Transmission of foil-focused relativistic annular electron beam in coaxial cylindrical waveguide

Combining the characteristics of foil focusing and electrostatically-charged-wire focusing, the transmission of foil-focused intense relativistic annular electron beam in a coaxial cylindrical waveguide is studied. The electric filed and the space-charge-limited current is derived by calculating Poisson equation via numerical calculation. The equilibrium conditions and tracks of envelope electrons are attained through motion the electron equation．