arXiv subjects

Ian Abel

Publications and source records attributed to Ian Abel.

4 recordsLinked to original sources

arXiv2026

Gyrokinetic Theory of Linear Gravitational Flute Interchanges with Flow Shear Stabilization

A collisionless electrostatic gyrokinetic theory is developed to describe how the presence of a differential velocity shear can help stabilize linear gravitational flute interchanges in slab geometry. This is made possible because the velocity shear acts to increase the perpendicular wavenumber of the unstable modes with time. Eventually, a threshold wavenumber is crossed where the effect of gyroaveraging, captured by the Bessel function in the gyrokinetic equation, results in a damping of the instability by nature of these Bessel functions being a decaying sinusoidal. However, transient amplification, responsible for subcritical turbulence, can still occur. Numerical comparisons are made with a Magnetohydrodynamic model with gyroviscous corrections as well as the GX gyrokinetic code. It is demonstrated that an increasing shear acts not only to accelerate the stabilization effect but also to reduce the overall transient amplification.

physics.plasm-ph↗

arXiv2019

An adjoint method for neoclassical stellarator optimization

Stellarators are a promising route to steady-state fusion power. However, to achieve the required confinement, the magnetic geometry must be highly optimized. This optimization requires navigating high-dimensional spaces, often necessitating the use of gradient-based methods. The gradient of the neoclassical fluxes is expensive to compute with classical methods, requiring $O(N)$ flux computations, where $N$ is the number of parameters. To reduce the cost of the gradient computation, we present an adjoint method for computing the derivatives of moments of the neoclassical distribution function for stellarator optimization. The linear adjoint method allows derivatives of quantities which depend on solutions of a linear system, such as moments of the distribution function, to be computed with respect to many parameters from the solution of only two linear systems. This reduces the cost of computing the gradient to the point that the finite-collisionality neoclassical fluxes can be used within an optimization loop. With the neoclassical adjoint method, we compute solutions of the drift kinetic equation and an adjoint drift kinetic equation to obtain derivatives of neoclassical quantities with respect to geometric parameters. When the number of parameters in the derivative is large ($\mathcal{O}(10^2)$), this adjoint method provides up to a factor of 200 reduction in cost. We demonstrate adjoint-based optimization of the field strength to obtain minimal bootstrap current on a surface. With adjoint-based derivatives, we also compute the local sensitivity to magnetic perturbations on a flux surface and identify regions where tight tolerances on error fields are required for control of the bootstrap current or radial transport. Furthermore, the solve for the ambipolar electric field is accelerated using a Newton method with derivatives obtained from the adjoint method.

physics.plasm-ph↗

arXiv2018

Multiscale Modelling for Tokamak Pedestals

Pedestal modelling is crucial to predict the performance of future fusion devices. Current modelling efforts suffer either from a lack of kinetic physics, or an excess of computational complexity. To ameliorate these problems, we take a first-principles multiscale approach to the pedestal. We will present three separate sets of equations, covering the dynamics of Edge Lo- calised Modes, the inter-ELM pedestal, and pedestal turbulence, respectively. Precisely how these equations should be coupled to each other are covered in detail. This framework is completely self-consistent; it is derived from first principles by means an asymptotic expansion in appropriate small parameters. The derivation exploits the narrowness of the pedestal region, the smallness of the thermal gyroradius, and the low plasma $β$ typical of current pedestal operation to achieve its simplifications. The relationship between this framework and gyrokinetics is analysed, and possibilities to directly match this framework onto multiscale gyrokinetics are explored. A detailed comparison between our model and other models in the literature is performed. Finally, the potential for matching this framework onto an open-field-line region is discussed.

physics.plasm-ph↗

arXiv2014

Validating modelling assumptions of alpha particles in electrostatic turbulence

To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In the work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak parameters. Our results are consistent with known scalings and experimental evidence that alpha particles are generally well-confined: on the order of several seconds. It is also confirmed that the effect of alphas on the turbulence is negligible at realistically low concentrations, consistent with linear theory. It is demonstrated that the usual practice of using a high-temperature Maxwellian gives incorrect estimates for the radial alpha particle flux, and a method of correcting it is provided. Furthermore, we see that the timescales associated with collisions and transport compete at moderate energies, calling into question the assumption that alpha particles remain confined to a flux surface that is used in the derivation of the slowing-down distribution.

physics.plasm-ph↗