A class of rotating compact tori equilibria

Clemente, R. A.; Farengo, Ricardo

doi:10.1063/1.864695

Cited by 43 publications

(41 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since for fusion plasmas the thermal conduction along B is expected to be fast in relation to the heat transport perpendicular to a magnetic surface, equilibria with isothermal magnetic surfaces are a reasonable approximation [17,18,19,20,21,22]. In particular, the even simpler case of isothermal resistive equilibria has also been considered [23].…”

Section: B Isothermal Magnetic Surfacesmentioning

confidence: 99%

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

Throumoulopoulos

Tasso

2000

J. Plasma Phys.

View full text Add to dashboard Cite

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.

show abstract

Section: B Isothermal Magnetic Surfacesmentioning

confidence: 99%

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

Throumoulopoulos

Tasso

2000

J. Plasma Phys.

View full text Add to dashboard Cite

show abstract

“…The equations for axisymmetric plasmas with pure toroidal flow and anisotropic pressure are recovered when F vanishes (Mercier and Cotsaftis 1961, Clemente 1993, 1994. Isotropic pressure equilibria with pure toroidal rotation are described when F = σ − = 0 (Maschke and Perrin 1980, Clemente and Farengo 1984, Viana et al 1997.…”

Section: Discussionmentioning

confidence: 99%

On axisymmetric double adiabatic MHD equilibria with plasma flow

Clemente

Viana

1999

Plasma Phys. Control. Fusion

View full text Add to dashboard Cite

Abstract. The stationary equilibrium of an axisymmetric plasma characterized by toroidal and poloidal flows is considered within the framework of ideal double adiabatic magnetohydrodynamic equations. The problem is reduced to a nonlinear partial differential equation for the poloidal magnetic flux function, containing six surface functions, plus a nonlinear algebraic Bernoulli equation defining the plasma density. Ellipticity conditions and bifurcations of its solutions are discussed in the limit of small beta, appropriated for tokamak-like equilibria. Possible connections with the L-H transition are suggested.

show abstract

“…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%

“…To solve the equilibrium problem in the two elliptic regions, several computer codes have been developed (Semenzato et al 1984;Kerner and Tokuda 1987;Żelazny et al 1993). There is experimental evidence, however, that either the flow is purely toroidal (Suckewer et al 1979;Core et al 1987;Scott et al 1989;Tammen et al 1994) or its poloidal component is one order of magnitude lower than the toroidal one (Brau et al 1983). It was also found that the poloidal flow is efficiently damped by magnetic pumping (Hassam and Kulsrud 1978).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear axisymmetric resistive magnetohydrodynamic equilibria with toroidal flow

Throumoulopoulos

1998

J. Plasma Phys.

View full text Add to dashboard Cite

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.

show abstract

A class of rotating compact tori equilibria

Abstract: A class of semi-analytical equilibria for rotating compact tori with toroidal current density vanishing at the separatrix is presented.

Cited by 43 publications

References 6 publications

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

On axisymmetric double adiabatic MHD equilibria with plasma flow

Nonlinear axisymmetric resistive magnetohydrodynamic equilibria with toroidal flow

Contact Info

Product

Resources

About