Relaxed plasma-vacuum systems

Spies, G. O.; Lortz, D.; Kaiser, Ralf

doi:10.1063/1.1383286

Cited by 17 publications

(43 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In Spies [10] the condition δ 2 W¨0 was re-formulated as a highly nonlinear eigenvalue problem. That is, the functional δ 2 W has been minimized subject to the constraint of constant N A , where…”

Section: Multiple Interface Plasma-vacuum Modelmentioning

confidence: 99%

“…Given the vessel with boundary , the interfaces i , and the magnetic field B, Eqs. (9)- (12) constitute a boundary problem for the plasma pressure P i in each region The second variation is a straightforward generalization of Spies [10,11] to multiple interfaces. That is,…”

Section: Multiple Interface Plasma-vacuum Modelmentioning

confidence: 99%

“…Our working builds principally upon a variational model developed by Spies et al [10], which comprised a plasma/vacuum/conducting wall system. In Spies [10] the theory is applied to a plasma slab equilibrium, with boundary conditions designed to simulate a torus.…”

Section: Introductionmentioning

confidence: 99%

“…In Spies [10] the theory is applied to a plasma slab equilibrium, with boundary conditions designed to simulate a torus. Later analysis by Spies [11] extended the plasma model to include finite pressure.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Equilibria and stability in partially relaxed plasma–vacuum systems

2007

View full text Add to dashboard Cite

We develop a multiple interface variational model, comprising multiple Taylor-relaxed plasma regions, each of which are separated by an ideal MHD barrier. A principle motivation is the development of a mathematically rigorous ideal MHD model to describe intrinsically 3D equilibria, with nonzero internal pressure. A second application is the description of transport barriers as constrained minimum energy states. As a first example, we calculate the plasma solution in a periodic cylinder, generalizing the analysis of the treatment of Kaiser and Uecker, Q. Jl. Mech. Appl. Math.,57(1), 2004, who treated the single interface in cylindrical geometry. Expressions for the equilibrium field are generated, and equilibrium states computed. Unlike other Taylor relaxed equilibria, for the equilibria investigated here, only the plasma core necessarily has reverse magnetic shear. We show the existence of tokamak like equilibria, with increasing safety factor and stepped-pressure profiles. A stability treatment of the multiple barrier configuration reduces to an eigenvalue problem, where the eigenvectors are the normal displacements of the ideal barriers, and the eigen-matrix has tridiagonal structure. Next, marginal stability thresholds are explored in parameter space. For a single interface, results are benchmarked to Kaiser and Uecker. For multiple interfaces, we check our working via convergence tests, which reveal that the system approaches the single barrier case in the limit of vanishing interface width. The analysis provides a foundation upon which to study the stability of systems with a single internal barrier, placed at the reverse shear point.

show abstract

Section: Multiple Interface Plasma-vacuum Modelmentioning

confidence: 99%

Section: Multiple Interface Plasma-vacuum Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Equilibria and stability in partially relaxed plasma–vacuum systems

2007

View full text Add to dashboard Cite

show abstract

“…Therefore, in [7] relaxed states in plasma-vacuum systems have been investigated. For simplicity it has been assumed that plasma and vacuum region are separated by a sharp, highly conducting interface.…”

Section: Introductionmentioning

confidence: 99%

Relaxed plasma-vacuum states in cylinders

Kaiser¹,

Uecker²

2004

The Quarterly Journal of Mechanics and Applied Mathematics

Self Cite

View full text Add to dashboard Cite

The variational principle for relaxed toroidal plasma-vacuum systems with pressure is applied to axially periodic circular cylinders. More precisely, equilibria with cylindrical symmetry are investigated for their potential to be a relaxed state. Such equilibria are characterized by their pinch ratio µ, the jump δ of the pitch angle of the magnetic field across the plasma-vacuum interface, a constant plasma pressure β, and the ratio l of wall radius over interface radius. In the limit of an infinitely long cylinder the necessary and sufficient condition for the equilibrium to be a relaxed state defines one or two intervals of allowed values of the pinch ratio µ, which depend still on the other parameters. These intervals are contained in the interval known from Taylor's theory, but are generally smaller. They are shrinking with increasing plasma pressure β or increasing radius ratio l. In particular, in the field-free limit case β = 1, for l exceeding the critical value l c ≈ 4.983, or for a vanishing δ, these intervals are zero.

show abstract

Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation

2006

View full text Add to dashboard Cite

One of the most important advances in magnetically confined fusion plasma physics has been the discovery of high confinement regimes, where at sufficiently high heating power, the plasma self-organizes to produce internal transport barriers (ITB's). A possible explanation for the existence of such barriers is that they represent constrained minimum energy states, where the plasma within the barrier satisfies ideal MHD, and the plasma between barriers is in a Taylor relaxed state. In this work we develop a multiple interface variational formulation, comprising multiple Taylor-relaxed plasma regions, each of which are separated by an ideal MHD barrier. Application to a plasma cylinder is a generalization of the analysis of the treatment of Kaiser and Uecker, Q. Jl. Mech. Appl. Math.,57(1), 2004, who treated the single interface in cylindrical geometry. Expressions for the equilibrium field are generated, and equilibrium states computed. Unlike other Taylor relaxed equilibria, for the equilibria investigated here, only the plasma core necessarily has reverse magnetic shear. We show the existence of tokamak like equilibria, with increasing safety factor and stepped-pressure profiles.

show abstract

Relaxed plasma-vacuum systems

Cited by 17 publications

References 12 publications

Equilibria and stability in partially relaxed plasma–vacuum systems

Equilibria and stability in partially relaxed plasma–vacuum systems

Relaxed plasma-vacuum states in cylinders

Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation

Contact Info

Product

Resources

About