Experimental-like Helical Self-Organization in Reversed-Field Pinch Modeling

Bonfiglio, D.; Veranda, M.; Cappello, S.; Escande, Dominique; Chacòn, Luis

doi:10.1103/physrevlett.111.085002

Cited by 47 publications

(73 citation statements)

References 63 publications

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“…These experimental and numerical results show that the validity of the criterion is more general than suggested by the perturbative approach used for its derivation: nonlinear corrections look weak, and the condition that the edge temperature is much smaller than the central one sounds as a leading factor. Helical boundary conditions for the radial magnetic field, mimicking a helical modulation of the plasma magnetic boundary similar to the experimental one, are found to play an essential role for the qualitative and quantitative agreement of MHD simulations with respect to experimental observations in both reversed-field pinch (RFP) and tokamak magnetic configurations [40,66,67].…”

Section: Single Helicity Ohmic Rfp Statesmentioning

confidence: 95%

What is a Reversed Field Pinch?

Escande¹

2015

Rotation and Momentum Transport in Magnetized Plasmas

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Section: Single Helicity Ohmic Rfp Statesmentioning

confidence: 95%

What is a Reversed Field Pinch?

Escande¹

2015

Rotation and Momentum Transport in Magnetized Plasmas

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“…This method works well for field or flow quantities given on a grid and is the basis for the NEMATO code. [1][2][3]5,30,31,38,42 It is important to have a non-uniform time stepping capability for this method, and this is the main objective of this paper. To do this, we assumed fðx; y; zÞDt ¼ Ds with Ds constant and investigated two possible methods of applying this volume-preserving scheme.…”

Section: Discussionmentioning

confidence: 99%

“…15, a method was developed to integrate such incompressible fields or flows while exactly preserving volume, for flows or magnetic fields that are given on a grid of points in three dimensions. This method is the basis for the NEMATO code, [1][2][3]5,30,31,38,42 which has been used extensively for tracing field lines in toroidal plasma configurations. Our main new result in this paper is a method of extending the scheme of Ref.…”

Section: Introductionmentioning

confidence: 99%

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

Finn

2015

Physics of Plasmas

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Properties of integration schemes for solenoidal fields in three dimensions are studied, with a focus on integrating magnetic field lines in a plasma using adaptive time stepping. It is shown that implicit midpoint (IM) and a scheme we call three-dimensional leapfrog (LF) can do a good job (in the sense of preserving KAM tori) of integrating fields that are reversible, or (for LF) have a "special divergence-free" (SDF) property. We review the notion of a self-adjoint scheme, showing that such schemes are at least second order accurate and can always be formed by composing an arbitrary scheme with its adjoint. We also review the concept of reversibility, showing that a reversible but not exactly volume-preserving scheme can lead to a fractal invariant measure in a chaotic region, although this property may not often be observable. We also show numerical results indicating that the IM and LF schemes can fail to preserve KAM tori when the reversibility property (and the SDF property for LF) of the field is broken. We discuss extensions to measure preserving flows, the integration of magnetic field lines in a plasma and the integration of rays for several plasma waves. The main new result of this paper relates to non-uniform time stepping for volumepreserving flows. We investigate two potential schemes, both based on the general method of Feng and Shang [Numer. Math. 71, 451 (1995)], in which the flow is integrated in split time steps, each Hamiltonian in two dimensions. The first scheme is an extension of the method of extended phase space, a well-proven method of symplectic integration with non-uniform time steps. This method is found not to work, and an explanation is given. The second method investigated is a method based on transformation to canonical variables for the two split-step Hamiltonian systems. This method, which is related to the method of non-canonical generating functions of Richardson and Finn [Plasma Phys. Controlled Fusion 54, 014004 (2012)], appears to work very well. V C 2015 AIP Publishing LLC. [http://dx.

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“…And, even though the curvature of the magnetic field induces effects absent in cylindrical geometry, 6 recent studies in cylindrical geometry show some agreement with experiments. 7,8 To study tokamaks, MHD has also been widely applied, see, for instance, Refs. 9-11.…”

mentioning

confidence: 99%

Dynamic equilibria and magnetohydrodynamic instabilities in toroidal plasmas with non-uniform transport coefficients

2015

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International audienceIt can be shown that in the presence of a toroidal magnetic field induced by poloidal coils, combined with the electromagnetic field induced by a central solenoid, no static equilibrium is possible within the MHD description, as soon as non-zero resistivity is assumed. The resulting dynamic equilibrium was previously discussed for the case of spatially homogeneous resisitivity. In the present work, it is shown how a spatial inhomogeneity of the viscosity and resisitivity coefficients influences this equilibrium. Parameters in both the stable, tokamak-like regime and unstable, reversed field pinch-like regime are considered. It is shown that, whereas the magnitudes of the velocity and magnetic field fluctuations are strongly modified by the spatial variation of the transport coefficients, the qualitative flow behaviour remains largely unaffected

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Experimental-like Helical Self-Organization in Reversed-Field Pinch Modeling

Cited by 47 publications

References 63 publications

What is a Reversed Field Pinch?

What is a Reversed Field Pinch?

Issues in measure-preserving three dimensional flow integrators: Self-adjointness, reversibility, and non-uniform time stepping

Dynamic equilibria and magnetohydrodynamic instabilities in toroidal plasmas with non-uniform transport coefficients

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