Particle motion in inhomogeneous magnetostatic and high-frequency fields at the gyroresonance is studied in the limit of a large number of particle revolutions in the resonance region. The role played by the magnetic mirror, Doppler and relativistic effects, wave attenuation and radiation pressure on particle acceleration is discussed. The time dependence of the orbital magnetic flux, the velocity along the magnetic lines of force and the width of the resonance region are calculated. An upper limit is found for the energy of the particle, when the effect of the magnetic field of the wave partially compensates for the change in mass with energy.The non-linear method we use is exact in the limit of many revolutions. It generalizes the results established by C.S. Roberts and S.J. Buchsbaum in a special case, to the more complex situation proposed by T. Consoli for injecting, accelerating and confining a hot plasma in a magnetic trap. A number of numerical examples are presented for various conditions. The energy transfer to the particles at the parametric resonances is also investigated.The space charge field which develops along the magnetic lines of force in a plasma accelerating structure is taken into account in the equations from the very beginning by assuming (Consoli) that the electron guiding centres move with the velocity of the ions.
Magnetic reconnection: from MHD to QED