On the transverse dispersion of a relativistic electron beam in the evolution of ion hose instability in the ion focusing regime

We investigate the transverse expansion of a relativistic electron beam propagating in a rarefied gas-plasma medium in the ion focusing regime during the development of ion hose instability. The expression is constructed for the pinch potential of the beam as a function of the amplitude of transverse deviation of the beam and on the parameter characterizing the ratio of the characteristic radial scales of the ion channel and of the electron beam. It is shown that this potential becomes substantially lower upon an increase in the hose oscillation amplitude and when the ion channel expands relative to the transverse size of the beam cross section.