A self-consistent theory of ferromagnetic waveguide accelerators driven by electron beams

A fully self-consistent theory of ferromagnetic waveguide accelerators driven by a relativistic electron beam is developed. The theoretical analysis is based on Faraday´s law, which provides a second-order partial-differential equation of the azimuthal magnetic field, under the assumption that με≫1 . Here μ and ε are the permeability and dielectric constant of the waveguide material. The azimuthal magnetic field and axial acceleration field are obtained in forms of integral equations for an arbitrary profile of the drive-beam current I(t)