Motion of a single charged particle in electromagnetic fields with cyclotron resonances

The general Hamiltonian-averaging transformation developed to study the motion of a charged particle in a strong magnetic field and various electromagnetic perturbations permits a clear definition of the dynamics of the guiding centre. In the case of a high-frequency electromagnetic perturbation, the equations of evolution of the phase-space co-ordinates are sums of guiding-centre terms, resonant terms at any of the cyclotron resonance frequencies n(υ''parallel''k''parallel''-ω) + lΩ ≅ 0 (l and n are integers) and ponderomotive terms. The n = 1 resonances giving a contribution one order stronger than the ponderomotive terms to the equations of motion are considered. The guiding-centre transformation therefore suffices to derive the leading terms of the averaged dynamics. A simple case of isolated resonance is then considered for which, depending on the value of the external parameters (initial particle energy, amplitude of the perturbation), the phase space may possess one or two trapping regions. Even in the latter situation, the particle trajectories can be described analytically by the set of 12 Jacobian elliptic functions. (author)