Relativistic Fluid Theory of Electromagnetic Instabilities

Electromagnetic instabilities are analyzed within the context of a manifestly covariant fluid formalism. Starting from an arbitrary adiabatic background fluid state, and using perturbation theory, we derive a minimal set of four 3$^{\mathrm{rd}}$ order PDEs in the 4-potential perturbation. A general dispersion relation is derived for plane waves, and analyzed for convective and absolute instabilities. This theory applies to several physical systems, such as coherent radiation sources, high-energy accelerators, ICF and astrophysical plasmas. Prepared by LLNL under Contract DE-AC52-07NA27344.