Equilibrium and destruction of a rep in a magnetic guide

The study of charged particle, in which space charge effect plays a significant role in their propagation behavior, has already a long history over several tens of years[1]. Recently a new way of producing a very intense beam far beyond the Alfven limit was developped and the characteristic features of such dense beam, including its equilibrium with or without external fields and the instabilities as nonneutral plasma have been considered in detail, related to the various fields of the application, espacially the ion collective acceleration, the inertial fusion, the high power microwave production, etc[2].