Asymptotic approximation for the dispersion relation of a hot magnetized plasma

An asymptotic expression for the dielectric tensor ε of a hot magnetized plasma is obtained employing the steepest descents method, via the transformation of the components of ε into their integral representation. The electrostatic Bernstein dispersion relation for oblique and perpendicular propagation is discussed under this treatment. It is shown that with this procedure the computation of the dispersion relation is up to 20 times faster when it is compared with the original expression, and the relative accuracy is usually as good as 0.1% for a typical case. (author)