The magnetosonic wave emission by an intense relativistic electron beam rotating within a plasma is calculated. This process follows the trapping of the beam in the plasma, and results in a transfer of approximately half the beam energy to the plasma ions. A nonlinear theory is given in accord with beam and plasma parameters of fusion interest. It is shown that dissipation balances the nonlinearity to produce a shock‐type flow resembling that of the linear theory. The primary nonlinear modification is an adjustment of the wave speed tovs=vAMs, wherev2A=B20/4&pgr;nmiandMs=1+B˜/B0is the mach number (B˜is the wave field,B0is the applied field). Estimates are made of power radiated to the waves and the resultant ion energies for some typical experimental parameters.