Nonlinear ion motion in the slow ion cyclotron mode

The nonlinear cyclotron resonance of a single ion in a coherent, electromagnetic slow ion cyclotron wave is treated analytically for arbitrary polarization and angle of propagation in a homogeneous magnetic field. For parameters of interest in CTR applications, the nonlinear phase space orbits are found to be characterized by the case of parallel propagation. For this case, approximate expressions are obtained for the gyroradius and parallel velocity of the resonant particle. In this approximation, the nonlinear period and adiabatic invariant are found. The treatment is shown to extend to a system with slowly changing parameters. It is shown that cooling of the parallel temperature is a natural feature of slow mode resonance heating, an effect which has been seen in a recent numerical simulation. Comparison of the nonlinear frequency with the linear ion cyclotron and electron Landau damping rates indicates that the ion cyclotron heating experiment carried out on the ST tokamak was pumping into a nonlinear resonance region, before the wave was finally damped by the linear mechanisms. It is found that nonlinear effects could account for the previously unexplained loss of high energy ions