Analysis of Smith-Purcell free-electron lasers

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Vinit Kumar and Kwang-Je Kim
Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

Received 19 September 2005; published 2 February 2006

Wepresent an analysis of the beam dynamics in a Smith-Purcellfree-electron laser (FEL). In this system, an electron beam interactsresonantly with a copropagating surface electromagnetic mode near the gratingsurface. The surface mode arises as a singularity in thefrequency dependence of the reflection matrix. Since the surface modeis confined very close to the grating surface, the interactionis significant only if the electrons are moving very closeto the grating surface. The group velocity of the surfacemode resonantly interacting with a low-energy electron beam is inthe direction opposite to the electron beam. The Smith-Purcell FELis therefore a backward wave oscillator in which, if thebeam current exceeds a certain threshold known as start current,the optical intensity grows to saturation even if no mirrorsare employed for feedback. We derive the coupled Maxwell-Lorentz equationsfor describing the interaction between the surface mode and theelectron beam, starting from the slowly varying approximation and thesingularity in the reflection matrix. In the linear regime, wederive an analytic expression for the start current and calculatethe growth rate of optical power in time. The analysisis extended to the nonlinear regime by performing a one-dimensionaltime-dependent numerical simulation. Results of our numerical calculation compare wellwith the analytic calculation in the linear regime and showsaturation behavior in the nonlinear regime. We find that asignificant amount of power grows in the surface mode dueto this interaction. Several ways to outcouple this power tofreely propagating modes are discussed.

URL:	http://link.aps.org/doi/10.1103/PhysRevE.73.026501
DOI:	10.1103/PhysRevE.73.026501
PACS:	41.60.Cr; 42.79.Dj; 52.59.Px 41.60.Cr Free-electron lasers 42.79.Dj Gratings 52.59.Px Plasma hard X-ray sources YEAR: 2006
KEYWORDS:	free electron lasers, laser beams, electron beams, numerical analysis

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