Relativistic structure of stochastic wave–particle interaction

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Abstract
Stochastic interactions of charged particles with electrostatic waves propagating at arbitrary angles to an external magnetic field are studied based on a relativistic canonical Hamiltonian formalism. The present theory, however, is valid also for electromagnetic waves after a slight modification. The stochasticity threshold is derived utilizing Chirikov’s criterion. It is found that relativistic effects are important for electrons interacting with relatively high phase velocity waves even at nonrelativistic initial energies. In particular, the relativistic generalization of a previous theory [Phys. Rev. Lett. 3 4, 1613 (1975); Phys. Fluids 2 1, 2230 (1978)] moves the degeneracy of primary resonances in nearly perpendicular directions to the angles where the parallel phase speed approximately equals the speed of light. It was also demonstrated for the first time that initially low energy electrons can gain relativistic energies (γ≫1) by means of the stochastic interaction with an electrostatic wave, where γ is the relativistic factor. Moreover, properties of second‐order islands that form within primary islands have been studied. Finally, the nature of the stochastic particle energization by electrostatic waves is compared with that by electromagnetic waves, and the results are applied to the problem of electron acceleration during ionospheric modification experiments.