Isidoro Kimel

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. >

A compact cw free electron laser

Abstract A compact, low-voltage, low-current, cw FEL is under construction at CREOL. With an electron-charge recovery of 99.9%, and depending on the power supply, the laser has the potential to generate up to 1 kW of average power in the 230–640 μm region, at a wall-power efficiency greater than 5%. This laser is also expected to operate in a very narrow bandwidth (single mode).

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.

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.

Micro-undulator Fields

Magnetic fields of several configurations for short-period undulators made of permanent magnets were studied analytically. These micro-undulators are made of blocks on which grooves are machined. First, the approximate two-dimensional fields were obtained by solving the Poisson equation using Fourier transforms. The finite-width corrections were added afterwards.

Computer simulation of mode evolution in long pulse FELs

Abstract The longest pulse FEL to date is presently under construction. The bandwidth will critically depend on the optical mode interaction. The set of coupled, nonlinear equations for modes evolution are solved numerically. Due to the strong mode coupling in long pulse FELs, the outcome is single mode operation.

A compact, bright and tunable CW source of soft X-rays

Abstract A bright, CW, tunable source of soft X-rays is proposed. The X-rays are obtained from the Compton backscattering of intense infrared laser radiation from a high quality electron beam. The incident infrared radiation is the intracavity beam in a high power Nd:YLF laser. This radiation is scatted from an relativistic electron beam generated by electrostatic accelerators. Such an X-ray source would constitute a low cost compact alternative to the more traditional synchrotron rings. Narrow bandwidth X-ray radiation can be obtained with the use of proper aperturing without the necessity of monochromators. Analytic expressions of the frequency spectrum of the radiation through a certain aperture, are given. These expressions are valid for small undulator parameter and large number of periods.

SASE X-ray radiation via Lienard-Wiechert fields

Abstract We present three-dimensional numerical results of self-amplified X-ray wiggler radiation from a relativistic electron beam using Lienard-Wiechert forces to drive self-consistently the motion of electrons. The exact three-dimensional self-consistent motion of a beam of electrons gives rise to exact three-dimensional radiation fields which can be calculated with very few approximations. As an example of this approach, we report here results of three-dimensional X-ray coherent wiggler radiation calculations for a short relativistic electron pulse.