Explicit dispersion relations for warm fluid waves in a uniform plasma (invited)

Classical dispersion relations for waves in a fluid plasma are expressed as implicit functions of wave frequency and wavenumber. The implicit dispersion relation must in general be solved numerically. This work introduces an astute method for obtaining an explicit dispersion relation for waves in a fluid plasma. The explicit expression has an advantage of providing eigenmodes without numerical computations and giving a dispersion relation more detailed than the implicit expression. As in the case of cold waves, the wavenumber for an arbitrary frequency can be directly obtained from the explicit formula. The explicit formula also enables an accurate evaluation of finite-temperature effects on a dispersion relation even near the cyclotron resonance, where a numerical analysis of the implicit relation is impractical. The analytic formula can be used to investigate temperature effects on electromagnetic waves.