Plasma wave equations of state

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Abstract
A systematic description of wave equations of state is presented for three categories of plasma waves distinguished by superthermal, subthermal, and superluminous phase velocities. Each class entails the formulation of a distinct Vlasov fluid model where only the first coincides with well‐known covariant fluid modeling. An investigation of the linearized version of this standard model is first undertaken. A complete, lowest‐order, warm fluid model is derived without the drawbacks that characterize previous models such as the generation of spurious modes and the absence of a Bernstein wave spectrum. The improved fluid model is obtained by avoiding a premature truncation of the hierarchy of linearized moment equations near cyclotron and acoustic resonance and is applied to representative types of waves in a warm, magnetized plasma. Relativistic corrections and anisotropic properties of the corresponding dispersion relations are used to illustrate the utility and rigor of the theory. The conspicuous absence of a subthermal wave within this improved model motivates the subsequent derivation of a novel fluid model with associated moments that involve averages of derivatives of the electron distribution function. The first moment equation reproduces the Boltzmann relation while succeeding equations in the hierarchy provide constraints on the spatial dependence of the distribution function. A linearized analysis yields the ion‐acoustic mode together with an isothermal equation of state in the long wavelength limit. The key distinction with previous work is the complete avoidance of a pressure and an appropriate (third) moment representation for temperature in the collisionless, subthermal regime. A relativistic analog to this unusual approach is developed for the case of ultrarelativistic electron plasma waves. This requires the formulation of a noncovariant near‐thermal equilibrium fluid modeling with associated moments that are not relativistically dilatated. An isothermal equation of state is recovered in tandem with the adoption of a third fluid moment definition for relativistic temperature. This definition of effective temperature differs from the relativistic thermodynamic version which follows from an assumed form invariance of the defining equations of nonrelativistic thermodynamics in the relativistic regime. The introduction of these two latter models is intended to provide a more general notion of equation of state without recourse to an assumption on the form of the stress‐energy tensor.

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