Scattering of relativistic electron beam by two counter-propagating laser pulses: A new approach to Raman X-ray amplification

Abstract

We present a detailed study of the properties of electron beam injected and trapped in an high intensity optical lattice. By using the hydrodynamic and kinetic approaches, we identified the beam trapping conditions, the high-frequency longitudinal beam eigenmodes and their dependence on the electron angular and energy spread. The coupling of these beam eigenmodes to the laser waves is also considered. This corresponds to the convective parametric instability: a stimulated scattering of two laser beams creating the optical lattice on the trapped electron beam mode. The amplification coefficients for the up-scattered Raman modes propagating parallel to the electron beam are calculated and their dependence on the beam characteristics is analyzed. The study of relativistic electron beams collective behaviour in a guiding and wiggling field has become a common interest for accelerator physics, plasma physics, nonlinear optics and laser science. By wiggling relativistic charged particles one may produce a scattered electromagnetic wave with a wavelength much shorter than the spatial period of the wigglers. This process lays at the basis of a number of techniques of XUV, X-ray and -ray generation, which find numerous applications in the diagnostics from medical physics to fusion science. Here we present a new approach to XUV/X-ray generation, based on the scattering of the bunch of relativistic electrons by a specific electromagnetic structure, called high intensity optical lattice. Such a field is created by the interference of two coherent laser pulses of equal frequencies and intensities, and it represents a standing wave pattern, where charged particles can be trapped. The electron oscillations in such a ponderomotive potential can be coupled to the laser wave field and emitted as high- and low- frequency electromagnetic waves. This process can be employed for generation of coherent radiation in a broad wavelength range extending from the infrared to X-ray domain (1). One of the promising applications of this technique is Raman XUV/X-ray amplification using a relativistic electron beam, propagating through an optical lattice (2, 3). The conventional schemes of backscattering amplification in stationary wigglers impose unrealistically severe limitations on the quality (angular and velocity spread) of the electron beam (4, 7). Raman amplifiers with optical lattices even for moderate laser intensities open a possibility to reduce strongly these limitations and to use laser accelerated electron bunches thus paving a way for compact all-optical systems.