The existence of a two-parameter set of dressed Langmuir solitons is shown numerically, resolving a discrepancy among earlier investigations.

Stochasticity of particles in a magnetized plasma as a result of many waves with common frequency ω and different wave vectors k is examined. A critical potential amplitude Φc(k)=εc/k4∥ is verified with the following property: Effective heating along the magnetic field B0 by small-amplitude waves is only possible in the velocity interval (ω/kmax) ≤v∥ ≤(ω/kmin), where kmin, kmax denote the interval for k∥ (parallel to B0) in which ‖Φ(k)‖≥‖Φc(k)‖. Heating perpendicular to B0 by circularly polarized waves with a Fourier spectrum peaked around a perpendicular wave vector k⊥ is strongly inhibited by the presence of an adiabatic invariant, but these barriers can be overcome by waves with a sufficiently broad spectrum in k⊥.

Dedicated to Professor Dieter Pfirsch on his 60th BirthdayThe Ham iltonian equations o f a particle in a random set of waves just above the stochasticity threshold are considered both theoretically and numerically. First we derive the diffusion coefficient and the autocorrelation time perturbatively without using the thermodynamic limit, and we discuss the relevance of the H am iltonian problem for particle acceleration and magnetic field line flow. Then we integrate the equations for an ensemble o f magnetic field lines numerically for a model problem [15] and show the time evolution of moments and correlations. Twice above the threshold we observe diffusive behaviour from the beginning, but the diffusion coefficient includes also the non-resonant modes. Just at threshold we find first a short phase o f free acceleration, later a diffusion which is slower than predicted by the theoretical formula. The best way to analyze the problem is in terms o f cumulants, but a reliable com pari son with any theory requires also a time integration of the corresponding kinetic equations.