Angular distribution and radial profile of a relativistic electron beam in vacuum

The injection of a relativistic electron beam ( nu mod gamma =0.16) into vacuum, results in the formation of a virtual cathode. As a consequence a hollow current density profile is measured beyond the virtual cathode. But the measurement of the angular distribution of the electron velocities indicates that it remains dominated by scattering in the anode foil. Transmitted beam currents are greater than the stationary vacuum limiting current of Bogdankevich, and Rukhadze (1971). Electron beam trajectory calculations, taking into account the electromagnetic beam potential and foil scattering, are capable of describing the virtual cathode. Similar to the calculations of Thode et al. (1979), the hollow profile is steeper than the measured profile and in both cases the calculated limiting current is too small.