A nonlinear bounce-kinetic equation for trapped electrons

A nonlinear bounce-kinetic equation that is suitable for studies of nonlinear trapped-electron dynamics in the presence of short wavelength electrostatic fluctuations is systematically derived. The equation is used to analyze the nonlinear response of trapped electrons to the short wavelength collisionless trapped-electron mode in a sheared magnetic field. It is shown that nonlinear trapped-electron–wave interaction (trapped-electron Compton scattering) transfers wave energy from long to short wavelengths. However, the transfer rate is significantly restricted by magnetic shear, which limits the interaction to a narrow region near the rational surface that is typically smaller than the linear mode width. Therefore, it is expected that, in a sheared magnetic field, ion Compton scattering rather than nonlinear trapped-electron–wave interaction will be the dominant nonlinear process in short wavelength trapped-electron mode turbulence.