Computation of symmetric ideal MHD flow equilibria

Semenzato, S.; Gruber, R.; Zehrfeld, H. P.

doi:10.1016/0167-7977(84)90011-x

Cited by 59 publications

(47 citation statements)

References 18 publications

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“…It is pointed out that, unlike to the usual procedure followed in equilibrium studies with flow [10,11,12,13,14,15] in the present work an equation of state is not included in the above set of equations from the outset and therefore the equation of state independent Eqs. (15) and (16) below are first derived.…”

Section: Equilibrium Equationsmentioning

confidence: 99%

“…Also, the poloidal electric field can then be obtained by Eq. (13). To determine ψ in the case of compressible flows with isentropic magnetic surfaces the set of Eqs.…”

Section: A σ = σ(R ψ)mentioning

confidence: 99%

“…(21) and (22), which are coupled through the density ρ, should be solved numerically under appropriate boundary conditions. This can be accomplished by the existing ideal MHD equilibrium codes [13,14,15]. The problem of compressible flows with isothermal magnetic surfaces [Eqs.…”

Section: A σ = σ(R ψ)mentioning

confidence: 99%

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On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

Throumoulopoulos

Tasso

2000

J. Plasma Phys.

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It is shown that the magnetohydrodynamic equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal magnetic flux function ψ coupled with a Bernoulli type equation for the plasma density (which are identical in form to the corresponding ideal MHD equilibrium equations) along with the relation ∆ ⋆ ψ = V c σ. (Here, ∆ ⋆ is the Grad-Schlüter-Shafranov operator, σ is the conductivity and V c is the constant toroidal-loop voltage divided by 2π). In particular, for incompressible flows the above mentioned partial differential equation becomes elliptic and decouples from the Bernoulli equation [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 5, 2378 (1998)]. For a conductivity of the form σ = σ(R, ψ) (R is the distance from the axis of symmetry) several classes of analytic equilibria with incompressible flows can be constructed having qualitatively plausible σ profiles, i.e. profiles with σ taking a maximum value close to the magnetic axis and a minimum value on the plasma surface. For σ = σ(ψ) consideration of the relation ∆ ⋆ ψ = V c σ(ψ) in the vicinity of the magnetic axis leads therein to a proof of the non-existence of either compressible or incompressible equilibria. This result can be extended to the more general case of non-parallel flows lying within the magnetic surfaces.

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Section: Equilibrium Equationsmentioning

confidence: 99%

“…Also, the poloidal electric field can then be obtained by Eq. (13). To determine ψ in the case of compressible flows with isentropic magnetic surfaces the set of Eqs.…”

Section: A σ = σ(R ψ)mentioning

confidence: 99%

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On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

Throumoulopoulos

Tasso

2000

J. Plasma Phys.

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“…However, the results obtained are clouded in some controversy because singularities arise at relatively modest poloidal Mach number in the single fluid model considered that are not manifest in more complete multifluid/kinetic descriptions [11]. This model is also the basis for the CLIO code [12]. The M3D hybrid MHD-kinetic code has been previously applied to NSTX axisymmetric equilibria and quite accurately recovers features of the density profile that is displaced radially outward when the toroidal rotation is strong [13].…”

Section: Introductionmentioning

confidence: 99%

An approximate single fluid 3-dimensional magnetohydrodynamic equilibrium model with toroidal flow

Cooper

Hirshman

Chapman

et al. 2014

Plasma Phys. Control. Fusion

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An approximate model for a single fluid three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium with pure isothermal toroidal flow with imposed nested magnetic flux surfaces is proposed. It recovers the rigorous toroidal rotation equilibrium description in the axisymmetric limit. The approximation is valid under conditions of nearly rigid or vanishing toroidal rotation in regions with significant 3D deformation of the equilibrium flux surfaces. Bifurcated helical core equilibrium simulations of long-lived modes in the MAST device demonstrate that the magnetic structure is only weakly affected by the flow but that the 3D pressure distortion is important. The pressure is displaced away from the major axis and therefore is not as noticeably helically deformed as the toroidal magnetic flux under the subsonic flow conditions measured in the experiment. The model invoked fails to predict any significant screening by toroidal plasma rotation of resonant magnetic perturbations in MAST free boundary computations.

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“…To solve the equilibrium problem in the two elliptic regions, several computer codes have been developed (e.g. [15][16][17]). For purely toroidal flow the partial differential equation becomes elliptic and can be solved analytically; analytic solutions were obtained in Refs.…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic equilibria of a cylindrical plasma with poloidal mass flow and arbitrary cross sectional shape

Throumoulopoulos

Pantis

1996

Plasma Phys. Control. Fusion

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The equilibrium of a cylindrical plasma with purely poloidal mass flow and cross section of arbitrary shape is investigated within the framework of the ideal MHD theory. For the system under consideration it is shown that only incompressible flows are possible and, conscequently, the general two dimensional flow equilibrium equations reduce to a single second-order quasilinear partial differential equation for the poloidal magnetic flux function ψ, in which four profile functionals of ψ appear. Apart from a singularity occuring when the modulus of Mach number associated with the Alfvén velocity for the poloidal magnetic field is unity, this equation is always elliptic and permits the construction of several classes of analytic solutions. Specific exact equlibria for a plasma confined within a perfectly conducting circular cylindrical boundary and having i) a flat current density and ii) a peaked current density *

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Computation of symmetric ideal MHD flow equilibria

Cited by 59 publications

References 18 publications

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

An approximate single fluid 3-dimensional magnetohydrodynamic equilibrium model with toroidal flow

Magnetohydrodynamic equilibria of a cylindrical plasma with poloidal mass flow and arbitrary cross sectional shape

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