arXiv subjects

Matthew Hole

Publications and source records attributed to Matthew Hole.

At least 19 recordsLinked to original sources

arXiv2026

First reduced model for integrated computations of helicon wave heating and current drive in magnetic fusion plasmas

Fast predictive modelling of radio-frequency heating and current drive is important for integrated tokamak scenario design, yet kinetic calculations of helicon-wave absorption remain too computationally expensive for large-scale parameter scans. We present a reduced model for helicon-wave heating and current drive that retains the dominant parallel electron Landau-damping channel. The wave response is evaluated on the cold-plasma dispersion root, and a single-Landau-pole correction is introduced to obtain compact expressions for the local damping rate and current-drive efficiency. The model is benchmarked against the Chiu-Chan heating model using approximately 1.6 million samples covering representative conditions of EAST, HL-3, DIII-D and KSTAR. The reduction error is found to be governed primarily by the electron Landau parameter and electron beta. Within an identified sub-lower-hybrid-frequency validity window, results from different devices collapse onto a common error curve, which enables an empirical correction that is further tested using ITER-like and BEST-like extrapolation cases. Near and above the lower-hybrid frequency, the agreement deteriorates rapidly owing to changes in the cold-dispersion root structure and the breakdown of the single-branch WKB description. When coupled to a reduced current-drive source, the corrected heating model gives a median deviation of 10.8 percent from the Landau-channel Ehst-Karney reference and reproduces published CFETR current-density profiles. The resulting model provides a computationally efficient reduced closure for helicon-wave heating and current-drive calculations, together with physically interpretable limits on its range of validity.

physics.plasm-ph↗

arXiv2026

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields: Curvilinear coordinates and multi-block domains

We present a robust and accurate numerical method for the anisotropic diffusion equation in curvilinear coordinates. This study extends the recent work [Muir et al., Computer Physics Communications, 2025] for solving the anisotropic diffusion equation in magnetic fields from Cartesian meshes to to curvilinear coordinates and complex geometries. The method uses summation by parts with simultaneous approximation terms for computing the diffusion perpendicular to field lines. The diffusion along field lines is computed using a penalty approach, similar to a simultaneous approximation term, but applied across the volume. To extend the method to complex geometry we use a multi-block approach with piecewise smooth structured meshes. That is, the domain is split into sub-grids, with locally adjacent boundaries coupled weakly using penalties. We prove the semi-discrete stability for the curvilinear implementation by deriving discrete energy estimates. The approach is verified though a number of numerical tests, which demonstrate the convergence properties of the method in multi-domain approach. Finally, we present a qualitative result generated in complex geometry and magnetic field, which is generated by the Stepped Pressure Equilibrium Code.

math.NA↗

arXiv2026

Relaxed magnetohydrodynamics with cross-field flow

The phase-space Lagrangian model of Dewar et al. (Phys. Plasmas 27, 062507, 2020) provides a framework for incorporating cross-field flow into relaxed equilibria while retaining ideal magnetohydrodynamics force balance. Here, we characterize the steady-state solution space and identify a solvability condition that couples the prescribed constrained flow to the geometry through the metric tensor. Using this condition, we construct equilibria in slab, cylindrical, and toroidal geometries. In toroidal geometry, the cross-field flow strongly correlates with magnetic-island structure: varying the rotation frequency modifies the dominant Fourier harmonic of the radial component of the magnetic field and can drive a transition from a primary (m = 1) island to secondary (m = 2) islands. In slab and cylindrical geometries, flow parameters weakly affect island width but strongly modify equilibrium profiles.

physics.plasm-ph↗

arXiv2026

Three Dimensional Multiphysics Modelling of Helicon Wave Heating and Antenna Plasma Coupling for Boundary Density Control in Toroidal Fusion Plasmas

Active control of scrape off layer density is emerging as a critical requirement for improving ion cyclotron resonance heating and enabling high performance steady state operation in future magnetic confinement fusion devices. Helicon wave excitation offers a promising physics based approach to generating high density boundary plasmas with high ionization efficiency and low impurity release. In this work, we develop THEMIS code, a fully three dimensional (3D) multiphysics model of helicon wave propagation and power deposition in a toroidal fusion relevant configuration, employing a finite temperature thermal dielectric tensor. The code quantifies the relative contributions of Doppler shifted cyclotron damping, anomalous Doppler damping, collisional damping, and Landau damping, and demonstrates that slow wave propagation and electron Landau damping dominate the accessible heating regime in Helimak device. A comparative study of four planar antenna geometries under the present protruding window configuration shows that geometric cutoffs and SOL density gradients severely limit power penetration into the core accessible region. To address this constraint, we introduce a recessed window launch scheme that positions the dielectric window inside the vacuum vessel and perform systematic parameter scans of window position, antenna geometry, and installation orientation. From these analyses, we identify the key physics driven principles governing efficient helicon wave coupling: the importance of open circuit termination, maximized strap length and width, controlled inter turn spacing, and sufficient clearance from metallic walls to avoid near field suppression. Guided by these principles, we designed an optimized racetrack spiral antenna that increases coupling efficiency by more than an order of magnitude compared with conventional short circuited rectangular spiral antenna.

physics.plasm-ph↗

arXiv2025

Shear Alfv\'en Waves in Chaotic Magnetic Fields

The shear Alfv\'en spectrum is computed in the presence of symmetry breaking perturbations that introduce chaotic magnetic field trajectories. Quadratic flux minimised surfaces allow the creation of pseudo straight field line coordinates in the chaotic region. With these coordinates, the reduced ideal MHD equations are cast into an eigenvalue problem and solved numerically. The spectrum is computed with varying perturbation strength, showing how shear Alfv\'en waves change as increasing number of flux surfaces are destroyed. Solutions on specific flux surfaces are shown to remain relatively unchanged while the flux surface remains intact, and retain some original features at large perturbations where the flux surface is destroyed.

physics.plasm-ph↗

arXiv2025

Evaluation and Verification of Physics-Informed Neural Models of the Grad-Shafranov Equation

Our contributions are motivated by fusion reactors that rely on maintaining magnetohydrodynamic (MHD) equilibrium, where the balance between plasma pressure and confining magnetic fields is required for stable operation. In axisymmetric tokamak reactors in particular, and under the assumption of toroidal symmetry, this equilibrium can be mathematically modelled using the Grad-Shafranov Equation (GSE). Recent works have demonstrated the potential of using Physics-Informed Neural Networks (PINNs) to model the GSE. Existing studies did not examine realistic scenarios in which a single network generalizes to a variety of boundary conditions. Addressing that limitation, we evaluate a PINN architecture that incorporates boundary points as network inputs. Additionally, we compare PINN model accuracy and inference speeds with a Fourier Neural Operator (FNO) model. Finding the PINN model to be the most performant, and accurate in our setting, we use the network verification tool Marabou to perform a range of verification tasks. Although we find some discrepancies between evaluations of the networks natively in PyTorch, compared to via Marabou, we are able to demonstrate useful and practical verification workflows. Our study is the first investigation of verification of such networks.

physics.plasm-ph↗

arXiv2025

Sawtooth crash in tokamak as a sequence of Multi-region Relaxed MHD equilibria

This study examines the sawtooth crash phenomenon in tokamak plasmas by modelling it as a sequence of Multi-region Relaxed Magnetohydrodynamic (MRxMHD) equilibria. Using the Stepped-Pressure Equilibrium Code (SPEC), we constructed a series of equilibria representing intermediate states during the sawtooth crash, with progressively increasing reconnection regions. Numerical results demonstrated that the system prefers the lower energy non-axisymmetric equilibria with islands and is eventually back to an axisymmetric state, capturing key features of the reconnection process. Comparisons with the nonlinear MHD code M3D-C1 showed remarkable agreement on the field-line topology, the safety factor, and the current profile. However, the simplified MRxMHD model does not resolve the detailed structure of the current sheet. Despite this limitation, MRxMHD offers an insightful approach and a complementary perspective to initial-value MHD simulations.

physics.plasm-ph↗

arXiv2024

Near-ideal relaxed MHD in slab geometry

We investigate the solutions of the relaxed MHD model (RxMHD) of Dewar \& Qu [J. Plasma Phys. {\bf 88}, 835880101 (2022)]. This model generalizes Taylor relaxation by including the ideal Ohm's law constraint using an augmented Lagrangian method, providing a pathway to extend the multi-region relaxed MHD (MRxMHD) model. We present the first numerical solution of the RxMHD model by Dewar \& Qu, demonstrating that it is mathematically well-defined and computationally feasible for constructing MHD equilibria in slab geometry. We also show that a cross-field flow can exist without enforcing an arbitrary constraint on the angular momentum, as is done in the case of MRxMHD with flow. Our results also demonstrate the self-organization of fully relaxed regions during the optimization, which was an important motivation behind developing this model.

physics.plasm-ph↗

arXiv2024

Automatic classification of magnetic field lines by persistent homology

A method for the automatic classification of the orbits of magnetic field lines into topologically distinct classes using the Vietoris-Rips persistent homology is presented. The input to the method is the Poincare map orbits of field lines and the output is a separation into three classes: islands, chaotic layers, and invariant tori. The classification is tested numerically for the case of a toy model of a perturbed tokamak represented initially in its geometric coordinates. The persistent $H_1$ data is demonstrated to be sufficient to distinguish magnetic islands from the other orbits. When combined with persistent $H_0$ information, describing the average spacing between points on the Poincare section, the larger chaotic orbits can then be separated from very thin chaotic layers and invariant tori. It is then shown that if straight field line coordinates exist for a nearby integrable field configuration, the performance of the classification can be improved by transforming into this natural coordinate system. The focus is the application to toroidal magnetic confinement but the method is sufficiently general to apply to generic $1\frac{1}{2}$d Hamiltonian systems.

physics.plasm-ph↗

arXiv2023

A structure-preserving particle discretisation for the Lenard-Bernstein collision operator

Collisions are an important dissipation mechanism in plasmas. In one-dimensional modelling, a commonly used collision operator is the Lenard-Bernstein operator, or its modified energy- and momentum-conserving counterpart. When approximating such operators numerically, it is important to respect their structure in order to satisfy the laws of thermodynamics. It is, however, challenging to discretise such operators in a structure-preserving way when considering particle methods. In this work, we present a macro-particle discretisation of the Lenard-Bernstein collision operator that is energy and momentum preserving.

physics.plasm-ph↗

arXiv2023

A provably stable numerical method for the anisotropic diffusion equation in confined magnetic fields

We present a novel numerical method for solving the anisotropic diffusion equation in magnetic fields confined to a periodic box which is accurate and provably stable. We derive energy estimates of the solution of the continuous initial boundary value problem. A discrete formulation is presented using operator splitting in time with the summation by parts finite difference approximation of spatial derivatives for the perpendicular diffusion operator. Weak penalty procedures are derived for implementing both boundary conditions and parallel diffusion operator obtained by field line tracing. We prove that the fully-discrete approximation is unconditionally stable. Discrete energy estimates are shown to match the continuous energy estimate given the correct choice of penalty parameters. A nonlinear penalty parameter is shown to provide an effective method for tuning the parallel diffusion penalty and significantly minimises rounding errors. Several numerical experiments, using manufactured solutions, the ``NIMROD benchmark'' problem and a single island problem, are presented to verify numerical accuracy, convergence, and asymptotic preserving properties of the method. Finally, we present a magnetic field with chaotic regions and islands and show the contours of the anisotropic diffusion equation reproduce key features in the field.

math.NA↗

arXiv2023

AREPO White Dwarf merger simulations resulting in edge-lit detonation and run-away hypervelocity companion

We present a series of high-resolution simulations generated with the moving-mesh code AREPO to model the merger of a $1.1 \, \mathrm{M_\odot}$ carbon-oxygen primary white dwarf with an outer helium layer and a $0.35\,\mathrm{M_\odot}$ secondary helium white dwarf. Our simulations lead to detonations that are consistent with the edge-lit scenario, where a helium detonation is ignited at the base of the helium layer of the primary WD, which triggers an off-centre carbon detonation. This produces an asymmetric ejecta pattern and differences in line-of-sight observables (e.g. mean atomic weight). The ejecta that are flung into space are dominated by $^{56}\mathrm{Ni}$, $^{4}\mathrm{He}$, $^{28}\mathrm{Si}$, and $^{32}\mathrm{S}$. Our simulations result in a surviving degenerate companion of mass $0.22-0.25$ $\mathrm{M_\odot}$ moving at $>1\,700$ $\mathrm{km}\,\mathrm{s}^{-1}$, consistent with the observational findings of hypervelocity WDs. The secondary's surface layers are enriched by heavy metals, with $^{56}\mathrm{Ni}$ making up approximately $0.8 \%$ of the remaining mass. We also analyse the sensitivity of the outcome on simulation parameters, including the "inspiral time", which defines a period of accelerated angular momentum loss. We find that the choice of "inspiral time" qualitatively influences the simulation result, including the survival of the secondary. We argue that the shorter inspiral cases result in qualitatively and quantitatively similar outcomes. We also investigate the sensitivity of our results on the primary's chemical profile by comparing simulations using isothermal, constant composition models with the same mass and central composition and characterised by either a bare carbon-oxygen core (no helium) or a carbon-oxygen core enveloped by a thick helium layer.

astro-ph.SR↗

arXiv2023

An efficient method for the anisotropic diffusion equation in magnetic fields

We solve the anisotropic diffusion equation in 2D, where the dominant direction of diffusion is defined by a vector field which does not conform to a Cartesian grid. Our method uses operator splitting to separate the diffusion perpendicular and parallel to the vector field. The slow time scale is solved using a provably stable finite difference formulation in the perpendicular to the vector field, and an integral operator for the diffusion parallel to it. Energy estimates are shown to for the continuous and semi-discrete cases. Numerical experiments are performed showing convergence of the method, and examples is given to demonstrate the capabilities of the method.

math.NA↗

arXiv2022

The shear Alfv\'en continuum with a magnetic island chain in tokamak plasmas

The shear Alfv\'en continuum spectrum is studied for a tokamak with a single island chain using the ideal Magnetohydrodynamics (MHD) theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the Mirror-induced Alfv\'en Eigenmode (MAE) gap and the Helicity-induced Alfv\'en Eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside Toroidal Alfv\'en Eigenmode (TAE) gap into the island. However, the combined TAE/MAE gap is getting narrower as the island grows, leaving only half of its original width with a moderate island size as much as 3.2% of the minor radius. In addition, the two-dimensional eigenfunction of the continuum mode on the lower tip of the MAE gap now has highly localised structures around the island's long axis, contrary to the usual oscillatory global solutions found with no or a low level of toroidal asymmetry - an indication of the continuous spectrum becoming discrete and dense. These results have implications for the frequency, mode structure and continuum damping of global TAEs residing in the gap.

physics.plasm-ph↗

arXiv2021

Node Failure Localisation Problem for Load Balancing Dynamic Networks

Network tomography has been used as an approach to the Node Failure Localisation problem, whereby misbehaving subsets of nodes in a network are to be determined. Typically approaches in the literature assume a statically routed network, permitting linear algebraic arguments. In this work, a load balancing, dynamically routed network is studied, necessitating a stochastic representation of network dynamics. A network model was developed, permitting a novel application of Markov Chain Monte Carlo (MCMC) inference to the Node Failure Localisation (NFL) problem, and the assessment of monitor placement choices. Two nuanced monitor placement algorithms, including one designed for the NFL problem by Ma et al. 2014 were tested, with the published algorithm performing significantly better.

cs.NI↗

arXiv2021

Simulation of convective transport during frequency chirping of a TAE using the MEGA code

We present a procedure to examine energetic particle phase-space during long range frequency chirping phenomena in tokamak plasmas. To apply the proposed method, we have performed self-consistent simulations using the MEGA code and analyzed the simulation data. We demonstrate a travelling wave in phase-space and that there exist specific slices of phase-space on which the resonant particles lie throughout the wave evolution. For non-linear evolution of an n=6 toroidicity-induced Alfven eigenmode (TAE), our results reveal the formation of coherent phase-space structures (holes/clumps) after coarse-graining of the distribution function. These structures cause a convective transport in phase-space which implies a radial drift of the resonant particles. We also demonstrate that the rate of frequency chirping increases with the TAE damping rate. Our observations of the TAE behaviour and the corresponding phase-space dynamics are consistent with the Berk-Breizman (BB) theory.

physics.plasm-ph↗

arXiv2020

Theoretical description of chirping waves using phase-space waterbags

The guiding centre dynamics of fast particles can alter the behaviour of energetic particle driven modes with chirping frequencies. In this paper, the applicability of an earlier trapped/passing locus model [H. Hezaveh et al 2017 Nucl. Fusion 57 126010] has been extended to regimes where the wave trapping region can expand and trap ambient particles. This extension allows the study of waves with up-ward and down-ward frequency chirping across the full range of energetic particle orbits. Under the adiabatic approximation, the phase-space of energetic particles is analysed by a Lagrangian contour approach where the islands are discretised using phase-space waterbags. In order to resolve the dynamics during the fast formation of phase-space islands and find an appropriate initialisation for the system, full-scale modelling is implemented using the bump-on-tail (BOT) code. In addition to investigating the evolution of chirping waves with deepening potentials in a single resonance, we choose specific pitch-angle ranges in which higher resonances can have a relatively considerable contribution to the wave-particle interaction. Hence, the model is also solved in a double-resonance scenario where we report on the significant modifications to the behaviour of the chirping waves due to the $2^{\text{nd}}$ resonance. The model presented in this paper gives a comprehensive 1D paradigm of long range frequency chirping signals observed in experiments with both up-ward and down-ward chirping and multiple resonances.

physics.plasm-ph↗

arXiv2019

Long range frequency chirping of Alfven eigenmodes

A theoretical framework has been developed for an NBI scenario to model the hard nonlinear evolution of Global Alfven Eigenmodes (GAEs) where the adiabatic motion of phase-space sturctures (holes and clumps), associated with the frequency chirping, occurs in generalized phase-space of slowing down energetic particles. The radial profile of the GAE is expanded using finite elements which allows update of the mode structure as the mode frequency chirps. Constants of motion are introduced to track the dynamics of energetic particles during frequency chirping by implementing proper Action-Angle variables and canonical transformations which reduce the dynamics essentially to 1D. Consequently, we specify whether the particles are drifting inward/outward as the frequency deviates from the initial MHD eigenfrequency. Using the principle of least action, we have derived the nonlinear equation describing the evolution of the radial profile by varying the total Lagrangian of the system with respect to the weights of finite elements. For the choice of parameters in this work, it is shown that the peak of the radial profile is shifted and also broadens due to frequency chirping. The time rate of frequency change is also calculated using the energy balance and we show that the adiabatic condition remains valid once it is satisfied. This model clearly illustrates the theoretical treatment to study the long range adiabatic frequency sweeping events observed for Alfven gap modes in real experiments.

physics.plasm-ph↗