arXiv subjects

P. J. Cargill

Publications and source records attributed to P. J. Cargill.

14 recordsLinked to original sources

arXiv2025

Heating and cooling at a coronal magnetic null

Conductive cooling of the solar corona at a magnetic null is examined. An initial equilibrium is set up, balancing thermal conduction and a constant, spatially uniform coronal heating. The heating is then turned off and the subsequent conductive cooling calculated. An equation for the cooling is obtained using the method of separation of variables and it is shown that the equations for the equilibrium between conduction and heating, and the time-dependent cooling are mathematically identical with a simple change of variables. Thus the properties of the cooling phase are automatically determined by the equilibrium state. For a two-dimensional null, the characteristic cooling timescale increases over that in a straight field by a factor of between 2 and 5, with a scaling determined by the ratio of the {\it{average}} and base areas of a flux element. There is {\it{no explicit dependence}} on the very large areas that can arise near the null.

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arXiv2021

Static and dynamic solar coronal loops with cross-sectional area variations

The Enthalpy Based Thermal Evolution of Loops (EBTEL) approximate model for static and dynamic coronal loops is developed to include the effect of a loop cross-sectional area which increases from the base of the transition region (TR) to the corona. The TR is defined as the part of a loop between the top of the chromosphere and the location where thermal conduction changes from an energy loss to an energy gain. There are significant differences from constant area loops due to the manner in which the reduced volume of the TR responds to conductive and enthalpy fluxes from the corona. For static loops with modest area variation the standard picture of loop energy balance is retained, with the corona and TR being primarily a balance between heating and conductive losses in the corona, and downward conduction and radiation to space in the TR. As the area at the loop apex increases, the TR becomes thicker and the density in TR and corona larger. For large apex areas, the coronal energy balance changes to one primarily between heating and radiation, with conduction playing an increasingly unimportant role, and the TR thickness becoming a significant fraction of the loop length. Approximate scaling laws are derived that give agreement with full numerical solutions for the density, but not the temperature. For non-uniform areas, dynamic loops have a higher peak temperature and are denser in the radiative cooling phase by of order 50% than the constant area case for the examples considered. They also show a final rapid cooling and draining once the temperature approaches 1 MK. Although the magnitude of the emission measure will be enhanced in the radiative phase, there is little change in the important observational diagnostic of its temperature dependence.

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arXiv2021

High resolution soft X-ray spectroscopy and the quest for the hot (5-10 MK) plasma in solar active regions

We discuss the diagnostics available to study the 5-10 MK plasma in the solar corona, which is key to understanding the heating in the cores of solar active regions. We present several simulated spectra, and show that excellent diagnostics are available in the soft X-rays, around 100 Angstroms, as six ionisation stages of Fe can simultaneously be observed, and electron densities derived, within a narrow spectral region. As this spectral range is almost unexplored, we present an analysis of available and simulated spectra, to compare the hot emission with the cooler component. We adopt recently designed multilayers to present estimates of count rates in the hot lines, with a baseline spectrometer design. Excellent count rates are found, opening up the exciting opportunity to obtain high-resolution spectroscopy of hot plasma.

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arXiv2020

Modelling the solar transition region using an adaptive conduction method

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.

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arXiv2019

The effects of numerical resolution, heating timescales and background heating on thermal non-equilibrium in coronal loops

Thermal non-equilibrium (TNE) is believed to be a potentially important process in understanding some properties of the magnetically closed solar corona. Through one-dimensional hydrodynamic models, this paper addresses the importance of the numerical spatial resolution, footpoint heating timescales and background heating on TNE. Inadequate transition region (TR) resolution can lead to significant discrepancies in TNE cycle behaviour, with TNE being suppressed in under-resolved loops. A convergence on the periodicity and plasma properties associated with TNE required spatial resolutions of less than 2 km for a loop of length 180 Mm. These numerical problems can be resolved using an approximate method that models the TR as a discontinuity using a jump condition, as proposed by Johnston et al. (2017a,b). The resolution requirements (and so computational cost) are greatly reduced while retaining good agreement with fully resolved results. Using this approximate method we (i) identify different regimes for the response of coronal loops to time-dependent footpoint heating including one where TNE does not arise and (ii) demonstrate that TNE in a loop with footpoint heating is suppressed unless the background heating is sufficiently small. The implications for the generality of TNE are discussed.

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arXiv2017

Comparison of Methods for modelling Coronal Magnetic Fields

Four different approximate approaches used to model the stressing of coronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent magnetohydrodynamic (MHD) code. The assumptions used for each of the approximate methods are tested by considering large photospheric footpoint displacements. We consider a simple model problem, comparing the full nonlinear magnetohydrodynamic evolution, determined with the Lare2D numerical code, with four approximate approaches. Two of these, magneto-frictional relaxation and a quasi-1D Grad-Shafranov approach, assume sequences of equilibria, whilst the other two methods, a second-order linearisation of the MHD equations and Reduced MHD, are time-dependent. The relaxation method is very accurate compared to full MHD for force-free equilibria for all footpoint displacements but has significant errors when the plasma $β_0$ is of order unity. The 1D approach gives an extremely accurate description of the equilibria away from the photospheric boundary layers, and agrees well with Lare2D for all parameter values tested. The linearised MHD equations correctly predict the existence of photospheric boundary layers that are present in the full MHD results. As soon as the footpoint displacement becomes a significant fraction of the loop length, the RMHD method fails to model the sequences of equilibria correctly. The full numerical solution is interesting in its own right, and care must be taken for low $β_0$ plasmas if the viscosity is too large.

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arXiv2017

A new approach for modelling chromospheric evaporation in response to enhanced coronal heating: II Non-uniform heating

We proposed that the use of an approximate "jump condition" at the solar transition region permits fast and accurate numerical solutions of the one dimensional hydrodynamic equations when the corona undergoes impulsive heating. In particular, it eliminates the need for the very short timesteps imposed by a highly resolved numerical grid. This paper presents further examples of the applicability of the method for cases of non-uniform heating, in particular, nanoflare trains (uniform in space but non-uniform in time) and spatially localised impulsive heating, including at the loop apex and base of the transition region. In all cases the overall behaviour of the coronal density and temperature shows good agreement with a fully resolved one dimensional model and is significantly better than the equivalent results from a 1D code run without using the jump condition but with the same coarse grid. A detailed assessment of the errors introduced by the jump condition is presented showing that the causes of discrepancy with the fully resolved code are (i) the neglect of the terms corresponding to the rate of change of total energy in the unresolved atmsophere, (ii) mass motions at the base of the transition region and (iii) for some cases with footpoint heating, an over-estimation of the radiative losses in the transition region.

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arXiv2017

A new approach for modelling chromospheric evaporation in response to enhanced coronal heating: I The method

We present a new computational approach that addresses the difficulty of obtaining the correct interaction between the solar corona and the transition region in response to rapid heating events. In the coupled corona, transition region and chromosphere system, an enhanced downward conductive flux results in an upflow (chromospheric evaporation). However, obtaining the correct upflow generally requires high spatial resolution in order to resolve the transition region. With an unresolved transition region, artificially low coronal densities are obtained because the downward heat flux jumps across the unresolved region to the chromosphere, underestimating the upflows. Here, we treat the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. To illustrate and benchmark this approach against a fully resolved one-dimensional model, we present field-aligned simulations of coronal loops in response to a range of impulsive (spatially uniform) heating events. We show that our approach leads to a significant improvement in the coronal density evolution than just when using coarse spatial resolutions insufficient to resolve the lower transition region. Our approach compensates for the jumping of the heat flux by imposing a velocity correction that ensures that the energy from the heat flux goes into driving the transition region dynamics, rather than being lost through radiation. Hence, it is possible to obtain improved coronal densities. The advantages of using this approach in both one-dimensional hydrodynamic and three-dimensional magnetohydrodynamic simulations are discussed.

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arXiv2016

Inference of Heating Properties from "Hot" Non-flaring Plasmas in Active Region Cores. II. Nanoflare Trains

Despite its prediction over two decades ago, the detection of faint, high-temperature ("hot") emission due to nanoflare heating in non-flaring active region cores has proved challenging. Using an efficient two-fluid hydrodynamic model, this paper investigates the properties of the emission expected from repeating nanoflares (a nanoflare train) of varying frequency as well as the separate heating of electrons and ions. If the emission measure distribution ($\mathrm{EM}(T)$) peaks at $T = T_m$, we find that $\mathrm{EM}(T_m)$ is independent of details of the nanoflare train, and $\mathrm{EM}(T)$ above and below $T_m$ reflects different aspects of the heating. Below $T_m$ the main influence is the relationship of the waiting time between successive nanoflares to the nanoflare energy. Above $T_m$ power-law nanoflare distributions lead to an extensive plasma population not present in a monoenergetic train. Furthermore, in some cases characteristic features are present in $\mathrm{EM}(T)$. Such details may be detectable given adequate spectral resolution and a good knowledge of the relevant atomic physics. In the absence of such resolution we propose some metrics that can be used to infer the presence of "hot" plasma.

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arXiv2016

Inference of Heating Properties from "Hot" Non-flaring Plasmas in Active Region Cores I. Single Nanoflares

The properties expected of "hot" non-flaring plasmas due to nanoflare heating in active regions are investigated using hydrodynamic modeling tools, including a two-fluid development of the EBTEL code. Here we study a single nanoflare and show that while simple models predict an emission measure distribution extending well above 10 MK that is consistent with cooling by thermal conduction, many other effects are likely to limit the existence and detectability of such plasmas. These include: differential heating between electrons and ions, ionization non-equilibrium and, for short nanoflares, the time taken for the coronal density to increase. The most useful temperature range to look for this plasma, often called the "smoking gun" of nanoflare heating, lies between $10^{6.6}$ and $10^7$ K. Signatures of the actual heating may be detectable in some instances.

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arXiv2015

An MHD avalanche model of multi-threaded coronal loop

For the first time, we demonstrate how an MHD avalanche might occur in a multi-threaded coronal loop. Considering 23 non-potential magnetic threads within a loop, we use 3D MHD simulations to show that only one thread needs to be unstable in order to start an avalanche even when the others are below marginal stability. This has significant implications for coronal heating in that it provides for energy dissipation with a trigger mechanism. The instability of the unstable thread follows the evolution determined in many earlier investigations. However, once one stable thread is disrupted, it coalesces with a neighbouring thread and this process disrupts other nearby threads. Coalescence with these disrupted threads then occurs leading to the disruption of yet more threads as the avalanche develops. Magnetic energy is released in discrete bursts as the surrounding stable threads are disrupted. The volume integrated heating, as a function of time, shows short spikes suggesting that the temporal form of the heating is more like that of \textit{nanoflares} than of constant heating.

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arXiv2015

Coronal heating in multiple magnetic threads

Context. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread. Aims. By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread. Methods. The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of non-potential magnetic threads that are initially in an equilibrium state. Results. The non-linear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads. Conclusions. It is possible to initiate an energy release in a nearby, non-potential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability.

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arXiv2008

Highly Efficient Modeling of Dynamic Coronal Loops

Observational and theoretical evidence suggests that coronal heating is impulsive and occurs on very small cross-field spatial scales. A single coronal loop could contain a hundred or more individual strands that are heated quasi-independently by nanoflares. It is therefore an enormous undertaking to model an entire active region or the global corona. Three-dimensional MHD codes have inadequate spatial resolution, and 1D hydro codes are too slow to simulate the many thousands of elemental strands that must be treated in a reasonable representation. Fortunately, thermal conduction and flows tend to smooth out plasma gradients along the magnetic field, so "0D models" are an acceptable alternative. We have developed a highly efficient model called Enthalpy-Based Thermal Evolution of Loops (EBTEL) that accurately describes the evolution of the average temperature, pressure, and density along a coronal strand. It improves significantly upon earlier models of this type--in accuracy, flexibility, and capability. It treats both slowly varying and highly impulsive coronal heating; it provides the differential emission measure distribution, DEM(T), at the transition region footpoints; and there are options for heat flux saturation and nonthermal electron beam heating. EBTEL gives excellent agreement with far more sophisticated 1D hydro simulations despite using four orders of magnitude less computing time. It promises to be a powerful new tool for solar and stellar studies.

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arXiv2007

Profiles of heating in turbulent coronal magnetic loops

Context: The location of coronal heating in magnetic loops has been the subject of a long-lasting controversy: does it occur mostly at the loop footpoints, at the top, is it random, or is the average profile uniform? Aims: We try to address this question in model loops with MHD turbulence and a profile of density and/or magnetic field along the loop. Methods: We use the ShellAtm MHD turbulent heating model described in Buchlin & Velli (2006), with a static mass density stratification obtained by the HydRad model (Bradshaw & Mason 2003). This assumes the absence of any flow or heat conduction subsequent to the dynamic heating. Results: The average profile of heating is quasi-uniform, unless there is an expansion of the flux tube (non-uniform axial magnetic field) or the variation of the kinetic and magnetic diffusion coefficients with temperature is taken into account: in the first case the heating is enhanced at footpoints, whereas in the second case it is enhanced where the dominant diffusion coefficient is enhanced. Conclusions: These simulations shed light on the consequences on heating profiles of the complex interactions between physical effects involved in a non-uniform turbulent coronal loop.

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