Theoretical astrophysics and plasma physics at RPC

Abstract:

Microinstabilities drive turbulent fluctuations in inhomogeneous, magnetised plasmas. In the context of magnetic confinement fusion devices, this leads to an enhanced transport of particles, momentum and energy, thereby degrading confinement. In this work, we describe an application of the adjoint method to efficiently determine variations of gyrokinetic linear growth rates on a general set of external parameters in the local δf-gyrokinetic model. We then offer numerical verification of this approach. When coupled with gradient-based techniques, this methodology can facilitate the optimisation process for the microstability of the confined plasmas across a high-dimensional parameter space. We present a numerical demonstration wherein the ion-temperature-gradient instability growth rate in a tokamak plasma is minimised with respect to flux surface shaping parameters. The adjoint method approach demonstrates a significant computational speed-up compared with a finite-difference gradient calculation.

Abstract:

We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 Phys. Fluids 19 1532). The numerical methods of the implementation in the δf-gyrokinetic code stella (Barnes et al 2019 J. Comput. Phys. 391 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver GS2 in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.