Instabilities and induced scattering due to nonlinear Landau damping of longitudinal plasma waves in a magnetic field

The matrix elements for nonlinear wave-particle scattering (nonlinear Landau damping) are obtained in explicit form for electrostatic waves from the Vlasov-Maxwell equations. The waves are allowed to propagate at arbitrary angles to the magnetic field, and no restrictions are imposed upon the Larmor radius or the frequencies. In the case k_⊥≫k_∥, the symmetry relations for mode-mode coupling are demonstrated by appropriate manipulations of the matrix elements. This allows one to cast the nonlinear Landau damping coefficients in a particularly simple form. The conditions for explosive instabilities are obtained, and a possible stabilization mechanism for these instabilities is pointed out. In the limit of either perpendicular or parallel propagation to the magnetic field, a comparison is made with previous results. The nonlinear stability of two types of velocity anisotropy instabilities are examined. Explosive instabilities are found to exist both for Harris modes and upper hybrid loss-cone modes. In addition, recent experimental results on nonlinear decay (induced scattering) of waves are discussed in the light of the present theory.