arXiv subjects

E. J. Paul

Publications and source records attributed to E. J. Paul.

10 recordsLinked to original sources

arXiv2026

Periodic Korteweg-de Vries soliton potentials generate quasisymmetric magnetic fields

Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, B, that effectively confines charged particles in a three-dimensional toroidal plasma equilibrium. Here, we show that QS has a deep connection to the underlying symmetry that makes solitons possible. Our approach uncovers a hidden lower dimensionality of B on a magnetic flux surface, which could make stellarator optimization schemes significantly more efficient. Recent numerical breakthroughs (M. Landreman and E. Paul, Phys. Rev. Lett. 128, 035001 (2022)) have yielded configurations with excellent volumetric QS and surprisingly low magnetic shear. Given B, it may be possible to deduce an upper bound on the maximum quasisymmetric toroidal volume which depends only on the properties of B. This has been verified for the Landreman-Paul precise quasiaxisymmetric (QA) stellarator configuration. In the neighborhood of the outermost surface, we show that B approaches the form of the 1-soliton reflectionless potential (I. Gjaja and A. Bhattacharjee, Phys. Rev. Lett. 68, 2413 (1992)). The connection length diverges, indicating the possible presence of an X-point or cusp that could potentially be used as a basis for a divertor. We present a non-perturbative approach based on ensuring single-valuedness of B, which directly leads to its Painleve property and the KdV and Gardner's equations. Finally, we use an approach based on machine learning, trained on a large dataset of numerically optimized quasisymmetric stellarators. We robustly recover the KdV and Gardner's equations from the data.

physics.plasm-ph↗

arXiv2026

On shear Alfvén wave-induced energetic ion transport in optimized stellarators

In this work, we investigate prompt ion drift orbit losses caused by shear Alfvén waves (SAW) in quasi-symmetric (QS) and quasi-isodynamic (QI) stellarators optimized for equilibrium confinement of energetic particles (EPs). We use the ideal reduced MHD model for SAW perturbations and study their impact on collisionless EP drift dynamics. We present a semi-analytical model for resonance between the passing EP and SAW, generalized to arbitrary quasi-symmetric configurations including the quasi-poloidal case relevant to QI equilibria. Analysis reveals that an increase in the number of field periods suppresses stochasticity in quasi-helical (QH) and quasi-isodynamic, but not quasi-axissymmetric (QA) stellarators. We show that wave-induced transitions between passing and trapped orbits cause significant losses in QA and QH, but not in QI configurations. For the considered equilibria at scales relevant to fusion power plants (FPPs), we numerically determine SAW amplitudes needed to induce prompt loss of fusion-born alpha particles. Using the weighted Birkhoff averaging technique, we confirm that the onset of prompt losses across all orbit classes occurs with the onset of stochasticity in ion motion. This motivates extending the stochasticity-onset criterion beyond passing orbits in future work.

physics.plasm-ph↗

arXiv2026

Overview of the Helios Design: A Practical Planar Coil Stellarator Fusion Power Plant

Thea Energy, Inc. has developed the preconceptual design for "Helios," a fusion power plant based on the planar coil stellarator architecture. In this overview paper, the design is summarized and the reader is referred to the other papers for more detail. The Helios design is based around a two-field-period quasi-axisymmetric ("QA") stellarator equilibrium with aspect ratio 4.5 and a novel tokamak-like X-point divertor. The natural stability, low recirculating power, and steady-state capability of the stellarator are leveraged. Stability and transport are calculated using state-of-the-art, high-fidelity codes and grounded in measured performance of existing experiments. The electromagnetic coil set is high-temperature superconducting ("HTS") and consists of 12 large, plasma-encircling coils like the toroidal field coils of a tokamak, and 324 smaller, field-shaping coils. All coils are planar and convex. A maximum of 20 T on-coil is enforced, a value which has been achieved in existing large-bore HTS coils. There is a minimum of 1.2 m between plasma and coils, leaving space for tritium breeding blanket and neutron shielding. Because of this thick shielding, all coils have a minimum 40-year operational lifetime, the same minimum lifetime of the power plant system. 1.1 GW of thermal power and 390 MW of net electric power are produced. The shaping coils are individually controllable, enabling a uniquely configurable magnetic field for relaxed manufacturing and assembly tolerances and plasma control. A practical maintenance architecture is a primary driver of the design; maintenance is performed on entire toroidal sectors that are removed from between the encircling coils. A biennial maintenance cycle is estimated to take approximately 84 days, resulting in an 88% capacity factor. Rigorous engineering constraints such as temperature and stress limits are enforced.

physics.plasm-ph↗

arXiv2025

Including the vacuum energy in stellarator coil design

Being three-dimensional, stellarators have the advantage that plasma currents are not essential for creating rotational-transform; however, the external current-carrying coils in stellarators can have strong geometrical shaping, which can complicate the construction. Reducing the inter-coil electromagnetic forces acting on strongly shaped 3D coils and the stress on the support structure while preserving the favorable properties of the magnetic field is a design challenge. In this work, we recognize that the inter-coil forces are the gradient of the vacuum magnetic energy. We introduce an objective functional built on the usual quadratic flux on a prescribed target surface together with a weighed penalty on the vacuum energy. The Euler-Lagrange equation for stationary states is derived, and numerical illustrations are computed using a modern stellarator optimization framework. A study of the effect of the energy functional on the inter-coil forces is conducted and the energy is shown to be a promising quantity in producing coils with low forces.

physics.plasm-ph↗

arXiv2025

Periodic Korteweg-de Vries soliton potentials generate quasisymmetric magnetic field strength in a finite plasma-beta equilibrium

Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, B, that enables effective confinement of charged particles in a fully three-dimensional (3D) toroidal plasma equilibrium. Such equilibria are typically modeled by the ideal magnetohydrostatic (MHS) equation. The nonlinear, overdetermined nature of the quasisymmetric MHS equations severely complicates our understanding of the interplay between 3D shaping, equilibrium properties such as pressure and rotational transform, and B. Progress has been made through expansions near the magnetic axis; however, a more comprehensive theory is desirable. Using a combination of analysis and regression on a large dataset of numerically optimized quasisymmetric stellarators, we demonstrate that there is a hidden lower dimensionality of B on a magnetic flux surface with connections to the theory of periodic solitons. We show that $B$ on a flux surface is determined by three or at most four flux functions, each of which is a critical value of the derivative of B along the field line. While being consistent with the near-axis models, our results are global and hold even on the last closed flux surface.

physics.plasm-ph↗

arXiv2025

Enhancing Stellarator Accessibility through Port Size Optimization

Access to the plasma chamber in a stellarator reactor is essential for maintenance and diagnostics. However, the complex geometry of stellarator coils, often characterized by their strong twisting, can severely limit the space available for access ports. This study introduces a novel optimization approach in which access ports are represented as closed curves on the plasma boundary. By carefully selecting a set of objectives and penalties related to the access port, we demonstrate the first stellarator coil optimization explicitly targeting improved access port size. The trade-off between magnetic field quality and port size is analyzed through the Pareto front of their respective objectives. The optimal location of a port is explained using a current potential approach. Finally, we show that additional shaping coils, such as windowpane coils, can enable the crossing of the Pareto front to achieve superior configurations.

physics.plasm-ph↗

arXiv2024

Integrating Novel Stellarator Single-Stage Optimization Algorithms to Design the Columbia Stellarator Experiment

The Columbia Stellarator eXperiment (CSX), currently being designed at Columbia University, aims to test theoretical predictions related to QA plasma behavior, and to pioneer the construction of an optimized stellarator using three-dimensional, non-insulated high-temperature superconducting (NI-HTS) coils. The magnetic configuration is generated by a combination of two circular planar poloidal field (PF) coils and two 3D-shaped interlinked (IL) coils, with the possibility to add windowpane coils to enhance shaping and experimental flexibility. The PF coils and vacuum vessel are repurposed from the former Columbia Non-Neutral Torus (CNT) experiment, while the IL coils will be custom-wound in-house using NI-HTS tapes. To obtain a plasma shape that meets the physics objectives with a limited number of coils, novel single-stage optimization techniques are employed, optimizing both the plasma and coils concurrently, in particular targeting a tight aspect ratio QA plasma and minimized strain on the HTS tape. Despite the increased complexity due to the expanded degrees of freedom, these methods successfully identify optimized plasma geometries that can be realized by coils meeting engineering specifications. This paper discusses the derivation of the constraints and objectives specific to CSX, and describe how two recently developed single-stage optimization methodologies are applied to the design of CSX. A set of selected configurations for CSX is then described in detail.

physics.plasm-ph↗

arXiv2022

Energetic particle loss mechanisms in reactor-scale equilibria close to quasisymmetry

Collisionless physics primarily determines the transport of fusion-born alpha particles in 3D equilibria. Several transport mechanisms have been implicated in stellarator configurations, including stochastic diffusion due to class transitions, ripple trapping, and banana drift-convective orbits. Given the guiding center dynamics in a set of six quasihelical and quasiaxisymmetric equilibria, we perform a classification of trapping states and transport mechanisms. In addition to banana drift convection and ripple transport, we observe substantial non-conservation of the parallel adiabatic invariant which can cause losses through diffusive banana tip motion. Furthermore, many lost trajectories undergo transitions between trapping classes on longer time scales, either with periodic or irregular behavior. We discuss possible optimization strategies for each of the relevant transport mechanisms. We perform a comparison between fast ion losses and metrics for the prevalence of mechanisms such as banana-drift convection [1], transitioning orbits, and wide orbit widths. Quasihelical configurations are found to have natural protection against ripple-trapping and diffusive banana tip motion leading to a reduction in prompt losses.

physics.plasm-ph↗

arXiv2018

An adjoint method for gradient-based optimization of stellarator coil shapes

We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a continuous current potential. We apply the adjoint method to calculate derivatives of the objective function, allowing for efficient computation of analytic gradients while eliminating the numerical noise of approximate derivatives. We are able to improve engineering properties of the coils by targeting the root-mean-squared current density in the objective function. We obtain winding surfaces for W7-X and HSX which simultaneously decrease the normal magnetic field on the plasma surface and increase the surface-averaged distance between the coils and the plasma in comparison with the actual winding surfaces. The coils computed on the optimized surfaces feature a smaller toroidal extent and curvature and increased inter-coil spacing. A technique for visualization of the sensitivity of figures of merit to normal surface displacement of the winding surface is presented, with potential applications for understanding engineering tolerances.

physics.plasm-ph↗

arXiv2017

Rotation and Neoclassical Ripple Transport in ITER

Neoclassical transport in the presence of non-axisymmetric magnetic fields causes a toroidal torque known as neoclassical toroidal viscosity (NTV). The toroidal symmetry of ITER will be broken by the finite number of toroidal field coils and by test blanket modules (TBMs). The addition of ferritic inserts (FIs) will decrease the magnitude of the toroidal field ripple. 3D magnetic equilibria with toroidal field ripple and ferromagnetic structures are calculated for an ITER steady-state scenario using the Variational Moments Equilibrium Code (VMEC). Neoclassical transport quantities in the presence of these error fields are calculated using the Stellarator Fokker-Planck Iterative Neoclassical Conservative Solver (SFINCS). These calculations fully account for $E_r$, flux surface shaping, multiple species, magnitude of ripple, and collisionality rather than applying approximate analytic NTV formulae. As NTV is a complicated nonlinear function of $E_r$, we study its behavior over a plausible range of $E_r$. We estimate the toroidal flow, and hence $E_r$, using a semi-analytic turbulent intrinsic rotation model and NUBEAM calculations of neutral beam torque. The NTV from the $\rvert n \rvert = 18$ ripple dominates that from lower $n$ perturbations of the TBMs. With the inclusion of FIs, the magnitude of NTV torque is reduced by about 75% near the edge. We present comparisons of several models of tangential magnetic drifts, finding appreciable differences only for superbanana-plateau transport at small $E_r$. We find the scaling of calculated NTV torque with ripple magnitude to indicate that ripple-trapping may be a significant mechanism for NTV in ITER. The computed NTV torque without ferritic components is comparable in magnitude to the NBI and intrinsic turbulent torques and will likely damp rotation, but the NTV torque is significantly reduced by the planned ferritic inserts.

physics.plasm-ph↗