Role of Stable Modes in the ITG-Driven Instability in a Mode-Coupled System

Abstract

Kinetic damping in linear gyrokinetic (GK) Vlasov simulations is found to exhibit a bifurcation at the collisionality β c = β c , above which, i.e. β c > β c , the damping is represented by a Landau eigenmode in velocity space, while below which, i.e. β c < β c , by the phase mixing of a finite number of marginally stable, discretized Case-van Kampen eigenmodes. The latter causes a recurrence that restricts the damping and then the energy transfer from wave to particles within a finite recurrence time. In order to address whether the stabilization effect due to such stable damped modes on unstable modes via mode coupling can be evaluated in long timescale GK simulations, we introduced a triad model consisting of stable and unstable modes incorporated with a tertiary vortex flow. We identified β c numerically and found that the stabilization effect works properly beyond the recurrence time even in the phase mixing regime across β c = β c . In plasma turbulence, stable modes play an important role in absorbing fluctuating free energy as a sink, which leads to saturation. Such a phenomenon commonly exists in various linear and nonlinear mode coupling processes. For example, nonlinear energy cascades occur through a three-wave coupling in drift wave turbulence. On the other hand, the unstable ion temperature gradient (ITG) mode is suppressed by the linear mode coupling produced by an externally imposed static vortex flow or magnetic island, forming a global ITG structure with the same growth rates and frequencies [1]. Mode coupling mediates the underlying suppression mechanisms of unstable modes by the dissipation effect of stable modes. Such stable modes originate from various damping processes. They are characterized by collisional (viscous) damping in a fluid model while they result from Landau damping and the so-called finite Larmor radius (FLR) effects in the kinetic system. Hence, Landau damping is crucial in energy transfer processes because it predominantly affects the fluctuation dynamics in both linear and nonlinear regimes.However, in collisionless gyrokinetic (GK) simulations, Landau damping exhibits different time evolutions depending on the choice of the initial distribution in velocity space due to the appearance of marginally stable Case-van Kampen (CvK) eigenmodes in the discretized velocity space. Namely, we observe a marginal behavior with neither growth nor damping for a random noise distribution. On the other hand, a damping accompanied by the recurrence phenomenon occurs for the Maxwellian author's e-mail: paul@center.iae.kyoto-u.ac.jp distribution [2], where damping is terminated within a finite time determined by the mesh size v. Consequently, the damping rate averaged over a timescale longer than the recurrence time becomes zero. Such damping with recurrence has been found to result not from Landau damping as a discrete eigenmode but from the phase mixing of a finite number of CvK eigenmodes. This is in contrast to the unstable ITG mode, which is always found to be an eigenmode of the GK Vla...

Spatial localization of resistive drift wave structure in tokamak edge plasmas with an embedded magnetic island

“…Recently, extensive investigations on the effect of magnetic island on the microinstabilities, e.g., the ion temperature gradient (ITG) mode have been carried out based on fluid (gyrofluid) and gyrokinetic simulations. [16][17][18][19][20][21][22][23][24][25][26][27] Theoretical analysis in a gyrokinetic framework is extended for small magnetic islands. 28 Among complicated linear and nonlinear interaction processes, the mutual relation between the profile relaxation inside island separatrix and the secondary excitation (or destabilization) is an interesting issue.…”