arXiv subjects

Todd Elder

Publications and source records attributed to Todd Elder.

6 recordsLinked to original sources

arXiv2025

Stellarator divertor design by optimizing coils for surfaces with sharp corners

In stellarators, achieving effective divertor configurations is challenging due to the three-dimensional nature of the magnetic fields, which often leads to chaotic field lines and fuzzy separatrices. This work presents a novel approach to directly optimize modular stellarator coils for a sharp X-point divertor topology akin to the Large Helical Device's (LHD) helical divertor using a target plasma surface with sharp corners. By minimizing the normal magnetic field component on this surface, we target a clean separatrix with minimal chaos. Notably, this approach demonstrates the first LHD-like helical divertor design using optimized modular coils instead of helical coils. Separatrices are produced with significantly lower chaos than in LHD, demonstrating that a wide chaotic layer is not intrinsic to the helical divertor. Additional optimization methods are implemented to improve engineering feasibility of the coils and reduce chaos, including weighted quadrature and manifold optimization, a method which does not rely on normal field minimization. The results outline several new strategies for divertor design in stellarators, though it remains to achieve these edge divertor features at the same time as internal field qualities like quasisymmetry.

physics.plasm-ph↗

arXiv2025

Surface Current Optimization and Coil-Cutting Algorithms for Stage-Two Stellarator Optimization

Stellarator optimization often takes a two-stage approach, where in the first stage the boundary is varied in order to optimize for some physics metrics, while in the second stage the boundary is kept fixed and coils are sought to generate a magnetic field that can recreate the desired stellarator. Past literature dealing with this stage lacks details on the coil cutting procedure and the mathematical and physical properties of the surface current potential which dictates it. In this work, some basic physical quantities of the surface current and how they relate to the parameters in the current potential are presented, and supported for the first time by explicit mathematical derivations. Additionally, the details of how to account for the presence of an external field in the surface current algorithm are explicitly presented. These relations underpin the procedure of discretizing the surface current into coils. Finally, the conventionally-used algorithm for discretizing the surface current into coils is detailed, along with an example coil optimization for both a modular and a helical coilset. The algorithm is implemented in the \texttt{DESC} code, with both modular and helical coil capabilities, where it is available for use in stellarator coil design.

physics.plasm-ph↗

arXiv2024

Current potential patches

A novel form of the current potential, a mathematical tool for the design of stellarators and stellarator coils, is developed. Specifically, these are current potentials with a finite-element-like basis, called \textit{current potential patches}. Current potential patches leverage the relationship between distributions of magnetic dipoles and current potentials to explore limits of the access properties of stellarator coil sets. An example calculation is shown using the Helically Symmetric Experiment (HSX) equilibrium, demonstrating the method's use in coil design and understanding the limits of the access properties of coil sets. Current potential patches have additional desirable properties such as of promoting sparse current sheet solutions and identifying crucial locations of shaping current placement. A result is found for the HSX equilibrium that shaping currents covering only 25\% of the winding surface is sufficient to produce the equilibrium to a good accuracy, provided a toroidal field is pre-supplied.

physics.plasm-ph↗

arXiv2021

Example of exponentially enhanced magnetic reconnection driven by a spatially-bounded and laminar ideal flow

In laboratory and natural plasmas of practical interest, the spatial scale $Δ_d$ at which magnetic field lines lose distinguishability differs enormously from the scale $a$ of magnetic reconnection across the field lines. In the solar corona, plasma resistivity gives $a/Δ_d\sim10^{12}$, which is the magnetic Reynold number $R_m$. The traditional resolution of the paradox of disparate scales is for the current density $j$ associated with the reconnecting field $B_{rec}$ to be concentrated by a factor of $R_m$ by the ideal evolution, so $ j\sim B_{rec}/μ_0Δ_d$. A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of arbitrarily chosen magnetic field lines, $Δ_{max}/Δ_{min}$, when calculated at various points in time. Reconnection becomes inevitable where $Δ_{max}/Δ_{min}\sim R_m$. A simple model of the solar corona will be used for a numerical illustration that the natural rate of increase in time is linear for the current density but exponential for $Δ_{max}/Δ_{min}$. Reconnection occurs on a time scale and with a current density enhanced by only $\ln(a/Δ_d)$ from the ideal evolution time and from the current density $B_{rec}/μ_0a$. In both resolutions, once a sufficiently wide region, $Δ_r$, has undergone reconnection, the magnetic field loses static force balance and evolves on an Alfvénic time scale. The Alfvénic evolution is intrinsically ideal but expands the region in which $Δ_{max}/Δ_{min}$ is large.

physics.plasm-ph↗

arXiv2021

Magnetic nulls in interacting dipolar fields

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field-lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance $Δ_d$. Electron inertia ensures $Δ_d\gtrsim c/ω_{pe}$. The lines that lie within a magnetic flux tube of radius $Δ_d$ at the place where the field strength $B$ is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where $B=0$,vanishes, then distinguishable lines come no closer to the null than $\approx (a^2c/ω_{pe})^{1/3}$, where $a$ is a characteristic spatial scale of the magnetic field. The behavior of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.

physics.plasm-ph↗

arXiv2019

Impact of a minority relativistic electron tail interacting with a thermal plasma containing high-atomic-number impurities

A minority relativistic electron component can arise in both laboratory and naturally-occurring plasmas. In the presence of high-atomic-number ion species, the ion charge state distribution at low bulk electron temperature can be dominated by relativistic electrons, even though their density is orders of magnitude lower. This is due to the relativistic enhancement of the collisional excitation and ionization cross sections. The resulting charge state effect can dramatically impact the radiative power loss rate and the related Bethe stopping power of relativistic electrons in a dilute plasma.

physics.plasm-ph↗