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  • 1
    Electronic Resource
    Electronic Resource
    Relaxed plasma-vacuum systems (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 8 (2001), S. 3652-3663 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Taylor's theory of relaxed toroidal plasmas (states of lowest energy with fixed total magnetic helicity) is extended to include a vacuum between the plasma and the wall. In the extended variational problem, one prescribes, in addition to the helicity and the magnetic fluxes whose conservation follows from the perfect conductivity of the wall, the fluxes whose conservation follows from the assumption that the plasma-vacuum interface is also perfectly conducting (if the wall is a magnetic surface, then one has the toroidal and the poloidal flux in the vacuum). Vanishing of the first energy variation implies a pressureless free-boundary magnetohydrostatic equilibrium with a Beltrami magnetic field in the plasma, and in general with a surface current in the interface. Positivity of the second variation implies that the equilibrium is stable according to ideal magnetohydrodynamics, that it is a relaxed state according to Taylor's theory if the interface is replaced by a wall, and that the surface current is nonzero (at least if there are no closed magnetic field lines in the interface). The plane slab, with suitable boundary conditions to simulate a genuine torus, is investigated in detail. The relaxed state has the same double symmetry as the vessel if, and only if, the prescribed helicity is in an interval that depends on the prescribed fluxes. This interval is determined in the limit of a thin slab. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1383286
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  • 2
    Electronic Resource
    Electronic Resource
    Stability of straight tokamak equilibria without wall stabilization (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 670-681 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A specific straight tokamak equilibrium surrounded by vacuum and without a conducting wall is proved to be stable to all ideal magnetohydrodynamic (MHD) modes by analytically evaluating linear stability. The analysis starts with a circular-cylindrically symmetric equilibrium which has a piecewise constant current profile. The effect of corrugation, which is of great importance to the stability of axisymmetric modes, is taken into account by using perturbation methods. Stability of axisymmetric modes is proved by solving the eigenvalue problem up to second order in the corrugation amplitude. Whereas elliptical corrugation (N=2) leads to instability for arbitrary current density, an equilibrium with N≥3 may be stabilized to axisymmetric modes by current reversal. To treat nonaxisymmetric global modes, the potential energy is evaluated using tokamak scaling. A sufficient stability criterion is derived according to which the equilibrium is stable to nonaxisymmetric modes if the current density in the outer plasma area is reversed and in the center sufficiently peaked, and if the safety factor q at the magnetic axis is greater than unity, increasing monotonically toward the plasma edge.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870812
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  • 3
    Electronic Resource
    Electronic Resource
    Interface localized instabilities in resistive magnetohydrodynamics (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 4494-4498 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Modes localized at a plasma–vacuum interface are studied in plane slab equilibria by using resistive magnetohydrodynamics. Such modes are unstable whenever the current density and the magnetic field are not perpendicular to each other in the interface. The perturbations have no radial nodes but large mode numbers in the other two directions. The instability occurs for a wide range of angles between the nodal lines and the magnetic field lines in the interface and does not depend on the presence of a mode resonant surface. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871007
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  • 4
    Electronic Resource
    Electronic Resource
    Spheromak instability (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 682-683 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The "classical spheromak'' (current density proportional to the magnetic field, spherical plasma–vacuum interface, homogeneous magnetic field at infinity) is unstable to global magnetohydrodynamic tilting modes, even if an arbitrary, perfectly conducting, rigid wall bounds the vacuum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870813
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  • 5
    Electronic Resource
    Electronic Resource
    Extended theory of interface localized modes (1998)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 5 (1998), S. 1255-1258 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The theory of resistive free boundary modes localized at the plasma–vacuum interface in a plane slab equilibrium is improved and extended. If one proceeds to sufficiently small wavelengths, then the stability criterion (the current density vector must not have a component along the magnetic field vector in the interface) remains unchanged, but the unstable eigenmodes become independent of resistivity, and their growth rates diverge like the inverse square root of the wavelength. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.872890
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  • 6
    Electronic Resource
    Electronic Resource
    Stability of force-free plasma–vacuum equilibria (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 1 (1994), S. 249-259 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The magnetohydrodynamic stability of force-free plasma–vacuum systems (curl B=μB in the plasma, with constant μ) is studied in circular cylinders with identified ends (topological torus). A necessary stability criterion is derived by considering large poloidal mode numbers. This takes a simple form (the magnetic rotation numbers at the axis and plasma–vacuum interface must have opposite signs) if the magnetic field lines in the interface are not closed. If they are closed, then violation of this simple condition does not imply instability unless the aspect ratio exceeds some value which depends on both the numerator and denominator of the rational magnetic rotation number at the interface. For aspect ratios greater than unity, combination with the criterion for stability to internal kinks implies that the inhomogeneity parameter ||μ|| must be above the threshold for reversal of the toroidal current density, but below that for reversal of the poloidal one. This condition is independent of the wall radius, in contrast to the well-known necessary and sufficient stability criterion in the limit of infinite aspect ratio, which remains sufficient for arbitrary aspect ratios, and which requires that ||μ|| be in a smaller interval that does depend on the wall radius.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870828
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  • 7
    Electronic Resource
    Electronic Resource
    Plasma corners. I: Constant toroidal current density (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 529-534 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: If a toroidal plasma–vacuum interface has a corner, then it contains a stagnation point of the poloidal magnetic field, thus being part of a separatrix. Plasma corners are studied in magnetohydrostatic equilibria with plane symmetry (the large-aspect-ratio limit of axially symmetric ones) and constant axial current density. Their structure depends only on the multiplicity n of the stagnation point (defined such that the separatrix divides a neighborhood into 2n sectors) and on the relative orientation of the axial current density and the poloidal magnetic field nearby (termed "ordinary'' or "extraordinary,'' depending on whether the latter can be viewed as being generated by the former): Simple (i.e., n=2) ordinary corners resemble simple X points in vacuum fields in that all four sectors are right angled, but differ in that, for small distances r from the X point, the poloidal magnetic field is O(r log r−1) rather than O(r), and in that the curvature of the separatrix is O(r−1) rather than O(1). Degenerate (i.e., n≥3) ordinary corners have a vanishing angle (plasma cusps), and all extraordinary corners have a straight angle (smooth plasma–vacuum interfaces).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860251
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  • 8
    Electronic Resource
    Electronic Resource
    Stabilization of axisymmetric modes in plasma–vacuum equilibria by current reversal (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 1517-1523 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Two-dimensional plasma–vacuum equilibria are constructed by solving a free-boundary problem for small deviations from a circular cross section, and their two-dimensional stability is studied by examining that eigenmode that reduces to the marginal rigid shift in the circular limit (all other two-dimensional modes are stable). The vacuum is assumed to extend to infinity (no wall), N axial external currents are assumed to be symmetrically placed far away from the plasma, and the plasma current density is assumed to be a linear function of the poloidal magnetic flux. It is found that instability always results for N=2 (elliptical corrugation), but that stability may result for N≥3 if the axial plasma current density changes sign across some pressure surface. It is concluded that axially symmetric modes in toroidal equilibria with large aspect ratio can be stabilized by current reversal, even if no conducting wall surrounds the vacuum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860456
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  • 9
    Electronic Resource
    Electronic Resource
    Spectrum of a resistive plasma slab
    Amsterdam : Elsevier
    Physics Letters A 101 (1984), S. 335-337 
    Details
    ISSN: 0375-9601
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0375-9601(84)90850-8
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  • 10
    Electronic Resource
    Electronic Resource
    Stability of axisymmetric MHD equilibria without stagnation point
    Amsterdam : Elsevier
    Physics Letters A 28 (1969), S. 509-510 
    Details
    ISSN: 0375-9601
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/0375-9601(69)90655-0
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