Numerical and diagnostic extensions to the gyrokinetic $\delta f$ code stella

Abstract

Understanding turbulence in magnetised plasmas requires robust numerical tools capable of capturing complex free-energy transfer processes across scales. We demonstrate the utility of free energy as a diagnostic for both physical turbulence characteristics and numerical stability in gyrokinetic simulations with the stella code. Applied to the W7-X high-mirror configuration, free-energy diagnostics reveal characteristic power-law behaviour in the turbulent cascade, act as sensitive indicators of numerical instabilities undetected by conventional diagnostics, and expose localised structures in real space not apparent in the electrostatic potential alone. To support these analyses, we present a systematic comparison of explicit time-integration schemes, showing that the optimal choice depends critically on the regime: SSP22 achieves the lowest computational cost in linear ITG simulations, while SSP33 is most efficient in the nonlinear saturated state, with nonlinear simulations requiring two to three orders of magnitude more computational cost than linear cases. These results establish free-energy diagnostics as a valuable tool for interpreting plasma turbulence and provide practical guidance for scheme selection in stella simulations.