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  • 1
    Electronic Resource
    Electronic Resource
    Separator current sheets: Generic features in minimum-energy magnetic fields subject to flux constraints (2001)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 8 (2001), S. 5277-5290 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Equations are found for force-free magnetic equilibria in the "coronal half-space" z〉0, subject to boundary conditions on the normal magnetic field at z=0. The distribution of normal field is assumed to be composed of NS isolated unipolar source regions of arbitrary shape, arranged arbitrarily on the plane. The equilibria are found by minimizing the magnetic energy subject to constraints on the total flux interconnecting pairs of source regions. For NS source regions interconnected in ND ways, there are Nc=ND−NS+1 distinct constraints on the field. Minimization subject to these constraints leads to an Nc-dimensional space of equilibria, for given boundary data. All field-lines connecting source regions are current-free, but the equilibrium contains Nc current-sheets lying at certain interfaces. In a two-dimensional magnetic field current sheets occur at points topologically equivalent to X-type neutral points in the potential field. In a three-dimensional field current sheets occur at points topologically equivalent to separators in the potential field. The free magnetic energy is a function of the Nc fluxes used to constrain the variation. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1418431
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  • 2
    Electronic Resource
    Electronic Resource
    Current sheet formation along three-dimensional magnetic separators (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 2885-2897 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: It was shown by Syrovatskii [Sov. Phys. JETP 33, 933 (1971)] that a perfectly conducting two-dimensional magnetic field stressed externally develops a current sheet at an X point. A generalization of this analysis shows that a generic three-dimensional magnetic field develops a closed ribbon of current along separators already existing in the field. A separator is a field line that begins and ends at different magnetic null points. A current ribbon will occur if there are two distinct separators beginning and ending at the same two nulls, thus forming a loop. The magnetic field containing the current ribbon is in force-free equilibrium. An expression is found for the net current induced in the ribbon, and the magnetic energy stored by it, in terms of the amount of external stress. An electric field parallel to the current will facilitate reconnection and will dissipate the current and release the stored energy. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871627
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  • 3
    Electronic Resource
    Electronic Resource
    The coalescence instability and the development of current sheets in two-dimensional magnetohydrodynamics (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 2858-2869 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A class of two-dimensional force-free equilibria are shown to be subject to an ideal linear instability. This instability is similar to the coalescence instability for chains of magnetic islands. Semianalytic methods are used to find second magnetic equilibrium which is accessible from the first and has lower magnetic energy. This equilibrium has a discontinuous magnetic field and current sheets at these discontinuities. Numerical simulations indicate that the nonlinear evolution of the instability allows the plasma to relax to this discontinuous equilibrium.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860673
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  • 4
    Electronic Resource
    Electronic Resource
    Dynamical evolution and structure of solar coronal magnetic fields (1992)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 2277-2285 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A simple dynamical system is presented which is analogous in many ways to a solar coronal loop. When this system is subject to slow, external driving, representing photospheric motion, it undergoes occasional impulsive relaxations. These relaxations release some fraction of the magnetic energy as Alfvén waves in the loop. When the model system is integrated for long times it reaches a statistical steady state in which relaxation events occur at random times with random amplitudes. The distributions of these quantities is compared to similar distributions for microflares occurring in the solar corona.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860197
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  • 5
    Electronic Resource
    Electronic Resource
    Ion beam divergence from unstable fluctuations in applied-B diodes (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1614-1624 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An electron plasma oscillation driven unstable by ion streaming is identified with the low-frequency mode observed in quicksilver [Computational Physics, edited by A. Tenner (World Scientific, Singapore, 1991), pp. 475–482] numerical simulations. This mode heats the electrons along the magnetic field and is ultimately stabilized by the thermal spread. A quasilinear theory determines the saturation level of the fluctuations, the ion divergence, and the ion energy and momentum spread as they exit the diode. The ion divergence is predicted to be independent of the ion mass for fixed diode voltage and scales as the product of the effective gap and the ion beam enhancement factor over Child–Langmuir current.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860901
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  • 6
    Electronic Resource
    Electronic Resource
    Renormalization group analysis of reduced magnetohydrodynamics with application to subgrid modeling (1991)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 3 (1991), S. 1945-1962 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The technique for obtaining a subgrid model for Navier–Stokes turbulence introduced by Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986); Phys. Rev. Lett. 57, 1772 (1986)], based on renormalization group analysis (RNG), is extended to the reduced magnetohydrodynamic (RMHD) equations. A RNG treatment of the Alfvén turbulence (perpendicular scale k−1⊥(very-much-less-than)k−1(parallel) parallel scale) supported by the RMHD equations leads to effective values of the viscosity and resistivity at large scales, k→0, dependent on the amplitude of turbulence. When the RNG analysis is augmented by the Kolmogorov argument for energy cascade the effective viscosity and resistivity become independent of the molecular quantities. This leads to a "universal'' subgrid model, which all models approach at the largest scales. A self-contained system of equations is derived for the range of scales, 0〈k〈K, where K=π/Δ, is the maximum wave number for a grid size Δ. In this system the resistive and viscous dissipation is represented by differential operators, whose coefficients depend upon the amplitudes of the large-scale quantities being computed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.859663
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  • 7
    Electronic Resource
    Electronic Resource
    A current ribbon model for energy storage and release with application to the flare of 7 January 1992 (1998)
    Springer
    Solar physics 179 (1998), S. 349-377 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Observations of the flare on 7 January 1992 are interpreted using a topological model of the magnetic field. The model, developed here, applies a theory of three-dimensional reconnection to the inferred magnetic field configuration for 7 January. In the model field a new bipole (∼ 1021 Mx) emerges amidst pre-existing active region flux. This emergence gives rise to two current ribbons along the boundaries (separators) separating the distinct, new and old, flux systems. Sudden reconnection across these boundary curves transfers ∼ 3 ×1020 Mx of flux from the bipole into the surrounding flux. The model also predicts the simultaneous (sympathetic) flaring of the two current ribbons. This explains the complex two-loop structure noted in previous observations of this flare. We subject the model predictions to comparisons with observations of the flare. The locations of current ribbons in the model correspond closely with those of observed soft X-ray loops. In addition the footpoints and apexes of the ribbons correspond with observed sources of microwave and hard X-ray emission. The magnitude of energy stored by the current ribbons compares favorably to the inferred energy content of accelerated electrons in the flare.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005071122577
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  • 8
    Electronic Resource
    Electronic Resource
    Gravitational ballooning instability of prominences (1994)
    Springer
    Solar physics 149 (1994), S. 63-72 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Prominences can be unstable to a gravitational ballooning instability of the Rayleigh-Taylor type. A two-dimensional generalized Kippenhahn-Schlüter prominence equilibrium is constructed. Its stability to ideal, three-dimensional, short-wavelength line-tied perturbations is analyzed. The instability requires a critical vertical density gradient. For a given magnetic field strength, the instability is sensitive to the angle at which the magnetic field lines cross the prominence. An approximate, sufficient, threshold condition is consistent with typical prominence parameters.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00645178
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  • 9
    Electronic Resource
    Electronic Resource
    Topology and current ribbons: A model for current, reconnection and flaring in a complex, evolving corona (1996)
    Springer
    Solar physics 169 (1996), S. 91-121 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Magnetic field enters the corona from the interior of the Sun through isolated magnetic features on the solar surface. These features correspond to the tops of submerged magnetic flux tubes, and coronal field lines often connect one flux tube to another, defining a pattern of inter-linkage. Using a model field, in which flux tubes are represented as point magnetic charges, it is possible to quantify this inter-linkage. If the coronal field were current-free then motions of the magnetic features would change the inter-linkage through implicit (vacuum) magnetic reconnection. Without reconnection the conductive corona develops currents to avoid changing the flux linkage. This current forms singular layers (ribbons) flowing along topologically significant field lines called separators. Current ribbons store magnetic energy as internal stress in the field: the amount of energy stored is a function of the flux tube displacement. To explore this process we develop a model called the minimum-current corona (MCC) which approximates the current arising on a separator in response to displacement of photospheric flux. This permits a model of the quasi-static evolution of the corona above a complex active region. We also introduce flaring to rapidly change the flux inter-linkage between magnetic features when the internal stress on a separator becomes too large. This eliminates the separator current and releases the energy stored by it. Implementation of the MCC in two examples reveals repeated flaring during the evolution of simple active regions, releasing anywhere from 1027–1029 ergs, at intervals of hours. Combining the energy and frequency gives a general expression for heat deposition due to flaring (i.e., reconnection).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00153836
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  • 10
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    Impulsive events in the evolution of a forced nonlinear system (1992)
    American Physical Society
    Details
    Publication Date: 1992-03-16
    Print ISSN: 0031-9007
    Electronic ISSN: 1079-7114
    Topics: Physics
    Published by American Physical Society
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