Equilibrium of intense electron beam in coaxial undulator with partially shielded cathode in guide homogeneous magnetic field

For the initial radii of charged-particle beam in a coaxial magnetic undulator with partially shielded cathode we formulate the equilibrium equations, which enforce the defocusing self-electric field compensation by the longitudinal and azimuthal components of self-magnetic field of the electron beam and account for the undulator focusing through the first (leading) harmonic of the undulator magnetic field. Numerical solutions of the equilibrium equations in a coaxial magnetic undulator with shielded and non-shielded cathode are analyzed and compared.