Small amplitude hydromagnetic waves for a plasma with a generalized polytrope law

A generalized set of hydromagnetic fluid equations is proposed for a fully ionized plasma with tensor pressure. Each of the two components of the diagonalized pressure tensor obeys a polytrope law where the pressure is proportional to a power of the mass density and magnitude of the magnetic field. The normal phase speeds are calculated for the Alfven and magnetoacoustic modes for infinitesimal waves. Normal phase speed diagrams are illustrated for three cases where are used the Chew-Goldberger-Low double adiabatic equations of state, isothermal equations of state and mixed adiabatic and isothermal equations of state respectively.