  We analyze the electromagnetic field of a short relativistic electron beam
propagating in a round, hollow dielectric channel. We show that if the beam
propagates with an offset relative to the axis of the channel, in a steady
state, its electromagnetic field outside of the channel extends to large radii
and carries an energy that scales as the Lorentz factor $\gamma$ squared (in
contrast to the scaling $\ln\gamma$ without the channel). When this energy is
converted into a terahertz pulse and focused on a target, the electric field in
the focus can greatly exceed typical values of the field that are currently
achieved by sending beams through thin metallic foils.
