Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria

Hirshman, S. P.

doi:10.1063/1.864116

Cited by 793 publications

(813 citation statements)

References 13 publications

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“…The variables u and v of the inverse coordinate system (s, u, v) represent the poloidal and toroidal angular variables, respectively, that are used in the ANIMEC code [19]. The number of equilibrium field periods is denoted by L and √ g is the Jacobian of the transformation from the Cartesian frame to the (s, u, v) coordinates.…”

Section: Equilibrium Energy Minimisationmentioning

confidence: 99%

See 1 more Smart Citation

Three-dimensional anisotropic pressure free boundary equilibria

Cooper

Hirshman

Merkel

et al. 2009

Computer Physics Communications

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Free boundary three-dimensional anisotropic pressure magnetohydrodynamic equilibria with nested magnetic flux surfaces are computed through the minimisation of the plasma energy functionalThe plasma-vacuum interface is varied to guarantee the continuity of the total pressure [p ⊥ + B 2 /(2μ 0 )] across it and the vacuum magnetic field must satisfy the Neumann boundary condition that its component normal to this interface surface vanishes. The vacuum magnetic field corresponds to that driven by the plasma current and external coils plus the gradient of a potential function whose solution is obtained using a Green's function method. The energetic particle contributions to the pressure are evaluated analytically from the moments of the variant of a biMaxwellian distribution function that satisfies the constraint B · ∇F h = 0. Applications to demonstrate the versatility and reliability of the numerical method employed have concentrated on high-β off-axis energetic particle deposition with large parallel and perpendicular pressure anisotropies in a 2-field period quasiaxisymmetric stellarator reactor system. For large perpendicular pressure anisotropy, the hot particle component of the p ⊥ distribution localises in the regions where the energetic particles are deposited. For large parallel pressure anisotropy, the pressures are more uniform around the flux surfaces.

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Section: Equilibrium Energy Minimisationmentioning

confidence: 99%

“…where R is the distance from the major axis, Z is the distance from the vertical midplane and λ is the poloidal angle renormalisation parameter that controls the spectral width of the representation [19]. The forces within the plasma are…”

Section: Equilibrium Energy Minimisationmentioning

confidence: 99%

Three-dimensional anisotropic pressure free boundary equilibria

Cooper

Hirshman

Merkel

et al. 2009

Computer Physics Communications

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“…The equilibrium state is obtained by varying the energy functional W with respect to an artificial time to yield (Hirshman & Whitson 1983) …”

Section: The 3-d Mhd Equilibrium Statementioning

confidence: 99%

A 3-D MHD equilibrium description of nonlinearly saturated ideal external kink/peeling structures in tokamaks

et al. 2015

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Novel free boundary magnetohydrodynamic equilibrium states with spontaneous three-dimensional (3-D) deformations of the plasma-vacuum interface are computed. The structures obtained look like saturated ideal external kink/peeling modes. Large edge pressure gradients yield toroidal mode number n = 1 distortions when the edge bootstrap current is large and higher n corrugations when this current is small. Linear ideal MHD stability analyses confirm the nonlinear saturated ideal kink equilibrium states produced and we can identify the Pfirsch-Schlüter current as the main linear instability driving mechanism when the edge pressure gradient is large. The dominant non-axisymmetric component of this Pfirsch-Schlüter current drives a near resonant helical parallel current density ribbon that aligns with the near vanishing magnetic shear region caused by the edge bootstrap current. This current ribbon is a manifestation of the outer mode previously found on JET (Solano 2010). We claim that the equilibrium corrugations describe structures that are commonly observed in quiescent H-mode tokamak discharges.

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“…Vacuum calculations suggest the formation of edge islands and stochastic regions when RMPs are applied to the axisymmetric equilibria. Self-consistent calculations of the plasma equilibrium with the VMEC [2] and SPEC [3] codes have been performed for an up-down symmetric shot (142603) in DIII-D. In these codes, a self-consistent calculation of the plasma response due to the RMP coils is calculated.…”

Section: D Equilibrium Effects Due To Rmp Application On Diii-d*mentioning

confidence: 99%

3D Equilibrium Effects Due to RMP Application on DIII-D

Lazerson¹,

Lazarus²,

Hudson³

et al. 2012

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The mitigation and suppression of edge localized modes (ELMs) through application of resonant magnetic perturbations (RMPs) in Tokamak plasmas is a well documented phenomenon (142603) in DIII-D. In these codes, a self-consistent calculation of the plasma response due to the RMP coils is calculated. The VMEC code globally enforces the constraints of ideal MHD; consequently, a continuously nested family of flux surfaces is enforced throughout the plasma domain. This approach necessarily precludes the observation of islands or field-line chaos. The SPEC code relaxes the constraints of ideal MHD locally, and allows for islands and field line chaos at or near the rational surfaces. Equilibria with finite pressure gradients are approximated by a set of discrete 'ideal-interfaces' at the most irrational flux surfaces and where the strongest pressure gradients are observed. Both the VMEC and SPEC calculations are initialized from EFIT reconstructions of the plasma that are consistent with the experimental pressure and current profiles. A 3D reconstruction using the STELLOPT code, which fits VMEC equilibria to experimental measurements, has also been performed. Comparisons between the equilibria generated by the 3D codes and between STELLOPT and EFIT are presented.

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Steepest-descent moment method for three-dimensional magnetohydrodynamic equilibria

Cited by 793 publications

References 13 publications

Three-dimensional anisotropic pressure free boundary equilibria

Three-dimensional anisotropic pressure free boundary equilibria

A 3-D MHD equilibrium description of nonlinearly saturated ideal external kink/peeling structures in tokamaks

3D Equilibrium Effects Due to RMP Application on DIII-D

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