Plasmas in Particle Accelerators: A Hydrodynamic Model of Three-Dimensional Electrostatic Instabilities

In an earlier paper, closed hydrodynamic equations were derived with possible application to the simulation of beam plasmas relevant to designs of heavy ion accelerators for inertial confinement fusion energy applications. The closure equations involved a novel feature of anisotropic stresses even transverse to the beam. A related hydrodynamic model is used in this paper to examine further the boundaries of validity of such hydrodynamic approximations. It is also proposed as a useful tool to provide an economic means for searching the large parameter space relevant to three-dimensional stability problems involving coupling of longitudinal and transverse motions in the presence of wall impedance.