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Free-boundary MRxMHD equilibrium calculations using the stepped-pressure equilibrium code

Journal Article · · Plasma Physics and Controlled Fusion

Here 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', , is computed, and the virtual-casing principle is used iteratively to compute the normal field on so that the equilibrium is consistent with an externally produced magnetic field. Recent modifications to SPEC are described, such as the use of Chebyshev polynomials to describe the radial dependence of the magnetic vector potential, and a variety of free-boundary verification calculations are presented.

Research Organization:
Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Fusion Energy Sciences (FES); Euratom; Australian Research Council (ARC); Simons Foundation/SFARI
Grant/Contract Number:
AC02-09CH11466
OSTI ID:
1661163
Alternate ID(s):
OSTI ID: 23028787
Journal Information:
Plasma Physics and Controlled Fusion, Journal Name: Plasma Physics and Controlled Fusion Journal Issue: 8 Vol. 62; ISSN 0741-3335
Publisher:
IOP ScienceCopyright Statement
Country of Publication:
United States
Language:
English

References (67)

Mathematical Methods of Classical Mechanics book January 1978
Regular and Chaotic Dynamics book January 1992
Noncanonical Hamiltonian mechanics and its application to magnetic field line flow journal November 1983
Three-dimensional free boundary calculations using a spectral Green's function method journal December 1986
Representations for vacuum potentials in stellarators journal June 1986
An integral equation technique for the exterior and interior neumann problem in toroidal regions journal September 1986
Existence of quasi-periodic orbits for twist homeomorphisms of the annulus journal January 1982
The twist map, the extended Frenkel-Kontorova model and the devil's staircase journal May 1983
Stable stellarators with medium β and aspect ratio journal February 1986
Stellarator symmetry journal January 1998
VENUS-LEVIS and its spline-Fourier interpolation of 3D toroidal magnetic field representation for guiding-centre and full-orbit simulations of charged energetic particles journal December 2014
Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan–Shepp ridge polynomials, Chebyshev–Fourier Series, cylindrical Robert functions, Bessel–Fourier expansions, square-to-disk conformal mapping and radial basis functions journal February 2011
The GBS code for tokamak scrape-off layer simulations journal June 2016
Taylor states in stellarators: A fast high-order boundary integral solver journal November 2019
Hamilton–Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity journal July 2010
Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation journal December 2006
Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics journal November 2015
Three-dimensional magnetohydrodynamic equilibria with continuous magnetic fields journal July 2017
Equilibrium 𝛽-limits in classical stellarators journal November 2017
Scrape-off-layer current loops and floating potential in limited tokamak plasmas journal December 2017
Explicit calculations of homoclinic tangles in tokamaks journal September 2003
Equilibrium of a Magnetically Confined Plasma in a Toroid journal January 1958
Magnetic Differential Equations journal January 1959
Toroidal Containment of a Plasma journal January 1967
Eigenvalue problems for Beltrami fields arising in a three-dimensional toroidal magnetohydrodynamic equilibrium problem journal May 2007
A regularized approach for solving magnetic differential equations and a revised iterative equilibrium algorithm journal November 2010
Computation of multi-region relaxed magnetohydrodynamic equilibria journal November 2012
The infinite interface limit of multiple-region relaxed magnetohydrodynamics journal March 2013
Self-consistent simulations of nonlinear magnetohydrodynamics and profile evolution in stellarator configurations journal May 2013
A new class of magnetic confinement device in the shape of a knot journal January 2014
Multi-region relaxed magnetohydrodynamics with flow journal April 2014
Multi-region relaxed magnetohydrodynamics with anisotropy and flow journal July 2014
Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria journal February 2015
Tokamak magneto-hydrodynamics and reference magnetic coordinates for simulations of plasma disruptions journal June 2015
Existence of three-dimensional ideal-magnetohydrodynamic equilibria with current sheets journal September 2015
Pressure-driven amplification and penetration of resonant magnetic perturbations journal May 2016
Multi-region relaxed Hall magnetohydrodynamics with flow journal August 2016
Verification of the SPEC code in stellarator geometries journal November 2016
HSX as an example of a resilient non-resonant divertor journal March 2017
Extension of the SIESTA MHD equilibrium code to free-plasma-boundary problems journal August 2017
Multi-region relaxed magnetohydrodynamic stability of a current sheet journal March 2019
Performance of Wendelstein 7-X stellarator plasmas during the first divertor operation phase journal August 2019
Resistive stability of cylindrical MHD equilibria with radially localized pressure gradients journal June 2019
Optimized Fourier representations for three-dimensional magnetic surfaces journal January 1985
Existence and calculation of sharp boundary magnetohydrodynamic equilibrium in three-dimensional toroidal geometry journal January 1986
Theory of pressure‐induced islands and self‐healing in three‐dimensional toroidal magnetohydrodynamic equilibria journal March 1995
Explicit spectrally optimized Fourier series for nested magnetic surfaces journal July 1998
Use of the virtual-casing principle in calculating the containing magnetic field in toroidal plasma systems journal September 1972
Solution of stellarator boundary value problems with external currents journal May 1987
Equilibrium and stability of a toroidal magnetohydrodynamic system in the neighbourhood of a magnetic axis journal September 1964
PIES free boundary stellarator equilibria with improved initial conditions journal July 2005
Development and application of HINT2 to helical system plasmas journal September 2006
Equilibria and stability in partially relaxed plasma–vacuum systems journal July 2007
Theory of plasma confinement in non-axisymmetric magnetic fields journal July 2014
Development of quasi-isodynamic stellarators journal November 2010
The virtual-casing principle for 3D toroidal systems journal November 2012
The virtual-casing principle and Helmholtz’s theorem journal September 2015
Fluid simulations of plasma filaments in stellarator geometries with BSTING journal December 2018
Numerical investigation of plasma edge transport and limiter heat fluxes in Wendelstein 7-X startup plasmas with EMC3-EIRENE journal January 2017
Observation of anomalous impurity transport during low-density experiments in W7-X with laser blow-off injections of iron journal February 2019
Multiple timescale calculations of sawteeth and other global macroscopic dynamics of tokamak plasmas journal January 2012
Class renormalization: Islands around islands journal September 1986
Calculation of cantori for Hamiltonian flows journal November 2006
Minimally Constrained Model of Self-Organized Helical States in Reversed-Field Pinches journal July 2013
Relaxation of Toroidal Plasma and Generation of Reverse Magnetic Fields journal November 1974
Relaxation and magnetic reconnection in plasmas journal July 1986
Symplectic maps, variational principles, and transport journal July 1992

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