Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria

Johnson, John L.; Dalhed, H. E.; Greene, J. M.; Grimm, R.C.; Hsieh, Yue-Lin; Jardin, S.C.; Manickam, J.; Okabayashi, M.; Storer, R. G.; Todd, A.M.M.; Voss, D. E.; Weimer, K.E.

doi:10.1016/0021-9991(79)90129-3

Cited by 125 publications

(49 citation statements)

References 27 publications

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“…On the flux surface ρ, they are defined such that dφ /dθ = q(ρ) = const. In this paper, we primarily use SFL coordinates (PEST-like [57]), where the Jacobian for the coordinate transformation with the cylindrical coordinates is proportional to R 2 . Moreover, the toroidal angle is the geometrical angle φ = φ and, thus, only the poloidal SFL angle θ has to be determined.…”

Section: Calculation Of Straight Field Line Coordinates and Poloidal mentioning

confidence: 99%

Plasma response measurements of external magnetic perturbations using electron cyclotron emission and comparisons to 3D ideal MHD equilibrium

Willensdorfer

Denk

Strumberger

et al. 2016

Plasma Phys. Control. Fusion

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Abstract. The plasma response from an external n = 2 magnetic perturbation field in ASDEX Upgrade has been measured using mainly electron cyclotron emission (ECE) diagnostics and a rigid rotating field. To interpret ECE and ECE-imaging (ECE-I) measurements accurately, forward modeling of the radiation transport has been combined with ray tracing. The measured data is compared to synthetic ECE data generated from a 3D ideal magnetohydrodynamics (MHD) equilibrium calculated by VMEC.The measured amplitudes of the helical displacement around the low field side midplane are in reasonable agreement with the one from the synthetic VMEC diagnostics. Both exceed the prediction from the vacuum field calculations and indicate the presence of a kink response at the edge, which amplifies the perturbation. VMEC and MARS-F have been used to calculate the properties of this kink mode. The poloidal mode structure of the magnetic perturbation of this kink mode at the edge peaks at poloidal mode numbers larger than the resonant components |m| > |nq|, whereas the poloidal mode structure of its displacement is almost resonant |m| ≈ |nq|. This is expected from ideal MHD in the proximity of rational surfaces. The displacement measured by ECE-I confirms this resonant response.

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Section: Calculation Of Straight Field Line Coordinates and Poloidal mentioning

confidence: 99%

Plasma response measurements of external magnetic perturbations using electron cyclotron emission and comparisons to 3D ideal MHD equilibrium

Willensdorfer

Denk

Strumberger

et al. 2016

Plasma Phys. Control. Fusion

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“…In principle, the solution should extend to the whole space outside the plasma. In reality, EFIT chooses a rectangular computational boundary, and the flux values on this computational boundary ψ(r B ) are computed to be consistent with the equilibrium with the integral form of the Ampere equation similar to equation (4):…”

Section: Formulation Of the Equilibrium Reconstruction Problem In Efitmentioning

confidence: 99%

High spatial resolution equilibrium reconstruction

Ren

Chu

Lao

et al. 2011

Plasma Phys. Control. Fusion

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The extension of the EFIT equilibrium reconstruction code to fine spatialgrid resolutions is discussed. The residue in the force-balance relation of the Grad-Shafranov (G-S) equation and the convergence property of these fine spatial-grid EFIT equilibria are studied in detail. The results suggest that fine spatial-grid equilibria generally better satisfy the force-balance constraint described by the G-S equation. Finer spatial-grid equilibria have typically smaller average error in satisfying the force-balance equation than coarse-grid equilibria and those extrapolated from coarse-grid results. Analysis of the equilibrium iteration algorithm employed in EFIT reveals that the iteration process is related to the spatial feedback stabilization of the plasma with flux control at various specified locations. Thus, for a converged equilibrium, axisymmetric stability is generally expected with feedback. The iteration error decreases self-similarly in the final stage of the iteration process and is related to the least stable axisymmetric mode in the feedback-stabilized equilibrium.

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“…ASEQ is a variant of the PEST(Princeton Equilibrium, Stability and Transport) ct, de [31 ]. The version we use here is a free boundary equilibrium solver.…”

Section: The Comparison With Aseqmentioning

confidence: 99%

Magnetic flux reconstruction methods for shaped tokamaks

Tsui¹

1993

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This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. _he Government reserves for itself and others acting on its behalf a royalty free, nonexclusive, irrevocable, worldwide license for governmental purposes to publish, distribute, translate, duplicate, exhibit, and perform any such data copyrighted the contractor.

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Numerical determination of axisymmetric toroidal magnetohydrodynamic equilibria

Cited by 125 publications

References 27 publications

Plasma response measurements of external magnetic perturbations using electron cyclotron emission and comparisons to 3D ideal MHD equilibrium

Plasma response measurements of external magnetic perturbations using electron cyclotron emission and comparisons to 3D ideal MHD equilibrium

High spatial resolution equilibrium reconstruction

Magnetic flux reconstruction methods for shaped tokamaks

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