arXiv subjects

M. J. Gerard

Publications and source records attributed to M. J. Gerard.

4 recordsLinked to original sources

arXiv2026

Characterizing Flux-Surface Shapes in Tokamaks and Quasi-Symmetric Stellarators

Modern stellarator designs routinely attain high levels of magnetic-field quasi-symmetry through flux-surface shaping. Here, we examine different methods for characterizing stellarator flux-surface shapes in a manner analogous to flux-surface shaping in tokamaks. The methods considered use a Fourier analysis to define the shaping modes (e.g. elongation, triangularity, squareness, etc.) of equilibrium cross-sections. Relative to an axisymmetric equilibrium, the additional degree of freedom in a non-axisymmetric equilibrium manifests as a rotation of each shaping mode about the magnetic axis. This analysis is performed on non-axisymmetric configurations with a high degree of quasi-symmetry and equilibria with varying quasi-symmetry quality from the QUASR database. One method in particular is shown to reduce shape complexity in quasi-symmetric equilibria by defining a set of cross-sections that efficiently fill out an equilibrium volume. This is accomplished by defining a cross-section as the set of points that occupy the shortest distance between the magnetic axis and an equilibrium flux-surface across all quasi-symmetry contours. Using this method, we find empirically an equilibrium geometry can be described with significantly fewer non-negligible shaping modes relative to other shape characterization methods. Moreover, the method reveals that quasi-symmetry quality is strongly correlated with equilibrium shapes that exhibit a highly constrained linear distribution of shaping modes, where an increase in shape complexity is proportional to an increase in shape rotation about the magnetic axis. It is therefore argued this method provides a way to efficiently characterize the shape of quasi-symmetric equilibria in a manner analogous to how equilibrium shapes are described in tokamaks.

physics.plasm-ph↗

arXiv2025

Resilient Stellarator Divertor Characteristics in the Helically Symmetric eXperiment

Resilient divertor features connected to open chaotic edge structures in the Helically Symmetric Experiment (HSX) are investigated. For the first time, an expanded vessel wall was considered that would give space for implementation of a physical divertor target structure. The analysis was done for four different magnetic configurations with very different chaotic plasma edges. A resilient plasma wall interaction pattern was identified across all configurations. This manifests as qualitatively very similar footprint behavior across the different plasma equilibria. Overall, the resilient field lines of interest with high connection length $L_C$ lie within a helical band along the wall for all configurations. This resiliency can be used to identify the best location of a divertor. The details of the magnetic footprint's resilient helical band is subject to specific field line structures which are linked to the penetration depth of field lines into the plasma and directly influence the heat and particle flux patterns. The differences arising from these details are characterized by introducing a new metric, the minimum radial connection $\text{min}(δ_N)$ of a field line from the last closed flux surface. The relationship, namely the deviation from a scaling law, between $\text{min}(δ_N)$ and $L_C$ of the field lines in the plasma edge field line behavior suggests that the field lines are associated with structures such as resonant islands, cantori, and turnstiles. This helps determine the relevant magnetic flux channels based on the radial location of these chaotic edge structures and the divertor target footprint. These details will need to be taken into account for resilient divertor design.

physics.plasm-ph↗

arXiv2024

On the effect of flux-surface shaping on trapped-electron modes in quasi-helically symmetric stellarators

Using a novel optimization procedure it has been shown that the Helically Symmetric eXperiment (HSX) stellarator can be optimized for reduced trapped-electron-mode (TEM) instability [M.J.~Gerard et al., \textit{Nucl.~Fusion} \textbf{63} (2023) 056004]. Presently, with a set of 563 experimental candidate configurations, gyrokinetic simulations are performed to investigate the efficacy of available energy $E_\mathrm{A}$, quasi-helical symmetry, and flux-surface shaping parameters as metrics for TEM stabilization. It is found that lower values of $E_\mathrm{A}$ correlate with reduced growth rates, but only when separate flux-surface shaping regimes are considered. Moreover, configurations with improved quasi-helical symmetry demonstrate a similar reduction in growth rates and less scatter compared to $E_\mathrm{A}$. Regarding flux-surface shaping, a set of helical shaping parameters is introduced that show increased elongation is strongly correlated with reduced TEM growth rates, however, only when the quasi-helical symmetry is preserved. Using a newly derived velocity-space-averaged TEM resonance operator, these trends are analyzed to provide insights into the physical mechanism of the observed stabilization. For elongation, stabilization is attributed to geometric effects that reduce the destabilizing particle drifts across the magnetic field. Regarding quasi-helical symmetry, the TEM resonance in the maximally resonant trapping well is shown to increase as the quasi-helical symmetry is broken, and breaking quasi-helical symmetry increases the prevalence of highly resonant trapping wells. While these results demonstrate the limitations of using any single metric as a linear TEM proxy, it is shown that quasi-helical symmetry and plasma elongation are highly effective metrics for reducing TEM growth rates in helical equilibria.

physics.plasm-ph↗

arXiv2023

Bounce-averaged drifts: Equivalent definitions, numerical implementations, and example cases

In this article we provide various analytical and numerical methods for calculating the average drift of magnetically trapped particles across field lines in complex geometries, and we compare these methods against each other. To evaluate bounce-integrals, we introduce a generalisation of the trapezoidal rule which is able to circumvent integrable singularities. We contrast this method with more standard quadrature methods in a parabolic magnetic well and find that the computational cost is significantly lower for the trapezoidal method, though at the cost of accuracy. With numerical routines in place, we next investigate conditions on particles which cross the computational boundary, and we find that important differences arise for particles affected by this boundary, which can depend on the specific implementation of the calculation. Finally, we investigate the bounce-averaged drifts in the optimized stellarator NCSX. From investigating the drifts, one can readily deduce important properties, such as what subset of particles can drive trapped-particle modes, and in what regions radial drifts are most deleterious to the stability of such modes.

physics.plasm-ph↗