Application of Weyl symbol calculus for quasilinear modeling of waves in plasmas

Plasmas are fascinatingly complex as dispersive media in that they support a wide variety of waves and these waves can significantly evolve due to background inhomogeneities and nonlinear interactions. This necessitates a particularly systematic approach to wave theory. It has long been recognized that phase-space methods from quantum physics, particularly Weyl symbol calculus and metaplectic transforms, can serve as a foundation for such an approach to classical waves (E. R. Tracy et al., “Ray Tracing and Beyond” (Cambridge Univ. Press, 2014)). These methods have proven useful for reduced modeling of linear-wave propagation and mode conversion in inhomogeneous media. As it turns out, though, they are also helpful for modeling quasilinear (QL) wave effects, specifically, QL diffusion, ponderomotive forces, and structure formation in wave turbulence.