Waves in a warm pair plasma: a relativistically complete two-fluid analysis

We present an ideal two-fluid wave mode analysis for a pair plasma, extending an earlier study for cold conditions to the warm pair plasma case. Starting from the completely symmetrized means for writing the governing linearized equations in the pair fluid rest frame, we discuss the governing dispersion relation containing all six pairs of forward and backward propagating modes, which are conveniently labelled as S, A, F, M, O and X. These relate to the slow (S), Alfvén (A) and fast (F) magnetohydrodynamic waves, include a modified (M) electrostatic mode, as well as the electromagnetic O and X branches. In the dispersion relation, only two parameters appear, which define the pair plasma magnetization $E^{2}\in [0,\infty ]$ and the squared pair plasma sound speed $v^{2}$ , measured in units of the light speed $c$ . The description is valid also in the highly relativistic regime, where either a high magnetization and/or a relativistic temperature (hence sound speed) is reached. We recover the exact relativistic single-fluid magnetohydrodynamic expressions for the S, A and F families in the low wavenumber–frequency regime, which can be obtained for any choice of the equation of state. We argue that, as in a cold pair plasma, purely parallel or purely perpendicular propagation with respect to the magnetic field vector $\boldsymbol{B}$ is special, and near-parallel or near-perpendicular orientations demonstrate avoided crossings of branches at computable wavenumbers and frequencies. The complete six-mode phase and group diagram views are provided as well, visually demonstrating the intricate anisotropies in all wave modes, as well as their transformations. Analytic expressions for all six wave group speeds at both small and large wavenumbers complement the analysis.