The authors investigate the excitation of unstable potential oscillations in an isothermal plasma in a strong magnetic field ( ≫ 4π n0 mec2) by means of a current flowing perpendicular to the magnetic field. When the current velocity only slightly exceeds the critical value determining the instability boundary, a non-linear dispersion equation having a non-local form in time is derived for the amplitudes of the unstable oscillations. The authors estimate the energy of the oscillations in a non-linear regime when the oscillation amplitude ceases to increase due to non-linear wave interaction. It is shown that the longitudinal temperature of the electrons and the transverse temperature of ions increase at the same rate due to scattering of the plasma electrons and ions by turbulent pulsations of the electric field produced by the unstable oscillations. The effective frequency of ion collisions with these oscillations is found to within an order of magnitude and an estimate made of the maximum temperature which can be attained by the electrons and ions in the regime of the instability under consideration.