Scenarios for the nonlinear evolution of alpha-particle-induced Alfvén wave instability

Various nonlinear scenarios are given for the evolution of energetic particles that are slowing down in a plasma and simultaneously excite the background plasma waves. Depending on the relationships between the source, the background damping, and the classical transport rate, either a steady state or pulsations arise. At the predicted saturation levels, anomalous particle transport is rather low. However, if the particle orbits are stochastic at the amplitude level needed to balance the growth rate with the wave trapping frequency, a phase space ``explosion'' occurs, giving enhanced transport.