Cylindrical ideal magnetohydrodynamic equilibria with incompressible flows

Throumoulopoulos, G. N.; Tasso, H.

doi:10.1063/1.872322

Cited by 38 publications

(53 citation statements)

References 4 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.

Self Cite

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.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In particular, analytic equilibrium solutions have been obtained as solutions to generalized Grad-Shafranov equations (Refs. [3,4,6,7,9,10,11,13]). An impact of the equilibrium flow related to the convective term in the momentum equation is that the isobaric surfaces deviate from the magnetic surfaces.…”

Section: Introductionmentioning

confidence: 99%

Magnetohydrodynamic counter-rotating vortices and synergetic stabilizing effects of magnetic field and plasma flow

Throumoulopoulos

Tasso

2010

Physics of Plasmas

Self Cite

View full text Add to dashboard Cite

A nonlinear two-dimensional steady state solution in the framework of hydrodynamics describing a row of periodic counter-rotating vortices is extended to the magnetohydrodynamic (MHD) equilibrium equation with incompressible flow of arbitrary direction. The extended solution covers a variety of equilibria because four surface quantities remain free. Similar to the case of the MHD cat-eyes equilibrium [Throumoulopoulos et al., J. Phys. A: Math. Theor. 42, 335501 (2009)] and unlike linear equilibria, the flow has a strong impact on isobaric surfaces by forming pressure islands located within the counter-rotating vortices even for values of β (defined as the ratio of the thermal pressure over the external axial magnetic-field pressure) on the order of 0.01. Also, the axial current density is appreciably modified by the flow. Furthermore, a magnetic-field-aligned flow of experimental fusion relevance, i.e for Alfvén Mach numbers of the order of 0.01, and the flow shear in combination with the variation of the magnetic field perpendicular to the magnetic surfaces have significant stabilizing effects potentially related to the equilibrium nonlinearity. The stable region is enhanced by an external axial magnetic field.

show abstract

“…On the other hand, under the simplifying condition of divergence-free flows, non field-aligned rotational equilibria could be readily solved. [23][24][25] Recently, in terms of spherical coordinates, 26 the non field-aligned equilibria have been solved under a set of transformed MHD variables. 27 With these new variables, the functional dependence of the rotational Grad-Shafranov equation, plasma pressure, normal electric field, on the plasma variables are sufficiently simple and explicit to allow an understanding of the L=H mode transition through a positive feedback cycle.…”

Section: Introductionmentioning

confidence: 99%

Tokamak L/H mode transition

Tsui

Navia

2012

Physics of Plasmas

View full text Add to dashboard Cite

Through the non field-aligned rotational tokamak equilibrium of a divergence-free plasma flow with a pair of transformed plasma variablesw Ã ¼ ðlqÞ 1=2ṽ and lp Ã ¼ ðlp þ w 2 Ã =2Þ [K. H. Tsui, Phys. Plasmas 18, 072502 (2011)], a preliminary understanding of the L=H equilibrium transition is proposed through a feedback cycle, where the higher plasma flux due to external drives enters the rotational Grad-Shafranov equation through the velocity dependent poloidal plasma b to generate the H equilibrium. This H rotational mode has the characteristics of higher normal electric field and plasma pressure. Coupled to the transport properties ofẼ ÂB drift transport barrier leading to a higher plasma pressure, this makes the H mode a self-sustained equilibrium. The higher plasma b then feeds back to the equilibrium and completes the feedback loop.

show abstract

Cylindrical ideal magnetohydrodynamic equilibria with incompressible flows

Cited by 38 publications

References 4 publications

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

Magnetohydrodynamic counter-rotating vortices and synergetic stabilizing effects of magnetic field and plasma flow

Tokamak L/H mode transition

Contact Info

Product

Resources

About