Advances in gyrokinetic fluctuation theory: The gyrokinetic fluctuation–dissipation theorem and dielectric function*

Thermal-equilibrium fluctuation spectra of finite-β gyrokinetic (GK) plasmas are calculated by means of a GK fluctuation–dissipation theorem. Agreement is found with the earlier heuristic electrostatic calculations of Krommes et al. [Phys. Fluids 29, 2421 (1986)]. The formulas are interpreted in terms of the concept of a GK vacuum, whose large dielectric permittivity and magnetic permeability embody the shielding effects of the polarization drift and the parallel electric field. The finite-β quasimode action density 𝒩k is calculated. This is used to interpret the result of a formal resonance integration over the normal modes in terms of the equipartition law ωk𝒩k = T/2.