Magnetohydrodynamic Equilibrium with Prolate Spheroidal Plasma-Vacuum Interface
15 Feb 1981-Journal of the Physical Society of Japan (The Physical Society of Japan)-Vol. 50, Iss: 2, pp 359-360
TL;DR: In this paper, an exact solution to the magnetohydrodynamic equilibrium equation for a prolate spheroidal plasma was obtained by using the prolate spatiotemporal coordinates and the pressure-balance condition on the plasma-vacuum interface.
Abstract: The Grad-Shafranov equation for a prolate spheroidal plasma is solved by using the prolate spheroidal coordinates. The magnetic field in the vacuum region surrounding the plasma is determined by use of the Maxwell equation and the pressure-balance condition on the plasma-vacuum interface. The result obtained in this letter is an exact solution to the magnetohydrodynamic equilibrium equation. The magnetic-field configuration of the spheroidal plasma is found to be considerably different from that of the spherical plasnla.
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TL;DR: In this article, a review is devoted to field reversed configurations and to related field reversed mirrors; both are compact toroids with little or no toroidal magnetic field, and experimental and theoretical results on the formation, equilibrium, stability and confinement properties of these plasmas are presented.
Abstract: The review is devoted to field reversed configurations and to the related field reversed mirrors; both are compact toroids with little or no toroidal magnetic field. Experimental and theoretical results on the formation, equilibrium, stability and confinement properties of these plasmas are presented. Although they have been known for about three decades, field reversed configurations have been studied intensively only in recent years. This renewed interest is due to the unusual fusion reactor potential of these high beta plasmas and also to their surprising macroscopic stability. At the present time, field reversed configurations appear to be completely free of gross instabilities and show relatively good confinement. The primary research goal for the near future is to retain these favourable properties in a less kinetic regime. Other important issues include the development of techniques for slow formation and stability, and a clearer assessment of the confinement scaling laws.
544 citations
TL;DR: In this article, the stability of axially symmetric force-free equilibrium plasma is investigated in a toroidal vessel with a rectangular cross-section and the radii of the inner and outer walls of the vessel are denoted by R i and R, and the height h.
Abstract: The stability of axially symmetric force-free equilibrium plasma is investigated. As a model of the flux conserver, a toroidal vessel with a rectangular cross section is considered. The radii of the inner and the outer walls of the vessel are denoted by R i and R , and the height h . The plasma is shown to be stable for the ideal magnetohydrodynamic perturbations when h / R <( h / R ) * , and unstable when R i / R <0.11 and ( h / R ) * <( h / R )<( h / R ) + . The values of the critical ratios ( h / R ) * and ( h / R ) + are evaluated as a function of R i / R .
9 citations
TL;DR: In this article, an analytic solution to the Grad-Shafranov equation was obtained for a prolate and an oblate spheroidal plasma by using Hill's vortex model.
Abstract: The analytic solutions to the Grad-Shafranov equation are obtained for a prolate and an oblate spheroidal plasma by using Hill's vortex model. Effects of a toroidal magnetic field B ϕ on the MHD equilibrium configurations are investigated by using these analytic solutions. When B ϕ is stronger than that of the force-free configuration, the spheroidal plasmas in a vacuum magnetic field are shown to be unable in the MHD equilibrium. The several physical quantities on the equilibrium configuration are evaluated. The spheromak plasma is proved to be unstable if d p /dψ≠0 and d 2 F /dψ 2 ≥0 on the magnetic axis. Here p is the pressure and V (ψ) the volume surrounded by a magnetic surface of ψ=const. The equilibrium configurations of the spheroidal plasmas by using Hill's vortex model are shown to satisfy the above conditions, i.e., to be unstable.
9 citations
TL;DR: In this article, the two-dimensional equilibria of field-reversed configuration with subsidiary coils are computed by integrating the ideal magnetohydrodynamic equilibrium equation, and the mirror coils have an effect to compress the plasma appreciably in the axial direction and hence sustain the compact torus.
Abstract: Two-dimensional equilibria of field-reversed configuration with subsidiary coils are computed by integrating the ideal magnetohydrodynamic equilibrium equation. The mirror coils have an effect to compress the plasma appreciably in the axial direction and hence sustain the compact torus. The cusp coils enlarge the plasma and consequently make the gradient of plasma density relaxed in the radial direction.
8 citations
TL;DR: In this paper, the Grad-Shafranov equations for an oblate and a prolate spheroidal plasmas are solved analytically under the assumptions, B ϕ = 0 and d p /dψ=constant.
Abstract: The Grad-Shafranov equations for an oblate and a prolate spheroidal plasmas are solved analytically under the assumptions, B ϕ =0 and d p /dψ=constant. Here B ϕ is the toroidal magnetic field, p is the kinetic pressure, and ψ is the magnetic flux function. The plasmas in magnetohydrodynamic equilibrium are shown to be toroidal . The equilibrium magnetic-field configurations outside the spheroidal plasmas are considerably different from that of a spherical plasma. A line cusp or two point cusps appear outside the oblate or the prolate spheroidal plasma, respectively.
7 citations
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30 Oct 2012
TL;DR: In this article, Rozhansky et al. studied the relationship between transverse conductivity and the generation of self-consistent electric fields in strongly ionized magnetized plasma.
Abstract: Mechanisms of transverse conductivity and generation of self-consistent electric fields in strongly ionized magnetized plasma V. Rozhansky. 1. Introduction.- 2. Conductivity tensor in partially ionized plasma.- 3. Main mechanisms of perpendicular conductivity in fully ionized plasma.- 4. Acceleration of plasma clouds in an inhomogeneous magnetic field.- 5. Alfven conductivity.- 6. Perpendicular viscosity, radial current, and radial electric field in an infinite cylinder.- 7. Current systems in front of a biased electrode (flush-mounted probe) and spot of emission.- 8. Currents in the vicinity of a biased electrode that is smaller than the ion gyroradius.- 9. Neoclassical perpendicular conductivity in a tokamak.- 10. Transverse conductivity in a reversed field pinch.- 11. Modeling of electric field and currents in the tokamak edge plasma.- 12. Mechanisms of anomalous perpendicular viscosity and viscosity-driven currents.- 13. Transverse conductivity in a stochastic magnetic field.- 14. Electric fields generated in the shielding layer between hot plasma and a solid state.-- Correlations and anomalous transport models O.G. Bakunin. 1. Introduction.- 2. Turbulent diffusion and transport.- 3. Non-local effects and diffusion equations.- 4. The Corrsin conjecture.- 5. Effects of seed diffusivity.- 6. The diffusive tracer equation and averaging.- 7. The quasi-linear approximation.- 8. The diffusive renormalization.- 9. Anomalous transport and convective cells.- 10. Stochastic instability and transport.- 11. Fractal conceptions and turbulence.- 12. Percolation and scalings.- 13. Percolation and turbulent transport scalings.- 14. The temporal hierarchy of scales and correlations.- 15. The stochastic magnetic field and percolation transport.- 16. Percolation in drift flows.- 17. Multiscale flows.- 18. Subdiffusion and traps.- 19. Continuous time random walks.- 20. Fractional differential equations and scalings.- 21. Correlation and phase-space.- 22. Conclusion.
3,684 citations
TL;DR: In this article, the spontaneous generation of reversed fields in toroidal plasmas is shown to be a consequence of relaxation under constraints, and the onset of the reversed field and other features of this model agree well with observations on ZETA.
Abstract: The spontaneous generation of reversed fields in toroidal plasmas is shown to be a consequence of relaxation under constraints. With perfect conductivity a topological constraint exists for each field line and the final state is not unique. With small departures from perfect conductivity, topological constraints are relaxed and the final state becomes unique. The onset of the reversed field and other features of this model agree well with observations on ZETA.
1,740 citations
TL;DR: In this article, an optimal force-free spherical plasma configuration was analyzed for its MHD stability properties, and it was shown that the spherical ellipse with = k (k independent of ) should be stable against all magnetically driven MHD and resistive tearing modes if surrounded by a conducting wall at about rw/r0 = 1.15.
Abstract: The 'Spheromak', an optimal force-free spherical plasma configuration, is analysed for its MHD stability properties. It is shown that flattened ellipse (oblimak) with = k (k independent of ) should be stable against all magnetically driven MHD and resistive tearing modes if surrounded by a conducting wall at about rw/r0 = 1.15. β's of at least 2% can be stably confined, equivalent to 20% in tokamaks.
326 citations
TL;DR: In this article, a solution for axially symmetric hydromagnetic equilibria with spherical plasma-vacuum interfaces is extended from a low-pressure paramagnetic regime to a high-pressure diamagnetic regime.
Abstract: Solutions representing axially symmetric hydromagnetic equilibria with spherical plasma‐vacuum interfaces are extended from a low‐pressure paramagnetic regime to a high‐pressure diamagnetic regime.
11 citations