Application of dynamically consistant closures to hydrodynamic models of beams

Hydrodynamic models have been used in particle beam research. Sometimes equations of state are assumed by dropping heat fluxes without a detailed attempt to model possible beam behavior such as anisotropic stresses even in the transverse directions. Recently, for the purpose of ion beam inertial fusion research, the authors have shown that dynamically consistent equations of state can be derived from the Vlasov equation for some beam models under the assumption that the particle orbits are allowed to be general rosette orbits in central fields except that the ratio of maximum to minimum radial excursion is limited by something less than a factor of two. They further advised that if the beam has zero net angular momentum then at least two counter-rotating beam components of this type should be considered. By remaining closely tied to the actual particle orbits the possibility of wave-particle resonances typical of resistive-hose instabilities is retained. In this paper the authors discuss the dynamically consistent closure of hydrodynamic models within adiabatic assumptions analogous to that of Chew, Goldberger and Low for magnetohydrodynamics and that of Berman and Mark for galactic dynamics. Numerical comparison with particle codes is discussed for pinched beams