The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. We derive a modified theory that takes both of these effects into account, while still treating DW quanta ("driftons") as particles in phase space. The drifton dynamics is described by an equation of the Wigner-Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. Numerical simulations are presented to illustrate the importance of these additional terms. The proposed formulation can be considered as a phase-space representation of the second-order cumulant expansion, or CE2.Comment: 14 pages, 4 figure

By restating geometrical optics within the field-theoretical approach, the classical concept of a photon (and, more generally, any elementary excitation) in arbitrary dispersive medium is introduced, and photon properties are calculated unambiguously. In particular, the canonical and kinetic momenta carried by a photon, as well as the two corresponding energy-momentum tensors of a wave, are derived from first principles of Lagrangian mechanics. As an example application of this formalism, the Abraham-Minkowski controversy pertaining to the definitions of these quantities is resolved for linear waves of arbitrary nature, and corrections to the traditional formulas for the photon kinetic energy-momentum are found. Several other applications of axiomatic geometrical optics to electromagnetic waves are also presented.

This work opens a series of papers where we develop a general quasioptical theory for modeconverting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general quasimonochromatic multi-component wave in a weakly inhomogeneous linear medium with no sources. For any given dispersion operator that governs the wave field, we explicitly calculate the approximate operator that governs the wave envelope ψ to the second order in the geometrical-optics parameter. Then, we further simplify this envelope operator by assuming that the gradient of ψ transverse to the local group velocity is much larger than the corresponding parallel gradient. This leads to a parabolic differential equation for ψ ("quasioptical equation") in the basis of the geometrical-optics polarization vectors. Scalar and mode-converting vector beams are described on the same footing. We also explain how to apply this model to electromagnetic waves in general. In the next papers of this series, we report successful quasioptical modeling of radiofrequency wave beams in magnetized plasma based on this theory.

The propagation of electromagnetic waves in vacuum is often described within the geometrical optics approximation, which predicts that wave rays follow null geodesics. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, diffraction can still be negligible, but the ray dynamics becomes affected by the evolution of the wave polarization. Hence, rays can deviate from null geodesics, which is known as the gravitational spin Hall effect of light. In the literature, this effect has been calculated ad hoc for a number of special cases, but no general description has been proposed. Here, we present a covariant Wentzel-Kramers-Brillouin analysis from first principles for the propagation of light in arbitrary curved spacetimes. We obtain polarization-dependent ray equations describing the gravitational spin Hall effect of light. We also present numerical examples of polarization-dependent ray dynamics in the Schwarzschild spacetime, and the magnitude of the effect is briefly discussed. The analysis reported here is analogous to that of the spin Hall effect of light in inhomogeneous media, which has been experimentally verified.