laser mirror design

Abstract Calculations of the coherent-spontaneous radiation at the harmonic frequencies of a 1 μm free electron laser employing a tapered wiggler with a prebuncher have been performed utilizing a transverse-averaged cavity-mode code. The relative harmonic power adsorbed per unit area has been calculated for three possible metal mirror candidates and shown to be a small fraction of the total power density absorbed by the mirror.

Theory of harmonic radiation using a single-electron source model

Significant progress has recently been made toward the understanding of the various mechanisms that generate harmonic radiation in plane-polarized free electron lasers. Within the context of a single-frequency coherent-spontaneous-emission model, a distributed transverse source function for a single electron has been derived. This source is multiply peaked, with the number of peaks being equal to the harmonic number. The peaks and nulls in the radiation source are analogous to the radiation peaks seen in the spontaneous-radiation pattern of a single electron. When the distributed source function is averaged over transverse space, the simplified one-dimensional results are recovered. The distributed-source-function model predicts the generation of even harmonic radiation with odd symmetry in the electron wiggle plane (for electrons traveling along the wiggler axis) and odd harmonic-radiation patterns with even transverse symmetry. A method for modeling the multipole nature of the harmonic radiation on a discrete grid is described. When the transverse electron-beam distribution is slowly varying, all the harmonics can be adequately modeled with multipoles having only a few peaks. This model has been incorporated into the 3D FEL simulation code FELEX. Simulations of the Los Alamos and Stanford FEL oscillators have been performed. How the harmonic transverse spatial electric-field profiles change for different operating conditions is examined.

Small-Signal Gain for a Planar FEL with a Periodic Magnetic Field

We describe computation of the small-signal normal modes for a Compton regime free-electron laser (FEL) with an arbitrary periodic magnetic field. Our work shows how to extend the previously known sinusoidal results into the low-energy regime and also how to describe consequences of periodic magnetic fields at arbitrary e-beam energy. The formalism has an a posteriori requirement that the calculated gain or phase shift be small over a wiggler period. The concept of coupling coefficients applies to these generalized conditlons, and provides a unified description of this large class of cases. The formalism is based on the classical one-dimensional Vlasov-Maxwell equations, without an Abraham-Lorentz model of radiation reaction. These results are specialized to a number of important limiting cases: the cold-beam limit, the sinusoidal limit, and the highly relativistic sinusoidal field limit that we compare to known results. The results of this formalism show that coupling to harmonics can be enhanced far beyond that achievable by purely sinusoidal magnetic fields.

Gain saturation and self‐focusing considerations in the design of optical amplifiers

We extend the stability analysis of the quasioptical equation given by Bespalov and Talanov and by Suydam to the case of Frantz‐Nodvik pulse propagation. When e ≈ (An0g0/2 π λ)2 ≪ 1, we find that the logarithm of the perturbation growth divided by the input intensity depends on the input illuminance and the media gain. This relationship is important in amplifier design. The asymptotic growth may be given in closed form even when e ≫ 1. This form is used for design refinements when indicated by an a posteriori estimate.

Field error lottery

Abstract The level of field errors in a free electron laser (FEL) is an important determinant of its performance. We have computed 3D performance of a large laser subsystem subjected to field errors of various types. These calculations have been guided by simple models such as SWOOP. The technique of choice is use of the FELEX free electron laser code that now possesses extensive engineering capabilities. Modeling includes the ability to establish tolerances of various types: fast and slow scale field bowing, field error level, beam position monitor error level, gap errors, defocusing errors, energy slew, displacement and pointing errors. Many effects of these errors on relative gain and relative power extraction are displayed and are the essential elements of determining an error budget. The random errors also depend on the particular random number seed used in the calculation. The simultaneous display of the performance versus error level of cases with multiple seeds illustrates the variations attributable to stochasticity of this model. All these errors are evaluated numerically for comprehensive engineering of the system. In particular, gap errors are found to place requirements beyond convenient mechanical tolerances of ± 25 μm, and amelioration of these may occur by a procedure using direct measurement of the magnetic fields at assembly time.

Small signal gain based on analytic models of thin intense electron beams

Abstract We develop the free electron laser theory of the effective energy distribution and the small signal gain for a thin electron beam. The assumption of thinness allows us to treat various transverse locations and electron beam trajectory angles as introducing phase shifts that have the same effect as those introduced by a change in energy of the electron. These ideas extend previous work of Colson et al., Dattoli et al., Scharlemann, and others in five important ways. The first is the ability to treat electron beams with three different classes of matching or symmetry conditions: (i) electron beams with separate betatron matching in each plane. (ii) those with aspect ratio matching, and (iii) crossed matched beams. Manifestations of these symmetries include elliptical cross-sections and electron beams that have modulated spatial profiles. For these we derive analytical expressions for effective energy distributions. Second, two emittance parameters for the electron beam are shown to consolidate into a single parameter that describes most of the energy variation of the effective energy distributions. Thus, the effective energy distribution for a 1:4 ribbon electron beam is nearly equivalent to a distribution for a beam of circular cross-section. Third, these calculations extend to energy distributions, angular distributions, and spatial distributions that all follow Gaussian profiles. Fourth, this model incorporates the description of the incident Gaussian optical beam and the above electron beam dynamics into a single influence function kernel. Emittance, energy spread, diffraction, and gain may be interpreted as limiting the length over which the bunching contributions of the propagating electric fields downstream are important. Fifth, three-dimensional profiles of the optical fields are computed. This work is complementary to the recent work of Yu, Krinsky and Gluckstern in that ours always describes the transition from low gain to high gain for a thin beam and not necessarily the high-gain regime itself. Therefore in this work the parameters of the incident optical beam are included, whereas, their work is not concerned with these parameters. The resulting transverse dependence of the fields may be characterized by an optical beam radius. This optical beam width starts out large compared to the thin electron beam and then, in the example given, contracts to a size that becomes so small that the thin-beam assumption is violated.

Parasitic oscillations in the static centered two-aperture limit

A class of stray-light parasitic oscillation problems observed in high-gain laser systems is attacked by the integral equation method of Selden. The feedback fraction product determined by this method is compared with a simple estimate based on the solid angles of the apertures and is found to differ by a factor lying between (2/π)4 and unity. This factor is computed numerically for all two-rectangular-aperture problems and analytically in special cases. We thus determine the static parasitic oscillation threshold for all these problems and deduce the corrections needed for the simple solid-angle method of computation.

Accurate and efficient free-electron laser performance model including nonideal effects

There are a number of codes that can calculate the performance of a free-electron laser (FEL) in 3D with nonideal electron beams, wigglers, and optics. Unfortunately, these codes can be very computationally intensive. So, given the large number of parameters associated with an FEL, it is often impractical to utilize such a large-scale code to develop a preliminary design. To overcome this problem we developed a reduced FEL model that is sufficiently accurate to provide a realistic performance estimate, while, at the same time, the algorithm is sufficiently efficient to investigate a large number of parameter variations. The low-level algorithms design the wiggler, determine the effective energy distribution of the electron beam inside the wiggler, determine the small-signal gain, determine the saturation gain and efficiency, and design the optics.

Detrapping from magnetic field errors as a random walk ESCAPE

Abstract We examine the effects of random magmetic field errors on the performance of a free electron laser. We report a modification of the straightest wiggler orbit operating point (SWOOP) theory for two very high efficiency systems. The first system utilizes a gapless pulsed cryogenic wiggler and the second a continuous wave gapless superconduction wiggler. We further show a method to improve the choice of separation of correctors. To establish this method we show that corrected steering errors, BPM errors and gap misadjustments are errors similarly construed as phase errors (ESCAPE). The corrected steering errors also have a component that requires retuning of the wiggler and this task is relegated to unoptimized SWOOP. Without this retuning, these errors are emittance cannot be removed by returning except for the resonant particle. The remaining part of the field errors are similar to similar to an effective emittance, but because the steering errors are homogeneous and the emittance is inhomogeneous, the phase errors and behave like a random force in the KMR potential. In a returned wiggler, the effective energy broadening from emittance is responsible for the initial trapping and the field errors are responsible for the detrapping. This work constitutes a complete high-efficiency model of phase, gap and corrected steering errors for an enmsemble of the free electron lasers. The classical bound-free transition, the detrapping phenomenon, is treated as the Kramers problem.