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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.

Plasma confinement characteristics of plasma sources, the side walls of which are surrounded by magnetic multipole fields, are analyzed using theoretical equations. Experimental data used are those obtained with microwave plasma sources. The plasma flux, the pressure range over which a uniform plasma is produced, the plasma density distribution at a plasma grid and the cusp leak width are discussed. If the leak width is the geometric mean value of the ion and electron Larmor diameters, the results estimated using the theoretical equations are consistent with the experimental ones. It has also been observed from the traces due to the plasma irradiation that the leak width corresponds to the geometric mean value. The validity of the equations has been confirmed. These equations can be used as a basis for the design of a plasma source capable of producing a uniform high-density plasma over a wide area.