Publications

  • 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...

  • 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...

  • The direct criterion of Newcomb for the ideal MHD stability of stepped-pressure stellarators*

  • 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
  • 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 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
  • Magnetic well and Mercier stability of stellarators near the magnetic axis

  • 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.

  • Near-axis expansion of stellarator equilibrium at arbitrary order in the distance to the axis *

    Rogerio Jorge; Wrick Sengupta; Matt Landreman
    2019
    Journal Article

    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...

Pages

* not fully supported by Simons Foundation