Modern wave theory with applications to radiofrequency waves in plasma*

Applications of radiofrequency (RF) waves in plasmas have been extensively studied for decades and enjoy great success. However, the basis of RF theory has not significantly changed since the early days of plasma physics, when research focused on the zoology of waves in homogeneous plasma and their transformations in idealized settings. Although ad hoc extensions of these early approaches have been fruitful, the precise modeling of waves in realistic plasmas requires a deeper, more systematic understanding. Such understanding can be gained from modern wave theory, which has been revolutionary in other areas of physics [Tracy et al., "Ray Tracing and Beyond" (2014)]. As opposed to considering waves in either a coordinate or spectral representation, as usually done, modern theory recognizes them as dynamical objects traveling in phase space. Many wave effects that otherwise appear miraculous turn out to be surprisingly simple and can be described with amazing generality in the properly chosen phase-space coordinates. Although an inhomogeneous plasma does not have a dielectric tensor per se, the new theory also explains how to rigorously introduce and calculate "the next best thing" to any given accuracy. Similar improvements are possible also in modeling dissipation and nonlinear effects. This means, for example, that numerical modeling of RF heating and current drive in fusion plasmas can be made more precise, especially in those plasmas where inhomogeneities are relatively strong. However, modern wave theory is yet to be embraced by the broader plasma community, and much work remains to be done, which opens new and exciting opportunities for research. This talk will overview the basics of modern wave theory and some of its applications to RF physics. The focus will be made on the modeling of linear-wave propagation, mode conversion, ponderomotive effects, and inhomogeneous turbulence.