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  • 2020-2022  (3)
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  • 1
    Publication Date: 2020-03-01
    Description: Modelling the solar Transition Region with the use of an Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, capturing the enthalpy exchange between the corona and transition region, when the corona undergoes impulsive heating. The TRAC method eliminates the need for highly resolved numerical grids in the transition region and the commensurate very short time steps that are required for numerical stability. When employed with coarse spatial resolutions, typically achieved in multi-dimensional magnetohydrodynamic codes, the errors at peak density are less than 5% and the computation time is three orders of magnitude faster than fully resolved field-aligned models. This paper presents further examples that demonstrate the versatility and robustness of the method over a range of heating events, including impulsive and quasi-steady footpoint heating. A detailed analytical assessment of the TRAC method is also presented, showing that the approach works through all phases of an impulsive heating event because (i) the total radiative losses and (ii) the total heating when integrated over the transition region are both preserved at all temperatures under the broadening modifications of the method. The results from the numerical simulations complement this conclusion.
    Print ISSN: 0004-6361
    Electronic ISSN: 1432-0746
    Topics: Physics
    Published by EDP Sciences
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  • 2
    Publication Date: 2020-01-01
    Description: The plasma heating associated with an avalanche involving three twisted magnetic threads within a coronal loop is investigated using three-dimensional magnetohydrodynamic simulations. The avalanche is triggered by the kink instability of one thread, with the others being engulfed as a consequence. The heating as a function of both time and location along the strands is evaluated. It is shown to be bursty at all times but to have no preferred spatial location. While there appears to be a level of “background” heating, this is shown to be comprised of individual, small heating events. A comparison between viscous and resistive (Ohmic) heating demonstrates that the strongest heating events are largely associated with the Ohmic heating that arises when the current exceeds a critical value. Viscous heating is largely (but not entirely) associated with smaller events. Ohmic heating dominates viscous heating only at the time of the initial kink instability. It is also demonstrated that a variety of viscous models lead to similar heating rates, suggesting that the system adjusts to dissipate the same amount of energy.
    Print ISSN: 0004-6361
    Electronic ISSN: 1432-0746
    Topics: Physics
    Published by EDP Sciences
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  • 3
    Publication Date: 2021-05-04
    Description: A ‘proof of principle’ is presented, whereby the Ohmic and viscous heating determined by a three-dimensional (3D) MHD model of a coronal avalanche are used as the coronal heating input for a series of field-aligned, one-dimensional (1D) hydrodynamic models. Three-dimensional coronal MHD models require large computational resources. For current numerical parameters, it is difficult to model both the magnetic field evolution and the energy transport along field lines for coronal temperatures much hotter than $1, mathrm{MK}$, because of severe constraints on the time step from parallel thermal conduction. Using the 3D MHD heating derived from a simulation and evaluated on a single field line, the 1D models give coronal temperatures of $1, mathrm{MK}$ and densities $10^{14}extrm {--}10^{15}, mathrm{m}^{-3}$ for a coronal loop length of $80, mathrm{Mm}$. While the temperatures and densities vary smoothly along the field lines, the heating function leads to strong asymmetries in the plasma flows. The magnitudes of the velocities in the 1D model are comparable with those seen in 3D reconnection jets in our earlier work. Advantages and drawbacks of this approach for coronal modelling are discussed.
    Print ISSN: 0035-8711
    Electronic ISSN: 1365-2966
    Topics: Physics
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