Mechanism for Nonlinear Excitation of the Mirror Mode in Resistive Interchange Turbulence

Gyrokinetic simulations indicate that instability-driven-turbulence creates fluctuations that have mirror symmetry relative to the instability, i.e., a complex conjugate frequency.¹ The so-called mirror mode is generally not part of the linear eigenmode spectrum, and its paired symmetry with the linear instability occurs despite arising from interactions mediated by triads, not pairs of modes. We investigate this phenomenon analytically in resistive interchange turbulence, showing how the nonlinearity drives a saturation-dominating mirror mode. We homogenize the resistive g-mode equations for a sheared magnetic field in a slab geometry using a Hermite polynomial expansion in a Fourier frequency domain. Via diagonalization of the linear coupling matrix we are able to invert the amplitude equations. We introduce a projection onto a nonlinear mode basis that combines two stable eigenmodes with equal decay rates and opposite frequencies, and find that its frequency response includes the mirror mode and other nonlinear frequencies. We show that this nonlinear fluctuation is preferentially excited in a nonlinear triad interaction that includes the instability and a zonal flow because it maximizes the nonlinear interaction time. The zonal flow is found to be the dominant field with zero poloidal wavenumber, has a singularly broad eigenmode structure with zero frequency and growth rate, but is well behaved in amplitude.

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