3D magnetohydrodynamic equilibria with anisotropic pressure

Cooper, W. A.; Hirshman, S. P.; Merazzi, S.; Gruber, R.

doi:10.1016/0010-4655(92)90002-g

Cited by 15 publications

(32 citation statements)

References 19 publications

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“…side [16] and by a factor (1 − μB min /E) to obtain large parallel anisotropy [17]. Here, B min is the minimum value of the magnetic field strength B on each flux surface, is an integer that controls the level of anisotropy while μ and E represent the particle magnetic moment and energy, respectively.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Three-dimensional anisotropic pressure free boundary equilibria

Cooper

Hirshman

Merkel

et al. 2009

Computer Physics Communications

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“…VMEC [5] and TERPSICHORE [6] have been adapted to encompass pressure anisotropy [7] in the equilibrium. A modified bi-Maxwellian [8] is used for hot particles in order to prescribe different pressure profiles parallel and perpendicular to the magnetic field.…”

Section: Anisotropic Equilibriummentioning

confidence: 99%

Impact of pressure anisotropy on tokamak equilibria and the toroidal magnetic precession

Jucker

Graves

Cooper

et al. 2008

Plasma Phys. Control. Fusion

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Abstract. Using a generalised anisotropic tokamak equilibrium and an exact guiding centre drift formulation, the effect of parallel and perpendicular anisotropy on the toroidal precession drift is investigated. Significant differences between parallel and perpendicular pressure anisotropy are observed. While the Shafranov shift is not sensitive to the ratio of the parallel and perpendicular pressures p ⊥ /p , the deepening of the magnetic well is found to be sensitive to p ⊥ /p . Here, the diamagnetic effect identified by Connor et al. [J. Connor, R. Hastie, and T. Martin, Nucl. Fusion 23, 1702 (1983)] is generalised and found to depend crucially on the deposition of the energetic ions on which the equilibrium depends, and leads to test particle precessional drifts that depend sensitively on pitch angle.

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“…For stellarator configuration, VMEC (Variational Moment Equilibrium Code) 13 was extended to include pressure anisotropy, and numerical solutions were presented. [14][15][16] Several experimental studies related to pressure anisotropy were also reported. Equilibrium reconstruction including pressure anisotropy was shown to agree with measurement in JET (Joint European Torus) and Tore Supra.…”

Section: Introductionmentioning

confidence: 94%

Effects of pressure anisotropy on magnetospheric magnetohydrodynamics equilibrium of an internal ring current system

Furukawa

2014

Physics of Plasmas

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Effects of pressure anisotropy on magnetospheric magnetohydrodynamics equilibrium are studied analytically and numerically, where the plasma is confined by only poloidal magnetic field generated by an internal ring current. The plasma current due to finite pressure can be divided into two components; one remains at isotropic pressure and the other arises from pressure anisotropy. When p⊥, the pressure perpendicular to the magnetic field, is larger than p∥, the pressure parallel to the magnetic field, those two components of plasma current tend to cancel each other to reduce the total amount of plasma current. Equilibrium beta limit is also examined, where the beta is a ratio of the plasma pressure to the magnetic pressure. The equilibrium beta limit decreases as the pressure anisotropy becomes strong. The beta value is strictly limited by ellipticity of the equilibrium equation when p∥>p⊥. On the other hand, when p⊥>p∥, although the tendency of the beta limit agrees with the ellipticity condition of the equilibrium equation, equilibria with a hyperbolic region can be obtained by iterative procedure with practically reasonable convergence criteria.

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3D magnetohydrodynamic equilibria with anisotropic pressure

Cited by 15 publications

References 19 publications

Three-dimensional anisotropic pressure free boundary equilibria

Three-dimensional anisotropic pressure free boundary equilibria

Impact of pressure anisotropy on tokamak equilibria and the toroidal magnetic precession

Effects of pressure anisotropy on magnetospheric magnetohydrodynamics equilibrium of an internal ring current system

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