Publications

* not fully supported by Simons Foundation

• Approximate symmetries of guiding-centre motion*

J W. Burby; N Kallinikos; R S. MacKay
2021
Journal Article

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...

• Calculating the linear critical gradient for the ion-temperature-gradient mode in magnetically confined plasmas

G.T. Roberg-Clark; G.G. Plunk; P. Xanthopoulos
2021
Journal Article

A first-principles method to calculate the critical temperature gradient for the onset of the ion-temperature-gradient 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*

Baillod; J. Loizu; Z. S. Qu; A. Kumar; J. Graves
2020
Journal Article
• Constructing stellarators with quasisymmetry to high order *

Matt Landreman; Wrick Sengupta
2019
Journal Article

A method is given to rapidly compute quasisymmetric stellarator magnetic fields for plasma confinement, without the need to call a three-dimensional 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*

R. Jorge; W. Sengupta; M. Landreman
2020
Journal Article
• Coordinate parameterisation and spectral method optimization for Beltrami field solver in stellarator geometry*

Z. S. Qu; D. Pfefferlé; S. R. Hudson; A. Baillod; A. Kumar; R. Dewar; M. Hole
2020
Journal Article
• Curl-free magnetic fields for stellarator optimization

Allen H. Boozer
2019
Journal Article

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...

• Designing stellarators using perpendicular permanent magnets

Zhu; M. Zarnstorff; D. Gates; A. Brooks
2020
Journal Article
• Differential forms for plasma physics*

R. S. MacKay
2020
Journal Article

Differential forms provide a coordinate-free 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 *

Matt Landreman; Wrick Sengupta
2018
Journal Article

The 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 *

Matt Landreman; Wrick Sengupta; Gabriel G. Plunk
2019
Journal Article

Quasisymmetric 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 black-box optimization algorithms to...

• Direct construction of optimized stellarator shapes. Part 3. Omnigenity near the magnetic axis *

Gabriel G. Plunk; Matt Landreman; Per Helander
2019
Journal Article

The condition of omnigenity is investigated, and applied to the near-axis expansion of Garren and Boozer (1991a). Due in part to the particular analyticity requirements of the near-axis expansion, we find that, excluding quasi-symmetric solutions, only one type of omnigenity, namely quasi-isodynamicity, can be satisfied at first order in the...

• Direct gradient-based stellarator coil design: Optimization for near-axis quasi-symmetry*

Giuliani; F. Wechsung; A. Cerfon; G. Stadler; M. Landreman
2020
Journal Article
• Direct gradient-based stellarator coil design: Stochastic and robust optimization*

F. Wechsung; A. Giuliani; M. Landreman; A. Cerfon; G. Stadler
2020
Journal Article
• Direct Prediction of Nonlinear Tearing Mode Saturation Using a Variational Principle*

J. Loizu; Y. M. Huang; S. M. Hudson; A. Baillod; A. Kumar; Z. S. Qu
2020
Journal Article

It is shown that the variational principle of multi-region 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 high-order singular quadrature schemes in magnetic fusion

D. Malhotra; A. Cerfon; M. O’Neil; E. Toler
2020
Journal Article

• Fast multipole methods for evaluation of layer potentials with locally-corrected quadratures*

L. Greengard; M. O'Neil; M. Rachh; F. Vico
2020
Journal Article
• Finding the Complement of the Invariant Manifolds Transverse to a Given Foliation for a 3D Flow

Robert S. MacKay
2019
Journal Article

A method is presented to establish regions of phase space for 3D vector fields through which pass no co-oriented invariant 2D submanifolds transverse to a given oriented 1D foliation. Refinements are given for the cases of volume-preserving or Cartan–Arnol’d Hamiltonian flows and for boundaryless submanifolds.

• Flexibility and rigidity in steady fluid motion

P. Constantin; T. Drivas; D. Ginsberg
2020
Journal Article
• Free-Boundary MRxMHD Equilibrium Calculations Using The Stepped-Pressure Equilibrium Code*

S. R. Hudson; J. Loizu; C. Zhu; Z. S. Qu; C. Nührenberg; S. Lazerson; C. B. Smiet; M. J. Hole
2020
Journal Article

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...

• Generalized Grad-Shafranov equation for non-axisymmetric magnetohydrostatic fields*

J. Burby; N. Kallinikos; R. MacKay
2020
Journal Article
• Ideal and resistive instability of Multi-region Relaxed MHD in Tokamak plasma*

Kumar; J. Doak; Z. S. Qu; S. R. Hudson; J. Loizu; R. Dewar; M. J. Hole
2020
Journal Article
• Improved performance of stellarator coil design optimization *

Jim-Felix Lobsien; Michael Drevlak; Thomas Kruger; Samuel Lazerson; Caoxiang Zhu; Thomas Sunn Pedersen
2020
Journal Article

Following 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*

J. Burby; N. Duignan; J. Meiss
0
Journal Article

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...

• A Liouville Formuation of Magnetic Fields Near an Axis

N. Duignan; J. Meiss
2020
Journal Article

• Magnetohydrodynamical equilibria with current singularities and continuous rotational transform *

Yao Zhou; Yi-Min Huang; Allen H. Reiman; Amitava Bhattacharjee
2019
Journal Article

We revisit the Hahm-Kulsrud-Taylor (HKT) problem, a classic prototype problem for studying resonant magnetic perturbations and 3D magnetohydrodynamical equilibria. We employ the boundary-layer techniques developed by Rosenbluth, Dagazian, and Rutherford (RDR) for the internal m=1 kink instability, while addressing the subtle difference in the...

• Multi-region relaxed magnetohydrodynamic stability of a current sheet *

Joaquim Loizu; Scott R. Hudson
2019
Journal Article

It is shown that the resistive magnetohydrodynamic stability of a slab force-free current sheet can be calculated using the variational principle of multi-region relaxed magnetohydrodynamics and that the corresponding stability boundary is in exact agreement with linear tearing mode theory.