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Near a magnetic neutral line, where the magnetic field vanishes, the adiabatic invariants of charged particle motion are destroyed, and hence the number of degrees of freedom increases. When a radio-frequency electric field is applied to the system, the particle motion becomes strongly chaotic. This effect can be used to produce heat in a plasma in the absence of any collisional process. The kinetic entropy of an electron orbit increases very rapidly by the mixing effect. The velocity distribution is approximated by a Gaussian function, so the thermodynamic entropy production can also be estimated. This collisionless heating mechanism enables high-efficiency plasma production at a low gas pressure.

When an electron is accelerated by an oscillating electric field in an inhomogeneous magnetic field which has a null point, it meanders along a chaotic orbit. The kinetic energy becomes larger than that of regular motion in an off-resonant homogeneous magnetic field. This effect explains the high efficiency of plasma production in the neutral line discharge (NLD).

Since a neutron has a magnetic moment, it interacts with a magnetic field. A possible configuration to confine ultracold neutrons (UCN) is a combination of a toroidal multipole field and a toroidal field; the latter prevents spin flip at the separatrix of the multipole field. It results in effective cooling to apply an appreciable ripple to the toroidal field which propagates at the resonant phase velocity. The cooling rate which is the power removed by a propagating toroidal magnetic wave was obtained through the quasilinear theory of the transit-time dumping for a plasma, and compared to the particle simulations.

A three-dimensional particle simulation scheme has been developed and applied to the study of relativistic charged particle beams. To simulate the nonlinear behaviors of beam electrons with self-induced space-charge effects, it simultaneously solves the canonical equations of motion and the integrated Maxwell equations of radiated waves for each particle. Verifications of this algorithm show that calculations for the retarded structure of radiated waves dominate the total throughput, and the near-field approximation to the calculations of space-charge potentials improves its numerical efficiency. The code has been applied to a simulation of the Raman regime free-electron laser (FEL) to demonstrate that this scheme simulates the parametric amplification of FEL properly and is suitable for relativistic treatments of such wave-particle resonances.