Abstract
We present an analysis of a \v{C}erenkov free-electron laser (FEL) driven by a flat electron beam. In this system, an electron beam travelling close to a dielectric slab placed at the top of an ideal conductor interacts with the co-propagating electromagnetic surface mode. The surface mode arises due to singularity in the reflectivity of the dielectric slab for the incident evanescent wave. Under suitable conditions, the surface mode grows as a result of interaction with the electron beam. We show that the interaction of the surface mode with the co-propagating electron beam can be rigorously understood by analyzing the singularity in the reflectivity. Using this approach, we set up coupled Maxwell-Lorentz equations for the system, in analogy with conventional undulator based FELs. We solve these equations analytically in the small signal regime to obtain formulae for the small signal gain, and the spatial growth rate. Saturation behaviour of the system is analyzed by solving these equations numerically in the nonlinear regime. Results of numerical simulations are in good agreement with the analytical calculations in the linear regime. We find that \v{C}erenkov FEL under appropriate conditions can produce copious coherent terahertz (THz) radiation.
Highlights
An electron moving in a close proximity to a dielectric material emits Čerenkov radiation [1] with angle of emission given by cos θ 1⁄41 βpffiεffiffiμffiffi : ð1ÞHere, ε and μ are relative permittivity and relative permeability respectively of the dielectric medium; β 1⁄4 v=c, v is the electron’s speed and c is the speed of light in vacuum
We have presented an analysis of Čerenkov free-electron laser (FEL) driven by a flat electron beam for the single slab geometry, by setting up Maxwell-Lorentz equations
For conventional undulator based FELs, the approach based on Maxwell-Lorentz equations has been extremely successful, to understand the behavior in the nonlinear regime, and to incorporate realistic effects
Summary
An electron moving in a close proximity to a dielectric material emits Čerenkov radiation [1] with angle of emission given by cos θ. The dispersion relation can be expanded in the Taylor series about the roots of no-beam dispersion to find the growth rate of electromagnetic field Using this approach, Owens and Brownell [16] performed two-dimensional (2D) analysis for a CFEL based on single slab geometry. Our approach incorporates the space charge effects, and it is extendible to the nonlinear regime, unlike the approach based on coupled MaxwellVlasov equations In this approach, the electromagnetic field due to a flat beam is presented as a spectrum of plane waves of different frequencies and having phase velocity equal to the electron beam velocity [32]. We set up the basic electromagnetic field equations for a single-slab geometry based CFEL driven by a flat electron beam This is followed by the detailed calculation of singularity in the reflection coefficient of the dielectric surface.
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