Electrostatic two-stream and electromagnetic filamentation instabilities for a light ion beam penetrating a plasma are investigated. The dispersion relations of these instabilities including the effect of plasma heating by the ion beam are solved analytically and numerically. Stability conditions are derived for propagation through a plasma. Attention is paid to the finite size effects of beams with small diameters of the order 0·1 cm typical for pinched gas discharges. The results are illustrated by plotting stability boundaries for a 100 keV proton beam propagating through a plasma.
