Eigenvalue formulation for linear modes in the homogeneous multiple-fluid plasma

Abstract

The linearized equations of the multiple-fluid model, including an isotropic pressure law, of a plasma are cast into a concise form directly suited for the calculation of the full set of characteristic modes of the system. A fully ionized, homogeneous, drift-free, magnetized plasma having an arbitrary number of finite-temperature components is considered. For oscillations of the form exp[i (k⋅r−ωt)], the three separate problems of determining ω vs (k,ϑ), k vs (ω,ϑ), and kx vs (ω,kz) are treated by formulating the set of algebraic equations into matrix eigenvalue problems for which the eigenvalues are ω2, k2, and k2x, respectively. For each of the three cases, an example of the results of numerical evaluation of the eigenvalues is presented for an electron, two-ion species plasma. A method is described which may be used for calculating, directly within the eigensystem formulation, the group velocity of the characteristic modes.