Symmetries of a reduced fluid-gyrokinetic system

Abstract

Symmetries of a fluid-gyrokinetic model are investigated using Lie group techniques. Specifically, the nonlinear system constructed by Zocco & Schekochihin (Phys. Plasmas, vol. 18, 2011, 102309), which combines nonlinear fluid equations with a drift-kinetic description of parallel electron dynamics, is studied. Significantly, this model is fully gyrokinetic, allowing for arbitrary $k_{\bot }\unicode[STIX]{x1D70C}_{i}$, where $k_{\bot }$ is the perpendicular wave vector of the fluctuations and $\unicode[STIX]{x1D70C}_{i}$ the ion gyroradius. The model includes integral operators corresponding to gyroaveraging as well as the moment equations relating fluid variables to the kinetic distribution function. A large variety of exact symmetries is uncovered, some of which have unexpected form. Using these results, new nonlinear solutions are constructed, including a helical generalization of the Chapman–Kendall solution for a collapsing current sheet.