Luis R. Elias

Relations between Hermite and Laguerre Gaussian modes

Relations between Hermite (HG) and Laguerre (LG) Gaussian modes are derived. With these, a LG mode is written as a sum of HG modes, and vice versa. These mode relations are derived from addition identities between a Laguerre polynomial and a pair of Hermite polynomials. The addition relations are derived in two appendices. One figure illustrates the contents of a LG mode in terms of HG modes while a second figure shows the translation in the opposite direction. >

Focusing permanent magnet undulator

Abstract A plane polarized undulator does not have the ability to focus an electron beam in the undulating plane (X-Z plane) because the magnetic field decreases away from the X-axis. To focus in the bending plane, a quadrupole field must be added to the undulating field. This can be achieved using curved magnets or trapezoid-shaped magnets. In this article, we analyze a few magnet configurations which produce X-Z focusing. It has been found that semicircular magnetics or trapezoid magnets having 1.2° angle are suitable as focusing permanent magnet undulator.

Electrostatic-accelerator FELs for power beaming

Abstract We propose the use of electrostatic-accelerator free-electron lasers (EAFELs) to generate intense, CW, single-mode, laser radiation for space power beaming applications such as envisioned by the project SELENE. We discuss two basic FEL configurations employing present electrostatic accelerator technology (≤25 MV), together with the electron gun and electron collector beam recovery technology first developed for the UC Santa Barbara FEL.

Mode competition in long-pulse FELs

Abstract The nonlinear mode interaction in FELs is studied in an analytic perturbative framework both for low as well as high gain regimes. The mode coupling depends on the saturation terms which mainly arise from third order perturbation. Both self- and crossed saturation are obtained and the ratio crossed/self characterizes the strength of the mode coupling. The mode competition is analyzed by studying the two mode problem. Mathematically, this entails a stability analysis of a system of two coupled integro-differential equations. In FELs the crossed saturation is twice as strong as the self-saturation. As a consequence of the strong crossed saturation, a dominant mode is able to suppress other competing modes and the result is single mode operation.

Self-consistent analysis of 3D undulator radiation and relativistic electron beam dynamics using Lienard-Wiechert fields

Abstract Lienard-Wiechert (LW) fields, which are exact solutions of the wave equation for a point charge in free space, and the Lorentz force equations are employed to formulate a self-consistent treatment of electron beam dynamics and radiation field evolution in magnetic undulators. In a relativistic electron beam the internal forces leading to the interaction of the electrons with each other can be computed by means of retarded LW fields. The resulting electron motion enables us to obtain three dimensional undulator radiation by summing up the field contribution of each electron in the beam. The approach used is particularly well suited to the investigation of self amplified spontaneous emission (SASE) without introducing a seed wave at start-up. In this paper, we present studies of non-periodic multi-bucket electron phase dynamics as well as temporal and angular characteristics of the electromagnetic fields radiated by a relativistic short filamentary electron beam interacting with a circularly polarized magnetic undulator.

Three-dimensional simulation of finite pulse effects in SASE via Lienard-Wiechert fields

Abstract The common method of modeling 3D free-electron laser physics is based on the numerical treatment of paraxial wave equation coupled to the relativistic single-particle equations of motion. The following analysis of self-amplified spontaneous emission (SASE) employs an alternative approach using Lienard-Wiechert solution of the four vector wave equation for point charges in conjunction with Lorentz force equations to determine electrons motion and the evolution of the resulting 3D radiation fields. Besides its inherent simplicity, the approach allows to include important aspects of SASE-FELs, such as start-up from initial spontaneous emission, slippage of the optical pulse, interelectron Coulomb fields, multifrequency effects and transverse mode behavior of the optical wave. Simulation results illustrating electron phase dynamics as well as temporal, spectral and spatial characteristics of the radiation fields generated by a short pulse are presented and compared with available theory.

FELTRON: a high-power microwave power source for high-gradient linear colliders

Abstract We discuss a design for a high-power pulsed electrostatic accelerator (1 GW) for a high gain microwave FEL operating in an expanded gain configuration. The resulting radiation generator, FELTRON, is tailored to power a high-gradient linac operating at 20 GHz with an accelerating gradient of 100 MV/m. The electron pulse duration is 0.5 μs and the rep rate is 1 kHz. Each electron-beam pulse is divided into ten pulses.

Confirmation of single-mode FEL operation

Abstract Experimental results from the UC Santa Barbara FEL are reviewed. At saturation, macroscopic and microscopic time-structure records give clear evidence of discrete time structure and single dominant longitudinal-mode operation.

Analytical study of multimode competition

Abstract A theoretical analysis of the multimode competition problem in a FEL is presented. For the three-mode problem the system is mathematically described by a set of three coupled differential equations. The coupling coefficients in the equations are obtained from a perturbation expansion of the current driving the FEL. The only asymptotically stable solutions are single-mode. Then a system of any number of modes is studied. In this case also only single-mode solutions are asymptotically stable.

Final construction of the CREOL 8 millimeter period hybrid undulator

Abstract The construction of an 8 millimeter period hybrid undulator for the CREOL high power far-infrared free electron laser has just been completed. This FEL is expected to come on-line in the spring of 1995 and produce close to a kilowatt of continuous power at wavelengths of 225–800 μm. The undulator has precise mechanical tolerances and high field uniformity allowing for high electron beam recovery rates. Almost complete beam recovery is required for DC operation at high currents. A simple method for measuring the magnetic properties of individual magnets and sorting the magnets to reduce the peak field errors and the phase errors will be reported. These errors are further reduced by inserting and tuning adjustable pole pieces. The reduction of magnetic field errors through these two techniques will be presented.