Transportation of high-current charged-particle beam in coaxial undulator with partially shielded cathode in guide homogeneous magnetic field

We derive the system of transcendental equations, which gives the equilibrium radii of charged-particle beam and the equilibrium value of square azimuthal momentum of beam boundary in a coaxial magnetic undulator with partially shielded cathode in guide homogeneous magnetic field. We formulate the dynamics equations, which describe the transportation of charged-particle beam. We receive an analytical estimate of the azimuthal and longitudinal momentum of beam boundary. We study the equilibrium and differential equation numerically, compare results received for a coaxial magnetic undulator with shielded and non-shielded cathode and different induction of guide magnetic field