Adiabatic invariants of charged particles in fields of certain symmetries

Adiabatic invariants of charged particles are constructed that can be utilized to investigate such processes as low-frequency wave propagation in REP, amplification (absorption) of Langmuir waves in a spherically symmetric gravitational field, and particle flux interaction with a nonlinear wave in longitudinal static electrical and magnetic fields. Construction of the adiabatic invariants is executed by reduction of the original problems to a one-dimensional Hamiltonian.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 13–17, January, 1990.