Analysis of Smith-Purcell free-electron lasers

Journal Article · Wed Feb 15 00:00:00 EST 2006 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PHYSREVE.73.0· OSTI ID:20778710

Kumar, Vinit; Kim, Kwang-Je ^[1]

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1. Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 (United States)

We present an analysis of the beam dynamics in a Smith-Purcell free-electron laser (FEL). In this system, an electron beam interacts resonantly with a copropagating surface electromagnetic mode near the grating surface. The surface mode arises as a singularity in the frequency dependence of the reflection matrix. Since the surface mode is confined very close to the grating surface, the interaction is significant only if the electrons are moving very close to the grating surface. The group velocity of the surface mode resonantly interacting with a low-energy electron beam is in the direction opposite to the electron beam. The Smith-Purcell FEL is therefore a backward wave oscillator in which, if the beam current exceeds a certain threshold known as start current, the optical intensity grows to saturation even if no mirrors are employed for feedback. We derive the coupled Maxwell-Lorentz equations for describing the interaction between the surface mode and the electron beam, starting from the slowly varying approximation and the singularity in the reflection matrix. In the linear regime, we derive an analytic expression for the start current and calculate the growth rate of optical power in time. The analysis is extended to the nonlinear regime by performing a one-dimensional time-dependent numerical simulation. Results of our numerical calculation compare well with the analytic calculation in the linear regime and show saturation behavior in the nonlinear regime. We find that a significant amount of power grows in the surface mode due to this interaction. Several ways to outcouple this power to freely propagating modes are discussed.

• OSTI ID: 20778710
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 73, Issue 2; Other Information: DOI: 10.1103/PhysRevE.73.026501; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BEAM CURRENTS
BEAM DYNAMICS
ELECTRON BEAMS
ELECTRONS
FEEDBACK
FREE ELECTRON LASERS
FREQUENCY DEPENDENCE
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
NUMERICAL ANALYSIS
ONE-DIMENSIONAL CALCULATIONS
REFLECTION
SATURATION
SIMULATION
SINGULARITY
TIME DEPENDENCE