Prof Michael Barnes

Abstract:

Efficient control of turbulent heat transport is crucial for magnetic confinement fusion reactors. This work discusses the complex interplay between density gradients and microinstabilities, shedding light on their impact on turbulent heat transport in different fusion devices. In particular, the influence of density gradients on turbulent heat transport is investigated through an extensive inter-machine study, including various stellarators such as W7-X, LHD, TJ-II and NCSX, along with the Asdex Upgrade tokamak (AUG) and the tokamak geometry of the Cyclone Base Case (CBC). Linear and nonlinear simulations are performed employing the δf-gyrokinetic code stella across a wide range of parameters to explore the effects of density gradients, temperature gradients, and kinetic electrons. A strong reduction in ion heat flux with increasing density gradients is found in NCSX and W7-X due to the stabilization of temperature-gradient-driven modes without significantly destabilizing density-gradient-driven modes. In contrast, the tokamaks exhibit an increase in ion heat flux with density gradients. Notably, the behavior of ion heat fluxes in stellarators does not align with that of linear growth rates, if only the fastest-growing mode is taken into account. Additionally, this study provides physical insights into the microinstabilities, emphasizing the dominance of trapped-electron-modes (TEMs) in CBC, AUG, TJ-II, LHD and NCSX, while both the TEM and the passing-particle-driven universal instability contribute significantly in W7-X.

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%.