Gyrokinetic simulations of turbulence and zonal flows driven by steep profile gradients using a delta-f approach with an evolving background Maxwellian

Abstract

Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation levels are high, for example, in strong gradient regions. For particle-in-cell simulations, statistical sampling noise accumulation from large marker weights due to large deviations from the control variate of a delta-f scheme makes such simulations often impractical. An adaptive control variate in the form of a flux-surface-averaged Maxwellian with a time-dependent temperature profile is introduced in an attempt to alleviate the former problem. Under simplified collisionless physics, this adaptive delta-f scheme is shown to reduce noise accumulation in the zonal flows and the simulated heat flux in a quasi-steady turbulent state. The method also avoids the collapse of the signal-to-noise ratio, which occurs in the standard non-adaptive scheme, and, therefore, allows one to reach numerically converged results even with lower marker numbers.