Three-dimensional anisotropic pressure free boundary equilibria

Cooper, W. A.; Hirshman, S. P.; Merkel, P.; Graves, J. P.; Kißlinger, J.; Wobig, H.; Narushima, Y.; Okamura, S.; Watanabe, K. Y.

doi:10.1016/j.cpc.2009.04.006

Cited by 56 publications

(76 citation statements)

References 24 publications

(35 reference statements)

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“…Typically, a bi-Maxwellian distribution function for the energetic species has formed the foundation of fixed and free boundary equilibrium investigations in the past. 16,17 This form was particularly useful and relevant for ICRH simulations. Alternatively, a modified slowing-down distribution given by F h ðs; E; kÞ ¼ 1 2p…”

Section: A Modified Slowing-down Fast Ion Distribution Functionmentioning

confidence: 99%

“…16 The free boundary extension, named ANI-MEC, has employed the bi-Maxwellian form and was applied to a two-field period quasiaxisymmetric stellarator. 17 In this work, we shall explore a combination of the slowing-down distributions treated in Refs. 14 and 15 and demonstrate that we can model neutral beam injection angles that span the range from the direction parallel to that perpendicular with respect to the magnetic field lines.…”

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confidence: 99%

“…The linear fluid MHD stability description and the kinetic energy normalisation developed are considered in a) e-mail: wilfred.cooper@epfl.ch. MHD equilibrium states with nested magnetic flux surfaces and anisotropic pressure are computed with the ANIMEC code, 17 and extended version of the VMEC code. [11][12][13] This formulation minimises the total energy…”

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confidence: 99%

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Equilibrium and stability in a heliotron with anisotropic hot particle slowing-down distribution

et al. 2012

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Perpendicular and tangential angularly resolved multi-sight neutral particle analyzer system in LHD Rev. Sci. Instrum. 83, 10D920 (2012) Diagnostics development for quasi-steady-state operation of the Wendelstein 7-X stellarator (invited) Rev. Sci. Instrum. 83, 10D730 (2012) Effect of superbanana diffusion on fusion reactivity in stellarators Phys. Plasmas 19, 082516 (2012) The internal disruption as hard The equilibrium and linear fluid Magnetohydrodynamic (MHD) stability in an inward-shifted large helical device heliotron configuration are investigated with the 3D ANIMEC and TERPSICHORE codes, respectively. A modified slowing-down distribution function is invoked to study anisotropic pressure conditions. An appropriate choice of coefficients and exponents allows the simulation of neutral beam injection in which the angle of injection is varied from parallel to perpendicular. The fluid stability analysis concentrates on the application of the Johnson-Kulsrud-Weimer energy principle. The growth rates are maximum at hbi $ 2%, decrease significantly at hbi $ 4:5%, do not vary significantly with variations of the injection angle and are similar to those predicted with a bi-Maxwellian hot particle distribution function model. Stability is predicted at hbi $ 2:5% with a sufficiently peaked energetic particle pressure profile. Electrostatic potential forms from the MHD instability necessary for guiding centre orbit following are calculated.

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Section: A Modified Slowing-down Fast Ion Distribution Functionmentioning

confidence: 99%

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confidence: 99%

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Equilibrium and stability in a heliotron with anisotropic hot particle slowing-down distribution

et al. 2012

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“…The equilibrium state for anisotropic pressure equilibria is computed with the ANIMEC code [18] to model the inwardshifted LHD configuration at high-β . To model the threedimensional equilibrium we choose to consider an anisotropic pressure bi-Maxwellian distribution function model to describe the fast particle species [19].…”

Section: The Mhd Equilibrium Statementioning

confidence: 99%

Drift stabilization of ballooning modes in a high-⟨β⟩ LHD configuration

et al. 2010

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Ideal MHD yields at best inconclusive predictions about the stability of the LHD heliotron for β 3%. We investigate the impact of the drift stabilization of ballooning modes for the inward-shifted LHD configuration (vacuum magnetic axis R 0 ∼ 3.5 m). The background equilibrium is considered anisotropic in which the neutral beam ions contribute about 1/4 fraction of the total diamagnetic beta, β dia . A drift corrected ballooning mode equation obtained from the linearized gyrokinetic equation is expanded assuming that the hot particle drifts are much larger than the mode frequency. The fast particle pressure gradients contribute weakly to both the instability drive and the diamagnetic drift stabilization (which is dominated by the thermal ion diamagnetic drifts) for β dia ∈ [0, 4.8]%. In the single-fluid limit (diamagnetic drifts ignored), the thermal pressure gradients drive ballooning modes in a broad region encompassing the outer 60-90% of the plasma volume at β dia ≈ 4.8%. To stabilize these modes, we find that diamagnetic drift corrections must be invoked (mainly due to the thermal ions). The energetic ion diamagnetic drifts play a role only for low wave number values, k α 8. It has been verified that the fast particle drift ordering imposed by the model is amply satisfied for on-axis hot particle to thermal density N h0 /N i0 ≈ 1% even at high β dia .

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“…Initial RFX-mod SHAx equilibrium state simulations in which seven-fold periodic 3D core helical structures develop have been published [18]. Bifurcated solutions of tokamak MHD equilibria are successfully obtained with the ANIMEC code (an anisotropic pressure version of VMEC, although scalar pressure is imposed in the simulations undertaken) [19]. Two solutions can spontaneously develop, but only the axisymmetric result can be calculated with a GradShafranov solver.…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic equilibrium and the stability of tokamak and reversed-field pinch systems with 3D helical cores

Cooper¹,

Graves²,

Sauter³

et al. 2011

Plasma Phys. Control. Fusion

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Bifurcated magnetohydrodynamic (MHD) equilibrium states are computed for ITER hybrid scenario and RFX-mod SHAx configurations with very flat or reversed core magnetic shear conditions. In the ITER studies, the minimum inverse rotational transform q min is near unity, while for RFX-mod it is 1/8. Two equilibrium states are obtained: one is axisymmetric, the other displays a 3D helical core. In tokamak devices, the structure resembles a saturated ideal MHD internal kink mode. In the reversed-field pinch, the structure is seven-fold toroidally periodic. The equilibrium magnetic field spectrum in the Boozer coordinate frame is calculated in both the ITER and RFX-mod configurations and the implications are discussed. The RFX-mod equilibria are strongly unstable to external ideal MHD kink modes, which become stabilized with a closely fitting conducting shell when the equilibrium state has a weak reversed core shear. It is marginally unstable with a monotonic q-profile. Unstable modes are driven by the Ohmic current, with pressure and PfirschSchlüter currents having a very weak effect. The external kink mode spectrum is dominated by coupled m = 1, n = 6 and m = 2, n = 13 Fourier components, which revert to m = 1, n = 8 and m = 2, n = 15 terms with a conducting wall in proximity to the plasma-vacuum interface.

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Three-dimensional anisotropic pressure free boundary equilibria

Cited by 56 publications

References 24 publications

Equilibrium and stability in a heliotron with anisotropic hot particle slowing-down distribution

Equilibrium and stability in a heliotron with anisotropic hot particle slowing-down distribution

Drift stabilization of ballooning modes in a high-⟨β⟩ LHD configuration

Magnetohydrodynamic equilibrium and the stability of tokamak and reversed-field pinch systems with 3D helical cores

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