Axisymmetric toroidal equilibrium with incompressible flows

Avinash, K.; Bhattacharyya, S. N.; Green, B J

doi:10.1088/0741-3335/34/4/006

Cited by 16 publications

(23 citation statements)

References 14 publications

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“…It is also noted that special cases of incompressible ideal equilibria have been investigated in Refs. [24] and [25]. Unlike to the corresponding sets of compressible S = S(ψ) equations (21) and (22), and T = T (ψ) equations (23) and (24), Eq.…”

Section: Incompressible Flowsmentioning

confidence: 99%

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: Incompressible Flowsmentioning

confidence: 99%

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

Throumoulopoulos

Tasso

2000

J. Plasma Phys.

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“…1, or something else, will therefore depend on the strength of the mechanism that drives poloidal rotation compared to the magnitude of the parallel heat conductivity. It has even been argued [51] that an assumption of incompressible equilibrium flow may be justified for tokamak experiments. Incompressibility entails that r Á u = 0 so that q is constant on magnetic surfaces and c f ?…”

Section: Poloidal Flowmentioning

confidence: 99%

The Brunt–Väisälä frequency of rotating tokamak plasmas

Haverkort

Blank

Koren

2012

Journal of Computational Physics

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a b s t r a c tThe continuous spectrum of analytical toroidally rotating magnetically confined plasma equilibria is investigated analytically and numerically. In the presence of purely toroidal flow, the ideal magnetohydrodynamic equations leave the freedom to specify which thermodynamic quantity is constant on the magnetic surfaces. Introducing a general parametrization of this quantity, analytical equilibrium solutions are derived that still posses this freedom. These equilibria and their spectral properties are shown to be ideally suited for testing numerical equilibrium and stability codes including toroidal rotation. Analytical expressions are derived for the low-frequency continuous Alfvén spectrum. These expressions still allow one to choose which quantity is constant on the magnetic surfaces of the equilibrium, thereby generalizing previous results. The centrifugal convective effect is shown to modify the lowest Alfvén continuum branch to a buoyancy frequency, or Brunt-Väisälä frequency. A comparison with numerical results for the case that the specific entropy, the temperature, or the density is constant on the magnetic surfaces yields excellent agreement, showing the usefulness of the derived expressions for the validation of numerical codes.

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“…axisymmetric incompressible β p = 1 equilibria with purely poloidal flow, was proved by Tasso (1970). To find out whether the above incompatibilities associated with the conductivity profile arise from the choice T = T (ψ), one alternatively can consider the cases of isentropic processes and incompressible flows, which has been the subject of extensive ideal MHD studies and are, respectively, associated with isentropic magnetic surfaces (Maschke and Perrin 1980;Morozov and Solovév 1980;Hameiri 1983;Semenzato et al 1984;Kerner and Tokuda 1987;Throumoulopoulos and Pantis 1989;Żelazny et al 1993) and constant density magnetic surfaces (Avinash et al 1992;Throumoulopoulos and Pantis 1996;Throumoulopoulos and Tasso 1997).…”

Section: Equilibria With Isothermal Magnetic Surfacesmentioning

confidence: 99%

“…Equilibria with incompressible flows are usually associated with constant density magnetic surfaces (Avinash et al 1992;Throumoulopoulos and Pantis 1996;Throumoulopoulos and Tasso 1997). For axisymmetric equilibria with purely toroidal flow, Eqs.…”

Section: Equilibria With Magnetic Surfaces Of Constant Densitymentioning

confidence: 99%

“…Although equilibrium studies of flowing plasmas began in the mid 1950s (e.g. Grad 1960), since the early 1980s there has been an increasing interest in the investigation of the equilibrium properties of plasmas with mass flow (Zehrfeld and Green 1972;Maschke and Perrin 1980;Morozov and Solovév 1980;Hameiri 1983;Clemente and Farengo 1984;Semenzato et al 1984;Kerner and Tokuda 1987;Throumoulopoulos and Pantis 1989;Avinash et al 1992;Żelazny et al 1993;Throumoulopoulos and Pantis 1996;Throumoulopoulos and Tasso 1997) which was motivated by the observation of plasma rotation in many tokamaks heated by neutral beams (Suckewer et al 1979;Brau et al 1983;Core et al 1987;Scott et al 1989;Tammen et al 1994) With the adoption of a specific equation of state, e.g. isentropic magnetic surfaces (Morozov and Solovév 1980), the axisymmetric ideal MHD equilibrium states obey to a partial differential equation for ψ, containing five surface quantities, in conjunction with a nonlinear algebraic Bernouli equation.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear axisymmetric resistive magnetohydrodynamic equilibria with toroidal flow

Throumoulopoulos

1998

J. Plasma Phys.

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The equilibrium of a resistive axisymmetric plasma with purely toroidal flow surrounded by a conductor is investigated within the framework of the nonlinear magnetohydrodynamic theory. It is proved that a) the poloidal current density vanishes and b) apart from an idealized case the pressure profile should vanish on the plasma boundary. For the cases of isothermal magnetic surfaces, isentropic magnetic surfaces and magnetic surfaces with constant density, the equilibrium states obey to an elliptic partial differential equation for the poloidal magnetic flux function, which is identical in form to the corresponding equation governing ideal equilibria. The conductivity, which can not be either uniform or a surface quantity, results however in a restriction of the possible classes of equilibrium solutions, e.g. for the cases considered the only possible equilibria with Spitzer conductivity are of cylindrical shape.

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Axisymmetric toroidal equilibrium with incompressible flows

Abstract: Printd i n F W * l Brilain.

Cited by 16 publications

References 14 publications

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

The Brunt–Väisälä frequency of rotating tokamak plasmas

Nonlinear axisymmetric resistive magnetohydrodynamic equilibria with toroidal flow

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