Publications
* not fully supported by Simons Foundation

Approximate symmetries of guidingcentre motion*
2021Journal ArticleIn a strong, inhomogeneous magnetic field, charged particle dynamics may be studied in the guidingcentre approximation, which is known to be Hamiltonian. When the magnetic field is quasisymmetric, the firstorder guidingcentre (FGC) Hamiltonian structure admits a continuous symmetry, and therefore a conserved quantity in addition to the...

Calculating the linear critical gradient for the iontemperaturegradient mode in magnetically confined plasmas
2021Journal ArticleA firstprinciples method to calculate the critical temperature gradient for the onset of the iontemperaturegradient mode (ITG) in linear gyrokinetics is presented. We find that conventional notions of the connection length previously invoked in tokamak research should be revised and replaced by a generalized correlation length to explain...

Computation of MRxMHD equilibria at fixed toroidal current profile*

Constructing stellarators with quasisymmetry to high order *
2019Journal ArticleA method is given to rapidly compute quasisymmetric stellarator magnetic fields for plasma confinement, without the need to call a threedimensional magnetohydrodynamic equilibrium code inside an optimization iteration. The method is based on direct solution of the equations of magnetohydrodynamic equilibrium and quasisymmetry using Garren and...

Construction of quasisymmetric stellarators using a direct coordinate approach*
2020Journal Article 
Coordinate parameterisation and spectral method optimization for Beltrami field solver in stellarator geometry*

Curlfree magnetic fields for stellarator optimization
2019Journal ArticleThis paper describes a new and efficient method of defining an annular region of a curlfree 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 curlfree initial state to a final fullpressure equilibrium. The large size of...

Designing stellarators using perpendicular permanent magnets

Differential forms for plasma physics*
2020Journal ArticleDifferential forms provide a coordinatefree way to express many quantities and relations in mathematical physics. In particular, they are useful in plasma physics. This tutorial gives a guide so that you can read the plasma physics literature that uses them and apply them yourself.

Direct construction of optimized stellarator shapes. Part 1. Theory in cylindrical coordinates *
2018Journal ArticleThe confinement of guiding center trajectories in a stellarator is determined by the variation of the magnetic field strength B in Boozer coordinates (r,θ,φ), but B(r,θ,φ) depends on the flux surface shape in a complicated way. Here we derive equations relating B(r,θ,φ) in Boozer coordinates and the rotational transform to the shape of flux...

Direct construction of optimized stellarator shapes. Part 2. Numerical quasisymmetric solutions *
2019Journal ArticleQuasisymmetric stellarators are appealing intellectually and as fusion reactor candidates since the guiding center particle trajectories and neoclassical transport are isomorphic to those in a tokamak, implying good confinement. Previously, quasisymmetric magnetic fields have been identified by applying blackbox optimization algorithms to...

Direct construction of optimized stellarator shapes. Part 3. Omnigenity near the magnetic axis *
2019Journal ArticleThe condition of omnigenity is investigated, and applied to the nearaxis expansion of Garren and Boozer (1991a). Due in part to the particular analyticity requirements of the nearaxis expansion, we find that, excluding quasisymmetric solutions, only one type of omnigenity, namely quasiisodynamicity, can be satisfied at first order in the...

The direct criterion of Newcomb for the ideal MHD stability of steppedpressure stellarators*

Direct gradientbased stellarator coil design: Optimization for nearaxis quasisymmetry*

Direct gradientbased stellarator coil design: Stochastic and robust optimization*
2020Journal Article 
Direct Prediction of Nonlinear Tearing Mode Saturation Using a Variational Principle*
2020Journal ArticleIt is shown that the variational principle of multiregion relaxed magnetohydrodynamics (MRxMHD) can be used to predict the stability and nonlinear saturation of tearing modes in strong guide field configurations without resolving the dynamics and without explicit dependence on the plasma resistivity. While the magnetic helicity is not a good...

Efficient highorder singular quadrature schemes in magnetic fusion

Elimination of MHD current sheets by modifications to the plasma wall in a fixed boundary model*

Fast multipole methods for evaluation of layer potentials with locallycorrected quadratures*

Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow
2019Journal ArticleA method is presented to establish regions of phase space for 3D vector fields through which pass no cooriented invariant 2D submanifolds transverse to a given oriented 1D foliation. Refinements are given for the cases of volumepreserving or Cartan–Arnol’d Hamiltonian flows and for boundaryless submanifolds.

Flexibility and rigidity in steady fluid motion

FreeBoundary MRxMHD Equilibrium Calculations Using The SteppedPressure Equilibrium Code*
2020Journal ArticleThe steppedpressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19, 112 502) is extended to enable freeboundary multiregion relaxed magnetohydrodynamic (MRxMHD) equilibrium calculations. The vacuum field surrounding the plasma inside an arbitrary 'computational boundary', ${\mathcal{D}}$, is computed, and the virtualcasing...

Generalized GradShafranov equation for nonaxisymmetric magnetohydrostatic fields*
2020Journal Article 
Ideal and resistive instability of Multiregion Relaxed MHD in Tokamak plasma*

Improved performance of stellarator coil design optimization *
2020Journal ArticleFollowing up on earlier work which demonstrated an improved numerical stellarator coil design optimization performance by the use of stochastic optimization (Lobsien et al., Nucl. Fusion, vol. 58 (10), 2018, 106013), it is demonstrated here that significant further improvements can be made – lower field errors and improved robustness – for a...

Integrability, Normal Forms and Magnetic Axis Coordinates*
0Journal ArticleIntegrable or nearintegrable 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 twotorus. In a neighborhood of a...

A Liouville Formuation of Magnetic Fields Near an Axis

Magnetic well and Mercier stability of stellarators near the magnetic axis

Magnetohydrodynamical equilibria with current singularities and continuous rotational transform *
2019Journal ArticleWe revisit the HahmKulsrudTaylor (HKT) problem, a classic prototype problem for studying resonant magnetic perturbations and 3D magnetohydrodynamical equilibria. We employ the boundarylayer techniques developed by Rosenbluth, Dagazian, and Rutherford (RDR) for the internal m=1 kink instability, while addressing the subtle difference in the...

Multiregion relaxed magnetohydrodynamic stability of a current sheet *
2019Journal ArticleIt is shown that the resistive magnetohydrodynamic stability of a slab forcefree current sheet can be calculated using the variational principle of multiregion relaxed magnetohydrodynamics and that the corresponding stability boundary is in exact agreement with linear tearing mode theory.