Surface currents on models of force-free solar magnetic flux tubes

Melrose, D. B.; Nicholls, Jennifer; Broderick, Neil G. R.

doi:10.1017/s0022377800017451

Cited by 11 publications

(11 citation statements)

References 8 publications

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“…The magnetic field is continuous everywhere, whereas the current has discontinuities, and the outer surface of the potential envelope, representing the background corona, is placed at R B = 3 (three times the loop radius); this is far enough away that the boundary conditions do not influence the plasma evolution. The fields are expressed in terms of the well-known Bessel function model, generalised to the concentric layer geometry (Melrose et al 1994;Browning & Van der Linden 2003;Browning et al 2008). The field equations for the four regions (core, outer layer, neutralisation layer and envelope) are as follows:…”

Section: Initial Configurationmentioning

confidence: 99%

Coronal heating by the partial relaxation of twisted loops

Bareford

Hood

Browning

2013

A&A

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Context. Relaxation theory offers a straightforward method for estimating the energy that is released when continual convective driving causes a magnetic field to become unstable. Thus, an upper limit to the heating caused by ensembles of nanoflaring coronal loops can be calculated and checked against the level of heating required to maintain observed coronal temperatures (T 10 6 K). Aims. We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. All of the initial loop configurations discussed are known to be linearly kink unstable. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. In addition, we show for two cases how the relaxation process unfolds. Methods. A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile, featuring three parameters. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicityconserving relaxation theory. Results. For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analytically-determined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion. Conclusions. The results presented here support the use of partial relaxation theory, specifically, when calculating the heating-event distributions produced by ensembles of kink-unstable loops. The energy release increases with relaxation radius; but, once the loop has expanded by more than 50%, further expansion yields little more energy. We conclude that the relaxation methodology may be used for coronal heating studies.

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Section: Initial Configurationmentioning

confidence: 99%

Coronal heating by the partial relaxation of twisted loops

Bareford

Hood

Browning

2013

A&A

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“…This two parameter model, previously used with some extra constraints to model coronal loops (Melrose et al 1994) and spheromaks (Brennan et al 1999), represents the wider space of α distributions; as well as smoothly twisted profiles it allows also distributions such as an inner core twisted one way surrounded by a layer of reverse twist. The field components, for α 1 , α 2 > 0, are given by the well known Bessel function solutions to (2)…”

Section: The Modelmentioning

confidence: 99%

Solar coronal heating by relaxation events

Browning¹,

Linden²

2003

A&A

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Abstract.A coronal heating model is proposed which predicts heating by a series of discrete events of various energies, analogous to the observed range of events from large scale flares through various transient brightening phenomena down to the often discussed "nanoflares". We suggest that an energy release event occurs when a field becomes linearly unstable to ideal MHD modes, with dissipation during the nonlinear phase of such an instability due to reconnection in fine-scale structures such as current sheets. The energy release during this complex dynamic period can be evaluated by assuming the field relaxes to a minimum energy state subject to the constraint of helicity conservation. A model problem is studied: a cylindrical coronal loop, with a current profile generated by slow twisting of the photospheric footpoints parameterised by two values of α (the ratio of current density to field strength). Different initial α profiles, corresponding to different footpoint twisting profiles, lead to energy release events of a wide range of magnitudes, but our model predicts an observationally realistic minimum size for these events.

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“…This formulation of the initial force-free state provides a convenient twoparameter family, which can approximate to a wide range of current profiles (Melrose et al 1994). The linear stability threshold for ideal m = 1 kink instability was calculated using the CILTS code (see Van der Linden & Hood 1999 for details about the method), and is reproduced here in Fig.…”

Section: Introductionmentioning

confidence: 99%

Heating the corona by nanoflares: simulations of energy release triggered by a kink instability

Browning

Gerrard

Hood

et al. 2008

A&A

105

144

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Context. The heating of solar coronal plasma to millions of degrees is likely to be due to the superposition of many small energyreleasing events, known as nanoflares. Nanoflares dissipate magnetic energy through magnetic reconnection. Aims. A model has been recently proposed in which nanoflare-like heating naturally arises, with a sequence of dissipation events of various magnitudes. It is proposed that heating is triggered by the onset of ideal instability, with energy release occurring in the nonlinear phase due to fast magnetic reconnection. The aim is to use numerical simulations to investigate this heating process. Methods. Three-dimensional magnetohydrodynamic numerical simulations of energy release are presented for a cylindrical coronal loop model. Initial equilibrium magnetic-field profiles are chosen to be linearly unstable, with a two-layer parameterisation of the current profile. The results are compared with calculations of linear instability, with line-tying, which are extended to account for a potential field layer surrounding the loop. The energy release is also compared with predictions that the field relaxes to a state of minimum magnetic energy with conserved magnetic helicity (a constant α force-free field). Results. The loop initially develops a helical kink, whose structure and growth rate are generally in accordance with linear stability theory, and subsequently a current sheet forms. During this phase, there is a burst of kinetic energy while the magnetic energy decays. A new relaxed equilibrium is established that corresponds quite closely to a constant α field. The fraction of stored magnetic energy released depends strongly on the initial current profile, which agrees with the predictions of relaxation theory. Conclusions. Energy dissipation events in a coronal loop are triggered by the onset of ideal kink instability. Magnetic energy is dissipated, leading to large or small heating events according to the initial current profile.

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Surface currents on models of force-free solar magnetic flux tubes

Cited by 11 publications

References 8 publications

Coronal heating by the partial relaxation of twisted loops

Coronal heating by the partial relaxation of twisted loops

Solar coronal heating by relaxation events

Heating the corona by nanoflares: simulations of energy release triggered by a kink instability

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