We present a series of numerical simulations aimed at understanding the nature and origin of turbulence in coronal loops in the framework of the Parker model for coronal heating. A coronal loop is studied via reduced magnetohydrodynamics simulations in Cartesian geometry. A uniform and strong magnetic field threads the volume between the two photospheric planes, where a velocity field in the form of a 1D shear flow pattern is present. Initially the magnetic field which developes in the coronal loop is a simple map of the photospheric velocity field. This initial configuration is unstable to a multiple tearing instability which develops islands with X and O points in the plane orthogonal to the axial field. Once the nonlinear stage sets in the system evolution is characterized by a regime of MHD turbulence dominated by magnetic energy. A well developed power law in energy spectra is observed and the magnetic field never returns to the simple initial state mapping the photospheric flow. The formation of X and O points in the planes orthogonal to the axial field allows the continued and repeated formation and dissipation of small scale current sheets where the plasma is heated. We conclude that the observed turbulent dynamics are not induced by the complexity of the pattern that the magnetic field-lines footpoints follow but they rather stem from the inherent nonlinear nature of the system.
The Parker hypothesis (Parker (1972)) assumes that heating of coronal loops occurs due to reconnection, induced when photospheric motions braid field lines to the point of current sheet formation. In this contribution we address the question of how the nature of photospheric motions affects heating of braided coronal loops. We design a series of boundary drivers and quantify their properties in terms of complexity and helicity injection. We examine a series of long-duration full resistive MHD simulations in which a simulated coronal loop, consisting of initially uniform field lines, is subject…
This work examines the relation between the fractal properties of the photospheric magnetic patterns and those of the coronal magnetic fields in solar active regions.Our results show no correlation between the fractal dimensions of the observed 2d photospheric structures and the extrapolated unstable volumes in the corona, when nonlinear force-free extrapolation is used. This result is independent of efforts to (1) bring the photospheric magnetic fields closer to a nonlinear force-free equilibrium and (2) omit the lower part of the modeled magnetic field volume that is almost completely filled…
In this review, our present day understanding of the Sun's global photospheric and coronal magnetic fields is discussed from both observational and theoretical viewpoints. Firstly, the large-scale properties of photospheric magnetic fields are described, along with recent advances in photospheric magnetic flux transport models. Following this, the wide variety of theoretical models used to simulate global coronal magnetic fields are described. From this, the combined application of both magnetic flux transport simulations and coronal modeling techniques to describe the phenomena of coronal hol…
Coronal Non-Thermal and Doppler Plasma Flows Driven by Photospheric Flux in 28 Active Regions
University College London, Mullard Space Science Laboratory（伦敦大学学院，穆拉德空间科学实验室）；University of Vienna, Institute of Astrophysics（维也纳大学，天体物理研究所）；Computational Physics, Inc.（计算物理公司）；Space Science Division, Naval Research Laboratory（海军研究实验室空间科学部）；NASA Goddard Space Flight Center, Solar Physics Laboratory, Heliophysics Science Division（美国国家航空航天局戈达德太空飞行中心，太阳物理学实验室，日球物理科学部）；Department of Mathematics, Physics and Electrical Engineering, Northumbria University（诺森比亚大学数学、物理与电气工程系）；INAF Osservatorio Astronomico di Roma（意大利国家天体物理研究所罗马天文台）
Chemical abundances in solar-type stars are a much debated topic. Planet-hosting stars are known to be metal-rich, but whether or not this peculiarity applies also to the chemical composition of the outer stellar atmospheres is still to be clarified. More in general, coronal and photospheric abundances in late-type stars appear to be different in many cases, but understanding how chemical stratification effects work in stellar atmospheres requires an observational base larger than currently available. We obtained XMM-Newton high-resolution X-ray spectra of Tau Bootis, a well known nearby star …
We developed a {\sl coronal non-linear force-free field (COR-NLFFF)} forward-fitting code that fits an approximate {\sl non-linear force-free field (NLFFF)} solution to the observed geometry of automatically traced coronal loops. In contrast to photospheric NLFFF codes, which calculate a magnetic field solution from the constraints of the transverse photospheric field, this new code uses coronal constraints instead, and this way provides important information on systematic errors of each magnetic field calculation method, as well as on the non-forcefreeness in the lower chromosphere. In this s…
Magnetic flux ropes are bundles of twisted magnetic field enveloping a central axis. They harbor free magnetic energy and can be progenitors of coronal mass ejections (CMEs), but identifying flux ropes on the Sun can be challenging. One of the key coronal observables that has been shown to indicate the presence of a flux rope is a peculiar bright coronal structure called a sigmoid. In this work, we show Hinode EUV Imaging Spectrometer (EIS) observations of sigmoidal active region 10977. We analyze the coronal plasma composition in the active region and its evolution as the sigmoid (flux rope) …
The ratio of the Fe abundance in the photosphere to that in coronal flare plasmas is determined by X-ray lines within the complex at 6.7~keV (1.9~Å) emitted during flares. The line complex includes the He-like Fe (\fexxv) resonance line $w$ (6.70~keV) and Fe K$α$ lines (6.39, 6.40~keV), the latter being primarily formed by the fluorescence of photospheric material by X-rays from the hot flare plasma. The ratio of the Fe K$α$ lines to the \fexxv\ $w$ depends on the ratio of the photospheric-to-flare Fe abundance, heliocentric angle $θ$ of the flare, and the temperature $T_e$ of the flaring plas…
We have performed MHD simulations of Alfven wave propagation along an open flux tube in the solar atmosphere. In our numerical model, Alfven waves are generated by the photospheric granular motion. As the wave generator, we used a derived temporal spectrum of the photospheric granular motion from G-band movies of Hinode/SOT. It is shown that the total energy flux at the corona becomes larger and the transition region height becomes higher in the case when we use the observed spectrum rather than white/pink noise spectrum as the wave generator. This difference can be explained by the Alfven wav…
We investigate the dynamics of a closed corona cartesian reduced magnetohydrodynamic (MHD) model where photospheric vortices twist the coronal magnetic field lines. We consider two corotating or counter-rotating vortices localized at the center of the photospheric plate, and additionally more corotating vortices that fill the plate entirely. Our investigation is specifically devoted to study the fully nonlinear stage, after the linear stage during which the vortices create laminar and smoothly twisting flux tubes. Our main goal is to understand the dynamics of photospheric vortices twisting th…
It is well known that magnetic fields dominate the dynamics in the solar corona, and new generation of numerical modelling of the evolution of coronal magnetic fields, as featured with boundary conditions driven directly by observation data, are being developed. This paper describes a new approach of data-driven magnetohydrodynamic (MHD) simulation of solar active region (AR) magnetic field evolution, which is for the first time that a data-driven full-MHD model utilizes directly the photospheric velocity field from DAVE4VM. We constructed a well-established MHD equilibrium based on a single v…
Solar filament are commonly thought to be supported in magnetic dips, in particular, of magnetic flux ropes (FRs). In this Letter, from the observed photospheric vector magnetogram, we implement a nonlinear force-free field (NLFFF) extrapolation of a coronal magnetic FR that supports a large-scale intermediate filament between an active region and a weak polarity region. This result is the first in that current NLFFF extrapolations with presence of FRs are limited to relatively small-scale filaments that are close to sunspots and along main polarity inversion line (PIL) with strong transverse …
We present a new improved version of our force-free electrodynamics (FFE) numerical code in spherical coordinates that extrapolates the magnetic field in the inner solar corona from a photospheric vector magnetogram. The code satisfies the photospheric boundary condition and the condition divB=0 to machine accuracy. The performance of our method is evaluated with standard convergence parameters, and is found to be comparable to that of other nonlinear force-free extrapolations.
We investigate in more detail the origin of chromospheric Alfven waves that give rise to the separation of ions and neutrals, the First Ionization Potential Effect (FIP), through the action of the ponderomotive force. In open field regions, we model the dependence of fractionation on the plasma upflow velocity through the chromosphere for both shear (or planar) and torsional Alfven waves of photospheric origin. These differ mainly through their parametric coupling to slow mode waves. Shear Alfven waves appear to reproduce observed fractionations for a wider range of model parameters, and prese…
Some models of coronal heating suppose that convective motions at the photosphere shuffle the footpoints of coronal magnetic fields and thereby inject sufficient magnetic energy upward to account for observed coronal and chromospheric energy losses in active regions. Using high-resolution observations of plage magnetic fields made with the Solar Optical Telescope aboard the Hinode satellite, we investigate this idea by estimating the upward transport of magnetic energy --- the vertical Poynting flux, S_z --- across the photosphere in a plage region. To do so, we combine: (i) estimates of photo…
Most models of solar eruptions assume that coronal field lines are anchored in the dense photosphere and thus the photospheric magnetic fields would not have rapid, irreversible changes associated with eruptions resulted from the coronal magnetic reconnection. Motivated by the recent work of Hudson, Fisher & Welsch (2008) on quantitatively evaluating the back reaction due to energy release from the coronal fields, in this Letter we synthesize our previous studies and present analysis of new events about flare-related changes of photospheric magnetic fields. For the 11 X-class flares where vect…
We study extreme-ultraviolet emission line spectra derived from three-dimensional magnetohydrodynamic models of structures in the corona. In order to investigate the effects of increased magnetic activity at photospheric levels in a numerical experiment, a much higher magnetic flux density is applied at photospheric levels as compared to the Sun. Thus, we can expect our results to highlight the differences between the Sun and more active, but still solar-like stars. We discuss signatures seen in extreme-ultraviolet emission lines synthesized from these models and compare them to signatures fou…
Context: Many previous studies have shown that the magnetic precursor of a coronal mass ejection (CME) takes the form of a magnetic flux rope, and a subset of them have become known as `hot flux ropes' due to their emission signatures in $\sim$10 MK plasma. Aims: We seek to identify the processes by which these hot flux ropes form, with a view of developing our understanding of CMEs and thereby improving space weather forecasts. Methods: Extreme-ultraviolet observations were used to identify five pre-eruptive hot flux ropes in the solar corona and study how they evolved. Confined flares were o…
We investigate the relation between characteristics of coronal mass ejections and parameterizations of the eruptive capability of solar active regions widely used in solar flare prediction schemes. These parameters, some of which are explored for the first time, are properties related to topological features, namely, magnetic polarity inversion lines (MPILs) that indicate large amounts of stored non-potential (i.e. free) magnetic energy. We utilize the Space Weather Database of Notifications, Knowledge, Information (DONKI) and the Large Angle and Spectrometric Coronograph (LASCO) databases to …
A new model has been proposed for magnetic field determination at different distances from the Sun during different solar cycle phases. The model depends on the observed large-scale non-polar photospheric magnetic fields and that measured at polar regions from 55N to 90N and from 55S to 90S,which are the visible manifestations of cyclic changes in the toroidal and poloidal components of the global magnetic field of the Sun. The modeled magnetic field is determined as the superposition of the non-polar and the polar photospheric magnetic field cycle variations. The agreement between the model p…
The SDO/HMI instruments provide photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semi-analytic and numeric equilibria and been applied before to vector magnetograms from Hinode and ground based observations. Recently we implemented a new version which takes measurement errors in photospheric vector magnetograms into account. Photospheric field measure…
The coronal magnetic field cannot be directly observed, but in principle it can be reconstructed from the comparatively well observed photospheric magnetic field. A popular approach uses a nonlinear force-free model. Non-magnetic forces at the photosphere are significant meaning the photospheric data are inconsistent with the force-free model, and this causes problems with the modeling (De Rosa et al., Astrophys. J. 696, 1780, 2009). In this paper we present a numerical implementation of the Grad-Rubin method for reconstructing the coronal magnetic field using a magnetostatic model. This model…
Quantifying coronal magnetic field remains a central problem in solar physics. Nowadays the coronal magnetic field is often modelled using nonlinear force-free field (NLFFF) reconstructions, whose accuracy has not yet been comprehensively assessed. Here we perform a detailed casting of the NLFFF reconstruction tools, such as pi-disambiguation, photospheric field preprocessing, and volume reconstruction methods using a 3D snapshot of the publicly available full-fledged radiative MHD model. Specifically, from the MHD model we know the magnetic field vector in the entire 3D domain, which enables …
In this study, we investigate in detail the photospheric magnetic structure of 98 coronal holes using line-of-sight magnetograms of SDO/HMI, and for a subset of 42 coronal holes using HINODE/SOT G-band filtergrams. We divided the magnetic field maps into magnetic elements and quiet coronal hole regions by applying a threshold at $\pm 25$ G. We find that the number of magnetic bright points in magnetic elements is well correlated with the area of the magnetic elements (cc=$0.83\pm 0.01$). Further, the magnetic flux of the individual magnetic elements inside coronal holes is related to their are…
Preferential Appearance of H$α$ Moreton Waves along Photospheric Magnetic Network Boundaries
School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Key Laboratory for Modern Astronomy and Astrophysics, Nanjing University（南京大学现代天文与天体物理重点实验室）；State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology（澳门科技大学月球与行星科学国家重点实验室）
Elemental abundances in the solar corona are known to be different from those observed in the solar photosphere. The ratio of coronal to photospheric abundance shows a dependence on the first ionisation potential (FIP) of the element. We estimate FIP bias from direct measurements of elemental abundances from soft X-ray spectra using data from multiple space missions covering a range of solar activity levels. This comprehensive analysis shows clear evidence for a decrease in FIP bias around maximum intensity of the X-ray flare with coronal abundances briefly tending to photospheric values and a…
Photospheric magnetic field not only plays important roles in building up free energy and triggering solar eruptions, but also has been observed to change rapidly and permanently responding to the coronal magnetic field restructuring due to coronal transients. The Helioseismic and Magnetic Imager instrument (HMI) on board the newly launched Solar Dynamics Observatory (SDO) produces seeing-free full-disk vector magnetograms at consistently high resolution and high cadence, which finally makes possible an unambiguous and comprehensive study of this important back-reaction process. In this study,…
The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free "potential field" extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnet…
Validating Coronal Magnetic Field Models Using Gaussian Separation
Sydney Institute for Astronomy, School of Physics, The University of Sydney（悉尼大学）；University of Wisconsin-Green Bay（威斯康星大学格林贝分校）；W.W. Hansen Experimental Physics Laboratory, Stanford University（斯坦福大学）；The University of Newcastle（纽卡斯尔大学）
The rapid, irreversible change of the photospheric magnetic field has been recognized as an important element of the solar flare process. This Letter reports such a rapid change of magnetic fields during the 2011 February 13 M6.6 flare in NOAA AR 11158 that we found from the vector magnetograms of the Helioseismic and Magnetic Imager with 12-min cadence. High-resolution magnetograms of Hinode that are available at ~-5.5, -1.5, 1.5, and 4 hrs relative to the flare maximum are used to reconstruct three-dimensional coronal magnetic field under the nonlinear force-free field (NLFFF) assumption. UV…
Photospheric horizontal magnetic field decrease preceding a major solar eruption
Planetary Environmental and Astrobiological Research Laboratory (PEARL), School of Atmospheric Sciences, Sun Yat-sen University（中山大学大气科学学院行星环境与天体生物学研究实验室）；CAS center for Excellence in Comparative Planetology（中国科学院比较行星学卓越中心）；Key Laboratory of Tropical Atmosphere-Ocean System, Sun Yat-sen University, Ministry of Education（中山大学热带海洋-大气系统教育部重点实验室）
Coronal and chromospheric magnetic fields are derived from polarization and spectral observations of the thermal free-free emission using the Nobeyama Radioheliograph (NoRH). In magnetized plasma, the ordinary and extraordinary modes of free-free emission have different optical depths. This creates a circularly polarized component in an atmosphere with a temperature gradient. We observed an active region on April 13, 2012 to derive its coronal and chromospheric magnetic fields. The observed degree of circular polarization was between 0.5 % and 1.7 %. The radio circular polarization images were…
Where does solar flare energy come from? More specifically, assuming that the ultimate source of flare energy is mechanical energy in the convection zone, how is this translated into energy dissipated or stored in the corona? This question appears to have been given relatively little thought, as attention has been focussed predominantly on mechanisms for the rapid dissipation of coronal magnetic energy by way of MHD instabilities and plasma micro instabilities. We consider three types of flare theory: the steady state "photospheric dynamo" model in which flare power represents coronal dissipat…
Understanding the nature and evolution of the photospheric helicity flux transfer is a key to reveal the role of magnetic helicity in coronal dynamics of solar active regions. Using SDO/HMI photospheric vector magnetograms and the derived flow velocity field, we computed boundary driven helicity flux with a 12 minute cadence during the emergence of AR 11928. Accounting the foot point connectivity defined by non-linear force-free magnetic extrapolations, we derived and analyzed the corrected distribution of helicity flux maps. The photospheric helicity flux injection is found to changes sign du…
For a better understanding of magnetic field in the solar corona and dynamic activities such as flares and coronal mass ejections, it is crucial to measure the time-evolving coronal field and accurately estimate the magnetic energy. Recently, a new modeling technique called the data-driven coronal field model, in which the time evolution of magnetic field is driven by a sequence of photospheric magnetic and velocity field maps, has been developed and revealed the dynamics of flare-productive active regions. Here we report on the first qualitative and quantitative assessment of different data-d…
A recent study using {\it Hinode} (SOT/FG) data of a sunspot revealed some unusually large penumbral jets that often repeatedly occurred at the same locations in the penumbra, namely at the tail of a penumbral filament or where the tails of multiple penumbral filaments converged. These locations had obvious photospheric mixed-polarity magnetic flux in \NaI\ 5896 Stokes-V images obtained with SOT/FG. Several other recent investigations have found that extreme ultraviolet (EUV)/X-ray coronal jets in quiet Sun regions (QRs), coronal holes (CHs) and near active regions (ARs) have obvious mixed-pol…
Coronal magnetic flux ropes are closely related to large-scale solar activities. Using a 2.5-dimensional time-dependent ideal magnetohydrodynamic (MHD) model in Cartesian coordinates, we carry out numerical simulations to investigate the evolution of a magnetic system consisting of a flux rope embedded in a fully-closed quadrupolar magnetic field with different photospheric flux distributions. It is found that, when the photospheric flux is not concentrated too much towards the polarity inversion line (PIL) and the constraint exerted by the background field is not too weak, the equilibrium sta…
Aims. We show how the build-up of magnetic gradients in the Sun's corona may be inferred directly from photospheric velocity data. This enables computation of magnetic connectivity measures such as the squashing factor without recourse to magnetic field extrapolation. Methods.Assuming an ideal evolution in the corona, and an initially uniform magnetic field, the subsequent field line mapping is computed by integrating trajectories of the (time-dependent) horizontal photospheric velocity field. The method is applied to a 12 hour high-resolution sequence of photospheric flows derived from Hinode…
Context: Knowledge about the coronal magnetic field is important to the understanding the structure of the solar corona. We compute the field in the higher layers of the solar atmosphere from the measured photospheric field under the assumption that the corona is force-free. Aims: Here we develop a method for nonlinear force-free coronal magnetic field medelling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure. Methods: We describe a newly developed code for the extrapolation of nonlinear force-free coronal magnetic fields in spherica…
Magnetic helicity (MH) is a measure of twist and shear of magnetic field. MH is injected in the active region (AR) corona through photospheric footpoint motions causing twisted and sheared magnetic fields. From the conservation property of the helicity, it was conjectured that an already twisted flux rope (FR) with continuous injection of MH inevitably erupts to remove the excess accumulated coronal helicity. Therefore, understanding the nature and evolution of the photospheric helicity flux transfer is crucial to reveal the intensity of the flare/CME activity. Using the time-sequence vector-m…
Three extreme-ultraviolet (EUV) jets recurred in about one hour on 2010 September 17 in the following magnetic polarity of active region 11106. The EUV jets were observed by the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO). The Helioseismic and Magnetic Imager (HMI) on board SDO measured the vector magnetic field, from which we derive the magnetic flux evolution, the photospheric velocity field, and the vertical electric current evolution. The magnetic configuration before the jets is derived by the nonlinear force-free field (NLFFF) extrapolation. We derive…
Presently, many models of the coronal magnetic field rely on photospheric vector magnetograms but these data have been shown to be problematic as the sole boundary information for nonlinear force-free field (NLFFF) extrapolations. Magnetic fields in the corona manifest themselves in high-energy images (X-rays and EUV) in the shapes of coronal loops, providing an additional constraint that at present is not used due to the mathematical complications of incorporating such input into numerical models. Projection effects and the limited number of usable loops further complicate the use of coronal …
Our aim is to study the photospheric flux distribution of a twisted flux tube that emerges from the solar interior. We also report on the eruption of a new flux rope when the emerging tube rises into a pre-existing magnetic field in the corona. To study the evolution, we use 3D numerical simulations by solving the time-dependent and resistive MHD equations. We qualitatively compare our numerical results with MDI magnetograms of emerging flux at the solar surface. We find that the photospheric magnetic flux distribution consists of two regions of opposite polarities and elongated magnetic tails…
3D picture of the coronal magnetic field remains an outstanding problem in solar physics, particularly, in active regions. Nonlinear force-free field reconstructions that employ routinely available full-disk photospheric vector magnetograms represent state-of-the-art coronal magnetic field modeling. Such reconstructions, however, suffer from an inconsistency between a force-free coronal magnetic field and non-force-free photospheric boundary condition, from which the coronal reconstruction is performed. In this study we focus on integrating the additional chromospheric and / or coronal magneti…
Context: The comparison of coronal and photospheric abundances in cool stars is an essential question to resolve. In the Sun an enhancement of the elements with low first ionization potential (FIP) is observed in the corona with respect to the photosphere. Stars with high levels of activity seem to show a depletion of elements with low FIP when compared to solar standard values; however the few cases of active stars in which photospheric values are available for comparison lead to confusing results, and an enlargement of the sample is mandatory for solving this longstanding problem. Aims: We c…
We investigate the recently quantified misalignment of $α_{mis} \approx 20^\circ-40^\circ$ between the 3-D geometry of stereoscopically triangulated coronal loops observed with STEREO/EUVI (in four active regions) and theoretical (potential or nonlinear force-free) magnetic field models extrapolated from photospheric magnetograms. We develop an efficient method of bootstrapping the coronal magnetic field by forward-fitting a parameterized potential field model to the STEREO-observed loops. The potential field model consists of a number of unipolar magnetic charges that are parameterized by dec…
We propose a novel one-dimensional model that includes both shock and turbulence heating and qualify how these processes contribute to heating the corona and driving the solar wind. Compressible MHD simulations allow us to automatically consider shock formation and dissipation, while turbulent dissipation is modeled via a one-point closure based on Alfvén wave turbulence. Numerical simulations were conducted with different photospheric perpendicular correlation lengths $λ_0$, which is a critical parameter of Alfvén wave turbulence, and different root-mean-square photospheric transverse-wave am…
We present simulations modeling closed regions of the solar corona threaded by a strong magnetic field where localized photospheric vortical motions twist the coronal field lines. The linear and nonlinear dynamics are investigated in the reduced magnetohydrodynamic regime in Cartesian geometry. Initially the magnetic field lines get twisted and the system becomes unstable to the internal kink mode, confirming and extending previous results. As typical in this kind of investigations, where initial conditions implement smooth fields and flux-tubes, we have neglected fluctuations and the fields a…
This paper is the third in a series of papers working towards the construction of a realistic, evolving, non-linear force-free coronal field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48 hr time series of synthetic magnetograms produced from the model of Meyer, Mackay, van Ballegooijen and Parnell, 2011, Solar Phys., 272, 29. Three simulations include a uniform, overlying coronal …
Nanoflare models for heating the solar corona usually assume magnetic braiding and reconnection as the source of the energy. However, recent observations at record spatial resolution from the {\sc Sunrise} balloon mission suggest that photospheric magnetic flux cancellation is much more common than previously realised. We therefore examine the possibility of three-dimensional reconnection driven by flux cancellation as a cause of chromospheric and coronal heating. In particular, we estimate how the heights and amount of energy release produced by flux cancellation depend on flux size, flux can…
Generation and annihilation of three dimensional magnetic nulls in extrapolated solar coronal magnetic field: Data-based Implicit Large Eddy Simulation
