A high-order moment simulation model

A beam transport system in which the particle motions in the two transverse directions (x and y) are coupled is considered. A beam with a distribution in energy in a magnetic field with nonlinear dependence on the spatial coordinates is discussed. Under the first condition, the spatial coordinate (z) along the beam motion cannot be confused with the time variable. Since fast particles will overtake the slower particles as time evolves, the beam envelope is a function of both z and time (t). Therefore, the beam envelope equations are a set of partial differential moment equations, instead of a set of ordinary differential moment equations. The authors also derive a relativistically covariant form of moment equations, based on the work of W.A. Newcomb (1982) and P. Amendt and H. Weitzner (1985).<>