Parallel heating associated with interaction of forward and backward electromagnetic cyclotron waves

We studied parallel heating of thermal particles in the presence of two forward and backward electromagnetic cyclotron waves propagating parallel to a static magnetic field in a plasma. Such two waves traveling in opposite directions are commonly excited by electromagnetic instabilities driven by a temperature anisotropy of energetic particles in a magnetized plasma. We developed a theory which gives a heating rate of thermal particles in the parallel direction and we also derived a threshold of the wave amplitude for nonlinear cyclotron trapping of the thermal particles. We performed a computer experiment using an electromagnetic hybrid code, where we assumed anisotropic hot protons as a free energy source. Forward and backward ion cyclotron waves were excited with frequencies below the helium cyclotron frequency. We observed heating of helium ions in the parallel direction. The heating rate agrees well with the theoretical estimate. (author)