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  • 1
    Electronic Resource
    Electronic Resource
    Resistive ballooning modes in line-tied coronal fields (1987)
    Springer
    Solar physics 109 (1987), S. 351-354 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The resistive stability of coronal loops to perturbations with short wavelength across the magnetic field is analysed, taking full account of the line tying effect due to the presence of the photosphere. The results presented are similar to those previously obtained for arcades: configurations with a pressure profile decreasing with distance from the loop axis at some point are found to be always unstable, the growth rate γ increasing monotonically with the wavenumber (n) and scaling approximately as γ ∼ (n 2 D r)1/3 in the limit of large n.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00160657
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  • 2
    Electronic Resource
    Electronic Resource
    The effects of parallel and perpendicular viscosity on resistive ballooning modes in line-tied coronal magnetic fields (1988)
    Springer
    Solar physics 115 (1988), S. 235-249 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The study of resistive ballooning instabilities in line-tied coronal magnetic fields is extended by including viscosity in the stability analysis. The equations that govern the resistive ballooning instabilities are derived and the effects of parallel and perpendicular viscosity are included using Braginskii's stress tensor. Numerical solutions to these equations are obtained under the rigid wall boundary conditions for arcades with cylindrically-symmetric magnetic fields. It is found that viscosity has a stabilizing effect on the resistive ballooning instabilities with perpendicular viscosity being more important by far than parallel viscosity. The strong stabilizing effect of perpendicular viscosity can lead to complete stabilization for realistic values of the equilibrium quantities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00148726
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  • 3
    Electronic Resource
    Electronic Resource
    Resistive ballooning modes in line-tied coronal fields (1986)
    Springer
    Solar physics 106 (1986), S. 353-364 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of coronal arcades to localized resistive interchange modes in the ballooning ordering, including photospheric line tying, is investigated. It is found that the anchoring of magnetic footpoints in the photosphere is not sufficient to stabilise ballooning modes, once resistivity is taken into account. All configurations with a pressure profile decreasing from the arcade axis at some point are unstable, a purely growing mode being excited. The dependence of the growth rate γ on the parameter Rm −1 ∼ k 2 η, where η is the resistivity and k the wavenumber in a direction perpendicular to the equilibrium field, can be described by a power law with varying index: for small values of k 2 and an ideally stable field one finds γ ∼ Rm −1. As k 2 is increased or marginal stability is approached one finds γ ∼ Rm−1/3. T implications of these localised instabilities to the temporal evolution and overall energy balance of arcade structures in the solar corona is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00158501
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  • 4
    Electronic Resource
    Electronic Resource
    Validity of the isobaric assumption to the solar corona (1996)
    Springer
    Solar physics 169 (1996), S. 33-45 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Many coronal heating mechanisms have been suggested to balance the losses from this tenuous medium by radiation, conduction, and plasma mass flows. A previous paper (Walsh, Bell, and Hood, 1995) considered a time-dependent heating supply where the plasma evolved isobarically along the loop length. The validity of this assumption is investigated by including the inertial terms in the fluid equations making it necessary to track the sound waves propagating in a coronal loop structure due to changes in the heating rate with time. It is found that the temperature changes along the loop are mainly governed by the variations in the heating so that the thermal evolution can be approximated to a high degree by the simple isobaric case. A typical isobaric evolution of the plasma properties is reproduced when the acoustic time scale is short enough. However, the cooling of a hot temperature equilibrium to a cool one creates supersonic flows which are not allowed for in this model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00153831
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  • 5
    Electronic Resource
    Electronic Resource
    The MHD stability of a twisted flux tube prominence model (1994)
    Springer
    Solar physics 154 (1994), S. 51-68 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The ideal MHD stability of the 2D twisted magnetic flux tube prominence model of Cartledge and Hood (1993) is investigated. The model includes a temperature profile that varies from realistic prominence values up to typical coronal values. The prominence is considered to be of finite-width and finite height. The stability properties of the prominence models are studied by using a method that generates a separate necessary condition and a sufficient condition. These conditions give bounds on the parameters that define marginal stability. In many cases these bounds are quite close so that further, more detailed, stability calculations are not necessary. A number of parameter regimes are examined, corresponding to different profiles of the prominence temperatures, densities, and magnetic field shear. It is found that the model admits realistic stable and unstable loop lengths for observed prominence parameters when the axial magnetic field component does not vanish.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00676777
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  • 6
    Electronic Resource
    Electronic Resource
    The ideal magnetohydrodynamic stability of a line-tied coronal magnetohydrostatic equilibrium (1986)
    Springer
    Solar physics 105 (1986), S. 291-306 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An energy method is used to determine a condition for local instability of field lines in magnetohydrostatic equilibrium which are rooted in the photosphere. The particular equilibrium studied is isothermal and two-dimensional and may model a coronal arcade of loops where variations along the axis of the arcade are weak enough to be ignorable. If line tying conditions are modelled by perturbations that vanish on the photosphere, then, when the field is unsheared, the condition for stability is necessary and sufficient. However, when the axial field component is non-zero, so that the field is sheared, the stability condition is only sufficient. It is found that when β 〈 0.34 the equilibrium is stable. When β = 0.34 a magnetic neutral line appears at the photosphere and it is marginally stable. When β 〉 0.34 a magnetic island is present and all the field lines inside the island are unstable as well as some beyond it. As β increases, the size of the island and the extent of unstable field lines increase. The effect of the instability is likely to be to create small-scale filamentation in the solar corona and to enhance the global transport coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00172048
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  • 7
    Electronic Resource
    Electronic Resource
    DISCRETE RANDOM HEATING EVENTS IN CORONAL LOOPS (1997)
    Springer
    Solar physics 171 (1997), S. 81-91 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The response of the coronal plasma in a magnetic loop to the release of discrete, random amounts of energy quanta over fixed time intervals is investigated. Nanoflare heating (1024 erg per event) with event lifetimes on a scale of 1–20 s are shown to be able to maintain a coronal loop at typical coronal temperatures, ≈ 2 x 106 K (Parker, 1988; Kopp and Poletto, 1993). Microflare events (1027 erg) observed by Porter et al. (1995) with a lifetime of approximately 1 min are also investigated and it is found that the loop apex temperature varies by at most 40% from its initial static condition. However, larger energy events of the order of 1028 erg (Schmieder et al., 1994) occur too infrequently and the plasma cools to chromospheric values. The implications of time-dependent heating of the corona upon observations are also discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004938610648
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  • 8
    Electronic Resource
    Electronic Resource
    Kink instability of solar coronal loops as the cause of solar flares (1979)
    Springer
    Solar physics 64 (1979), S. 303-321 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Solar coronal loops are observed to be remarkably stable structures. A magnetohydrodynamic stability analysis of a model loop by the energy method suggests that the main reason for stability is the fact that the ends of the loop are anchored in the dense photosphere. In addition to such line-tying, the effect of a radial pressure gradient is incorporated in the analysis. Two-ribbon flares follow the eruption of an active region filament, which may lie along a magnetic flux tube. It is suggested that the eruption is caused by the kink instability, which sets in when the amount of magnetic twist in the flux tube exceeds a critical value. This value depends on the aspect ratio of the loop, the ratio of the plasma to magnetic pressure and the detailed transverse magnetic structure. For a force-free field of uniform twist the critical twist is 3.3π, and for other fields it is typically between 2π and 6π. Occasionally active region loops may become unstable and give rise to small loop flares, which may also be a result of the kink instability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00151441
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  • 9
    Electronic Resource
    Electronic Resource
    Magnetic instability of coronal arcades as the origin of two-ribbon flares (1980)
    Springer
    Solar physics 66 (1980), S. 113-134 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The generally accepted scenario for the events leading up to a two-ribbon flare is that a magnetic arcade (supporting a plage filament) responds to the slow photospheric motions of its footpoints by evolving passively through a series of (largely) force-free equilibria. At some critical amount of shear the configuration becomes unstable and erupts outwards. Subsequently, the field closes back down in the manner modelled by Kopp and Pneuman (1976); but the main problem has been to explain the eruptive instability. The present paper analyses the magnetohydrodynamic stability of several possible arcade configurations, including the dominant stabilizing effect of line-tying at the photospheric footpoints. One low-lying force-free structure is found to be stable regardless of the shear; also some of the arcades that lie on the upper branch of the equilibrium curves are shown to be stable. However, another force-free configuration appears more likely to represent the preflare structure. It consists of a large flux tube, anchored at its ends and surrounded by an arcade, so that the field transverse to the arcade axis contains a magnetic island. Such a configuration is found to become unstable when either the length of the structure, the twist of the flux tube, or the height of the island becomes too great; the higher the tube is situated, the smaller is the twist required for instability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00150523
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  • 10
    Electronic Resource
    Electronic Resource
    Thermal nonequilibrium: A trigger for solar flares? (1981)
    Springer
    Solar physics 73 (1981), S. 289-311 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper, we suggest that a solar flare may be triggered by a lack of thermal equilibrium rather than by a magnetic instability. The possibility of such a thermal nonequilibrium (or catastrophe) is demonstrated by solving approximately the energy equation for a loop under a balance between thermal conduction, optically thin radiation and a heating source. It is found that, if one starts with a cool equilibrium at a few times 104 K and gradually increases the heating or decreases the loop pressure (or decreases the loop length), then, ultimately, critical metastable conditions are reached beyond which no cool equilibrium exists. The plasma heats up explosively to a new quasi-equilibrium at typically 107 K. During such a thermal flaring, any magnetic disruption or particle acceleration are secondary in nature. For a simple-loop (or compact) flare, the cool core of an active-region loop heats up and the magnetic tube of plasma maintains its position. For a two-ribbon flare, the material of an active-region (or plage) filament heats up and expands along the filament; it slowly rises until, at a critical height, the magnetic configuration becomes magnetohydrodynamically unstable and erupts violently outwards. In this case thermal nonequilibrium acts as a trigger for the magnetic eruption and subsequent magnetic energy release as the field closes back down.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00151683
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