Dynamics of particles trapping and detrapping in coherent wave packets

Particles interacting resonantly with large-amplitude coherent one-dimensional wave packets can trap and subsequently detrap or even reflect. Many resonant particles are strongly scattered in the process, and the long-time dynamics of such particles is stochastic throughout a large region of phase space when repeated wave-particle interactions occur. We apply adiabatic invariance theory and separatrix crossing theory to this Hamiltonian system, which is beyond the realm of quasilinear theory. We calculate the adiabatic invariant through first order in the (small) slowness parameter var-epsilon for all particle trajectories. Because the trajectories of resonant particles cross a separatrix, the adiabatic invariant is broken and separatrix-crossing theory must be used. Our Hamiltonian provides a simple model for the fundamental physics of narrow-spectrum plasma turbulence, for strong rf current drive in a tokamak, and for electron dynamics in a recirculating free-electron laser