  The electrostatic cumulation of current density in relativistic vacuum diodes
with ring-type cathodes is described theoretically and confirmed
experimentally. The distinctive feature of the suggested cumulation mechanism
is a very low energy spread of electrons. As a result of electrostatic
cumulation, a thin relativistic electron beam with a current density of 1
kA/mm$^2$ can be formed. This quantity exceeds typical current density values
in high-current Cherenkov sources by an order of magnitude. Such a beam can be
used as an active medium in high-power terahertz sources.
