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

TL;DR

This paper introduces an adaptive delta-f gyrokinetic simulation method using a flux-surface-averaged Maxwellian with a dynamic temperature profile, reducing noise and enabling convergence in high-gradient turbulence scenarios.

Contribution

It presents a novel adaptive control variate approach that mitigates noise in gyrokinetic Particle-in-Cell simulations of turbulence with steep profiles.

Findings

Reduces statistical noise in zonal flow and heat flux simulations.

Prevents collapse of signal-to-noise ratio in high-gradient turbulence.

Achieves convergence with fewer markers in challenging conditions.

Abstract

Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation level are high e.g. 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 make 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.