  The report is devoted to the results of the numerical study of the virtual
cathode formation conditions in the relativistic electron beam under the
influence of the self-magnetic and external axial magnetic fields. The
azimuthal instability of the relativistic electron beam leading to the
formation of the vortex electron structure in the system was found out. This
instability is determined by the influence of the self-magnetic fields of the
relativistic electron beam and it leads to the decrease of the critical value
of the electron beam current (current when the non-stationary virtual cathode
is formed in the drift space). The typical dependencies of the critical current
on the external uniform magnetic field value were discovered. The effect of the
beam thickness on the virtual cathode formation conditions was also analyzed.
