Generation of discrete structures in phase-space via charged particle trapping by an electrostatic wave

The wave-particle resonant interaction plays an important role in the charged particle energization by trapping (capture) into resonance. For the systems with waves propagating through inhomogeneous plasma, the key small parameter is the ratio of the wave wavelength to a characteristic spatial scale of inhomogeneity. When that parameter is very small, the asymptotic methods are applicable for the system description, and the resultant energy distribution of trapped particle ensemble has a typical Gaussian profile around some mean value. However, for moderate values of that parameter, the energy distribution has a fine structure including several maxima, each corresponding to the discrete number of oscillations a particle makes in the trapped state. We explain this novel effect which can play important role for generation of unstable distributions of accelerated particles in many space plasma systems.