Optimisation of Gyrokinetic Microstability Using Adjoint Methods
Journal of Plasma Physics, 2024, 90 (4)
G. Acton, M. Barnes, S. Newton, and H. Thienpondt
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.
Influence of the Density Gradient on Turbulent Heat Transport at Ion-Scales: An Inter-Machine Study with the Gyrokinetic Code stella
Nuclear Fusion, 2024, 65 (1)
H. Thienpondt, J. M. García-Regaña, I. Calvo, G. Acton, and M. 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.
Overview of Wendelstein 7-X high-performance operation
Nuclear Fusion, 2026, 66 (11)
O. Grulke et al.
Abstract: The Wendelstein 7-X (W7-X) stellarator has completed two consecutive experimental campaigns OP 2.2 (Sep.-Dec. 2024) and OP 2.3 (Feb.-May 2025) under a new operational strategy enabling more than one year of uninterrupted device availability. This approach, supported by exceptionally high subsystem reliability, allowed sustained high-efficiency plasma operations with up to 80–100 discharges per day across a broad range of magnetic configurations. Several key technical upgrades-most notably the first operation of a 1.5 MW class steady-state gyrotron, a new steady-state pellet injector, and advanced real-time feedback control systems significantly enhanced heating, fueling, and plasma control capabilities. Together, these improvements enabled major advances in long-pulse performance, high-β operation, and confinement optimization. Long-pulse discharges achieved 1.8 GJ of injected energy under fully detached divertor conditions, while reduced-field scenarios facilitated record volume-averaged β values approaching 3%. High-performance plasmas with centrally peaked density profiles, created via neutral beam injection (NBI) or sustained pellet fueling, demonstrated strongly reduced turbulent transport and stellarator-record fusion triple products. Complementary studies of power exhaust and divertor heat loads revealed the role of scrape-off-layer drift physics in shaping strike-line patterns under attached conditions. Together, the results from OP 2.2 and OP 2.3 significantly expand the operational space of W7-X and strengthen its role as a leading platform for steady-state stellarator research and reactor-relevant plasma scenarios.
A Weakly Nonlinear Theory of Zonal-Flow Forcing in Gyrokinetic Turbulence
G. Acton, E. Rodríguez, G. Roberg-Clark, and A. Zocco
Abstract: The forced generation of zonal flows by microinstability-driven turbulence is investigated within the framework of local gyrokinetic theory far from marginality. We use a numerically and physically informed three-wave truncation scheme, which allows the prediction of the zonal-flow kx-spectrum during the early phase of nonlinear gyrokinetic simulations. The model reproduces the known 2-ɣ growth rate resulting from nonlinear beating of linearly unstable primary modes, in line with previous results, without any marginal stability point. The phase-space structure of such zonal flow is strongly constrained by that of the driving fluctuations, which is essential to understand its behaviour in the region of validity. It is shown that this leads to an enhanced residual spectrum compared to the classic Rosenbluth-Hinton calculation.
Full Flux Version of stella
G. Acton, M. Barnes, S. Newton, and H. Thienpondt
Modelling and Optimising Turbulence in 3D Magnetic Geometries for Enhanced Microstability
G. Acton
Abstract: This thesis investigates microturbulence in three-dimensional magnetised plasma geometries, with a specific focus on the impact of turbulence to plasma stability. Microturbulence is the small-scale turbulent fluctuations in a plasma caused by instabilities at or near the ion and electron gyroradius scales. Microturbulence remains a critical challenge within the field of plasma physics, and in order to control the effects of turbulence, we first need to accurately model it. This task is particularly complex in non-axisymmetric geometries, where mode-coupling occurs across non-identical field lines, leading to potential inconsistencies in the common representation of zonal flows.
The first part of the thesis focuses on the development and validation of a novel δf-gyrokinetic code, designed to model microturbulence across a full flux-annulus in non-axisymmetric magnetic configurations. This is especially important when considering turbulent dynamics in stellarators and tokamaks with 3D magnetic perturbations, as capturing the coupling of modes across different field lines is necessary to accurately resolve 'zonal' modes, that are constant across a flux surface. The code is benchmarked against the current flux-tube implementation of the stella code, along with other existing gyrokinetic codes. Novel results incorporating kinetic electrons are also presented.
The second part of the thesis addresses microstability, which poses unique optimisation challenges due to the large number of tunable parameters in magnetic confinement devices. To tackle this problem, an efficient method for calculating the derivative of the linear growth rate with respect to multiple externally-controllable parameters, has been developed using an adjoint method. The theoretical framework is derived in the limit of no field-line coupling, including electromagnetic effects and collisions. Numerical simulations then demonstrate the efficacy of the approach in the electrostatic, collisionless regime.