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Stochastic motion of relativistic electrons under conditions of the nonlinearresonance interaction of particles with space plasma waves is studied.Particular attention is given to the problem of the stability and variabilityof the Earth's radiation belts. It is found that the interaction betweenwhistler-mode waves and radiation-belt electrons is likely to involve thesame mechanism that is responsible for the dynamical balance between theaccelerating process and relativistic electron precipitation events. We havealso considered the efficiency of the mechanism of stochastic surfingacceleration of cosmic electrons at the supernova remnant shock front, andthe accelerating process driven by a Langmuir wave packet in producing cosmicray electrons. The dynamics of cosmic electrons is formulated in terms of adissipative map involving the effect of synchrotron emission. We presentanalytical and numerical methods for studying Hamiltonian chaos anddissipative strange attractors, and for determining the heating extent andenergy spectra

Stochastic electron motion driven by space plasma waves