Nonlinear Mechanisms of Mirror-Mode Excitation

Pseudospectral analysis of ITG turbulence in gyrokinetics has shown that the nonlinearity excites fluctuations with mirror symmetry to the unstable ITG mode even though such stable modes are not linear eigenmodes.¹ The mechanism for the excitation and conditions it requires are not understood. To this end we employ analytic theory to examine in detail the saturation of resistive interchange turbulence. Besides its relevance in edge plasmas, resistive interchange modes have a linear eigenmode spectrum with no mirror mode, but are configured like viscous Kelvin-Helmholtz instability where the inviscid eigenmode spectrum and its mirror mode provide an excellent basis for studying nonlinear behavior. We introduce an expansion of the nonlinear system in Hermite polynomials, perform a statistical closure in the eigenmode basis, and examine both the frequency spectrum of the nonlinear terms that mediate saturation and the power density of each eigenmode in the saturated state. We look at resonance and near resonance in the triplet correlation time involving zonal modes and interactions with the opposite-frequency stable modes. We investigate whether the latter become phase locked in the nonlinear state, given the symmetries of the stable-mode spectrum. We examine the response of the eigenmode-projected linear operator and its resonances. This work seeks to provide the nonlinear rationale for excitation of non-eigenmode mirror modes.

¹D.R. Hatch et al., NJP 18, 075018 (2016).