Dielectric response and thermal fluctuations in gyrokinetic plasma

A gyrokinetic fluctuation–dissipation theorem is deduced and used to predict unusual thermal‐equilibrium fluctuation spectra for both electrostatic and weakly electromagnetic gyrokinetic plasmas in the limit of weak coupling. The results are in agreement with an application of the test‐particle superposition principle. They are interpreted physically in terms of the concept of the ‘‘gyrokinetic vacuum,’’ whose large (tensor) dielectric constant embodies the shielding effects of the polarization drift and the inductive electric field. The calculations are performed entirely with gyrokinetic response functions, although the relations to the conventional Vlasov dielectric are also described. The previous heuristic results of Krommes et al. [Phys. Fluids 29, 2421 (1986)] are recovered systematically. A nonrelativistic covariant formalism is used to derive the finite‐β results (where β is the plasma pressure). The wave‐number power spectra of the charge density, electrostatic potential, and perpendicular elect...