The dispersive evolution of charged-particle bunches in random magnetic fields

Shortly after a strongly anisotropic beam of charged particles is injected along a guiding magnetic field on which is superimposed a small random conponent, the particle density can be represented by a Gaussian profile whose center moves with the coherent velocity and whose width increases with time at a rate controlled by the coefficient of dispersion. Both parameters depend upon the mean free path, which characterizes scattering by the random fields, and the focusing length, which characterizes spatial variations of the guiding field. These dependencies are known explicitly for the coherent velocity. Formulae for coefficient of dispersion are available only in the limits of very weak and very strong focusing. A new expression for coefficient of dispersion, which spans this gap, is presented.