Quasi-linear and nonlinear theory of dissipative trapped particle instabilities

An examination of particle linear orbits reveals how charged particles nonresonantly exchange energy with trapped particle modes in the presence of collisions. Phase space diffusion coefficients are constructed which describe the changes in the equilibrium particle distributions and which allow computation of the linear growth rates of the dissipative trapped particle instabilities. Wave-induced detrapping and resonance broadening are considered as nonlinear modifications of the particle-wave interaction and found to be ineffective as mechanisms to saturate growth of the dissipative trapped ion mode. Mode coupling with plasma diffusion across the magnetic field is a stronger effect for this and the dissipative trapped electron mode. Final evaluation of plasma diffusion coefficients is complicated by an ignorance of the nonlinear spectral shape.