** partially supported by Simons Foundation*

## A

*Nucl. Fusion*, Vol. 45, 731

*Nuclear Fusion*, Vol. 61, Dec 2021, 126040

In the Wendelstein 7-X (W7-X) stellarator, the vacuum rotational transform, ι, has a flat radial profile and does not cross any major rational resonance. Nevertheless, during plasma operation the ι‐profile can be strongly modified by electron cyclotron current drive in such a way that the resulting ι-profile passes through low-order rational…

## B

*Phys. Rev. Lett.*, Vol. 33, 1139

*in preparation (2020)*

*Physics of Plasmas*, Vol. 29, 042505

*Physics of Plasmas*, Vol. 29, Apr 2022, 042505

Good magnetic surfaces, as opposed to magnetic islands and chaotic field lines, are generally desirable for stellarators. In previous work, Landreman *et al.* [Phys. of Plasmas **28**, 092505 (2021)] showed that equilibria computed by the Stepped-Pressure Equilibrium Code (SPEC) [Hudson *et al.*,…

*Nuclear Fusion*, Vol. 61, Aug 2021, 096024

This paper is focused on three points: (1) overcoming obstacles to tokamak power plants may require a configuration modification as large as that of a stellarator. (2) The demonstrated reliability of the computational design of stellarators should change fusion strategy. (3) Deployment of carbon-free energy sources is mandated by the thirty…

*Physics of Plasmas*, Vol. 26, Oct 2019

This paper describes a new and efficient method of defining an annular region of a curl-free magnetic field with specific physics and coil properties that can be used in stellarator design. Three statements define the importance: (1) Codes can follow an optimized curl-free initial state to a final full-pressure equilibrium. The large size of…

Deuterium-tritium (DT) burning requires a long energy confinement times compared to collision times, so the particle distribution functions must approximate local-Maxwellians. Non-equilibrium thermodynamics is applicable, which gives relations among transport, entropy production, the collision frequency, and the deviation from a Maxwellian. The…

*Journal of Physics A: Mathematical and Theoretical*, Vol. 54, Mar 2021, 125202

In a strong, inhomogeneous magnetic field, charged particle dynamics may be studied in the guiding-centre approximation, which is known to be Hamiltonian. When the magnetic field is quasisymmetric, the first-order guiding-centre (FGC) Hamiltonian structure admits a continuous symmetry, and therefore a conserved quantity in addition to the…

In a magnetic field, transitions between classes of guiding-centre motion can lead to cross-field diffusion and escape. We say a magnetic field is isodrastic if guiding centres make no transitions between classes of motion. Therefore, this is an important ideal for enhancing confinement. First, we present a weak formulation, based on the…

*submitted to the Physics of Plasmas (2020)*

Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation consisting entirely of invariant submanifolds. A regular leaf, known as a flux surface,of this foliation must be diffeomorphic to the two-torus. In a neighborhood of a…

*Journal of Physics A: Mathematical and Theoretical*, Vol. 54, Mar 2021, 125202

In a strong, inhomogeneous magnetic field, charged particle dynamics may be studied in the guiding-centre approximation, which is known to be Hamiltonian. When the magnetic field is quasisymmetric, the first-order guiding-centre (FGC) Hamiltonian structure admits a continuous symmetry, and therefore a conserved quantity in addition to the…

*Journal of Mathematical Physics*, Vol. 61, Sep 2020, 093503

Quasi-symmetry of a steady magnetic field means integrability of first-order guiding-center motion by a spatial symmetry. Here, we derive many restrictions on the possibilities for a quasi-symmetry. We also derive an analog of the Grad–Shafranov equation for the flux function in a quasi-symmetric magnetohydrostatic field.

## C

*Phys. Plasmas*, Vol. 28, 092505

*J. Open Source Software*, Vol. 6, 3525

*Phys. Rev. Lett.*, Vol. 89, 275003

*in preparation (2020)*

In this work, we consider optimal control problems constrained by elliptic partial differential equations (PDEs) with lognormal random coefficients, which are represented by a countably infinite-dimensional random parameter with i.i.d. normal distribution. We approximate the optimal solution by a suitable truncation of its Hermite polynomial…

*submitted (2020)*

*submitted (2020)*

We describe a method to construct smooth and compactly supported solutions of 3D incompressible Euler equations and related models. The method is based on localizable Grad-Shafranov equations and is inspired by the recent result.

## D

*Rev. Mod. Phys.*, Vol. 64, 795

*Journal of Plasma Physics*, Vol. 88, Feb 2022

The gap between a recently developed dynamical version of relaxed magnetohydrodynamics (RxMHD) and ideal MHD (IMHD) is bridged by approximating the zero-resistivity "Ideal" Ohm's Law (IOL) constraint using an augmented Lagrangian method borrowed from optimization theory. The augmentation combines a pointwise vector Lagrange multiplier method…

*Physics of Plasmas*, Vol. 27, Jun 2020

A new formulation of time-dependent Relaxed Magnetohydrodynamics (RxMHD) is derived variationally from Hamilton's Action Principle using microscopic conservation of mass, and macroscopic conservation of total magnetic helicity, cross helicity and entropy, as the only constraints on variations of density, pressure, fluid velocity, and magnetic…

*Physics of Plasmas*, Vol. 28, Dec 2021, 122501

A formal series transformation to Birkhoff–Gustavson normal form is obtained for toroidal magnetic field configurations in the neighborhood of a magnetic axis. Bishop's rotation minimizing coordinates are used to obtain a local orthogonal frame near the axis in which the metric is diagonal, even if the curvature has zeros. We treat the cases of…

*Chaos*, Vol. 31, Jan 2021

Invariant manifolds are of fundamental importance to the qualitative understanding of dynamical systems. In this work, we explore and extend MacKay’s converse Kolmogorov–Arnol’d–Moser condition to obtain a sufficient condition for the nonexistence of invariant surfaces that are transverse to a chosen 1D foliation. We show how useful foliations…

## E

## G

*to be submitted to the Journal of Computational Physics (2020)*

*Physics of Plasmas 27, 042509 (2020)*, Vol. 27

The Floquet exponents of periodic field lines are studied through the variations of the magnetic action on the magnetic axis, which is assumed to be elliptical. The near-axis formalism developed by Mercier, Solov’ev and Shafranov is combined with a Lagrangian approach. The on-axis Floquet exponent is shown to coincide with the on-axis…

## H

*Comput. Phys. Commun.*, Vol. 43, 157

*Physical Review Letters*, Vol. 124, Mar 2020

It is shown that the magnetic-field coils of a stellarator can, at least in principle, be substantially simplified by the use of permanent magnets. Such magnets cannot create toroidal magnetic flux but they can be used to shape the plasma and thus to create poloidal flux and rotational transform, thereby easing the requirements on the magnetic…

*Journal of Plasma Physics*, Vol. 87, May 2021, 905870226

Combined plasma–coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the…

*Physics of Plasmas*, Vol. 26, Sep 2019

Analytic scaling relations are derived for a phenomenological model of the plasmoid instability in an evolving current sheet, including the effects of reconnection outflow. Two scenarios are considered, where the plasmoid instability can be triggered either by an injected initial perturbation or by the natural noise of the system (here…

*Plasma Physics and Controlled Fusion*, Vol. 62, Jul 2020

The stepped-pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19, 112 502) is extended to enable free-boundary multi-region relaxed magnetohydrodynamic (MRxMHD) equilibrium calculations. The vacuum field surrounding the plasma inside an arbitrary 'computational boundary', ${\mathcal{D}}$, is computed, and the virtual-casing…

## J

*Plasma Phys. Controlled Fusion*, Vol. 62, 084002

*J. Plasma Phys.*, Vol. 87, 905870403

*Plasma Phys. Controlled Fusion*, Vol. 62, 124004

*submitted to Plasma Physics and Controlled Fusion (2020)*

*Journal of Plasma Physics*, Vol. 86, Jan 2020

A direct construction of equilibrium magnetic fields with toroidal topology at arbitrary order in the distance from the magnetic axis is carried out, yielding an analytical framework able to explore the landscape of possible magnetic flux surfaces in the vicinity of the axis. This framework can provide meaningful analytical insight on the…

*Nuclear Fusion 60, 076021 (2020)*, Vol. 60

## K

*Plasma Physics and Controlled Fusion 62, 044002 (2020)*, Vol. 62

*Plasma Physics and Controlled Fusion*, Vol. 63, Feb 2021, 045006

Over the last decade, a variational principle based on a generalisation of Taylor’s relaxation, referred to as multi-region relaxed magnetohydrodynamics (MRxMHDs) has been developed. The numerical solutions of the MRxMHD equilibria have been constructed using the Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19…