scholarly journals An Optimization Principle for Computing Stationary MHD Equilibria with Solar Wind Flow

Solar Physics ◽  
2020 ◽  
Vol 295 (10) ◽  
Author(s):  
Thomas Wiegelmann ◽  
Thomas Neukirch ◽  
Dieter H. Nickeler ◽  
Iulia Chifu
Keyword(s):  
Magnetic Field ◽  
Free Field ◽  
Coronal Magnetic Field ◽  
Optimization Method ◽  
Field Configuration ◽  
Optimization Principle ◽  
Mhd Equilibria ◽  
Solar Wind Flow ◽  
Nonlinear Force ◽  
Flow Effects

Abstract In this work we describe a numerical optimization method for computing stationary MHD equilibria. The newly developed code is based on a nonlinear force-free optimization principle. We apply our code to model the solar corona using synoptic vector magnetograms as boundary condition. Below about two solar radii the plasma $\beta $ β and Alfvén Mach number $M_{A}$ M A are small and the magnetic field configuration of stationary MHD is basically identical to a nonlinear force-free field, whereas higher up in the corona (where $\beta $ β and $M_{A}$ M A are above unity) plasma and flow effects become important and stationary MHD and force-free configuration deviate significantly. The new method allows for the reconstruction of the coronal magnetic field further outwards than with potential field, nonlinear force-free or magnetostatic models. This way the model might help to provide the magnetic connectivity for joint observations of remote sensing and in-situ instruments on Solar Orbiter and Parker Solar Probe.

Global coronal and heliospheric magnetic field modelling for Solar Orbiter

2021 ◽  
Author(s):  
Thomas Wiegelmann ◽  
Thomas Neukirch ◽  
Iulia Chifu ◽  
Bernd Inhester
Keyword(s):  
Magnetic Field ◽  
Solar Rotation ◽  
Coronal Magnetic Field ◽  
Important Research ◽  
Parker Spiral ◽  
Important Research Topic ◽  
Mhd Equilibria ◽  
Solar Wind Flow ◽  
Nonlinear Force

<p>Computing the solar coronal magnetic field and plasma<br>environment is an important research topic on it's own right<br>and also important for space missions like Solar Orbiter to<br>guide the analysis of remote sensing and in-situ instruments.<br>In the inner solar corona plasma forces can be neglected and<br>the field is modelled under the assumption of a vanishing<br>Lorentz-force. Further outwards (above about two solar radii)<br>plasma forces and the solar wind flow has to be considered.<br>Finally in the heliosphere one has to consider that the Sun<br>is rotating and the well known Parker-spiral forms.<br>We have developed codes based on optimization principles<br>to solve nonlinear force-free, magneto-hydro-static and<br>stationary MHD-equilibria. In the present work we want to<br>extend these methods by taking the solar rotation into account.</p>

scholarly journals Nonlinear force-free modeling of magnetic fields in flare-productive active regions

2015 ◽  
Vol 11 (S320) ◽  
pp. 167-174
Author(s):  
M. S. Wheatland ◽  
S. A. Gilchrist
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Boundary Data ◽  
Numerical Solutions ◽  
Free Field ◽  
Active Regions ◽  
Coronal Magnetic Field ◽  
Nonlinear Force ◽  
The Magnetic Field ◽  
Force Free Field

AbstractWe review nonlinear force-free field (NLFFF) modeling of magnetic fields in active regions. The NLFFF model (in which the electric current density is parallel to the magnetic field) is often adopted to describe the coronal magnetic field, and numerical solutions to the model are constructed based on photospheric vector magnetogram boundary data. Comparative tests of NLFFF codes on sets of boundary data have revealed significant problems, in particular associated with the inconsistency of the model and the data. Nevertheless NLFFF modeling is often applied, in particular to flare-productive active regions. We examine the results, and discuss their reliability.

scholarly journals Computing nonlinear force free coronal magnetic fields

2003 ◽  
Vol 10 (4/5) ◽  
pp. 313-322 ◽  
Author(s):  
T. Wiegelmann ◽  
T. Neukirch
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Boundary Conditions ◽  
Random Noise ◽  
Coronal Magnetic Field ◽  
Optimization Method ◽  
Numerical Code ◽  
Coronal Magnetic Fields ◽  
Nonlinear Force ◽  
Free Fields

Abstract. Knowledge of the structure of the coronal magnetic field is important for our understanding of many solar activity phenomena, e.g. flares and CMEs. However, the direct measurement of coronal magnetic fields is not possible with present methods, and therefore the coronal field has to be extrapolated from photospheric measurements. Due to the low plasma beta the coronal magnetic field can usually be assumed to be approximately force free, with electric currents flowing along the magnetic field lines. There are both observational and theoretical reasons which suggest that at least prior to an eruption the coronal magnetic field is in a nonlinear force free state. Unfortunately the computation of nonlinear force free fields is way more difficult than potential or linear force free fields and analytic solutions are not generally available. We discuss several methods which have been proposed to compute nonlinear force free fields and focus particularly on an optimization method which has been suggested recently. We compare the numerical performance of a newly developed numerical code based on the optimization method with the performance of another code based on an MHD relaxation method if both codes are applied to the reconstruction of a semi-analytic nonlinear force-free solution. The optimization method has also been tested for cases where we add random noise to the perfect boundary conditions of the analytic solution, in this way mimicking the more realistic case where the boundary conditions are given by vector magnetogram data. We find that the convergence properties of the optimization method are affected by adding noise to the boundary data and we discuss possibilities to overcome this difficulty.

scholarly journals Hinode magnetic-field observations of solar flares for exploring the energy storage and trigger mechanisms

2015 ◽  
Vol 11 (S320) ◽  
pp. 175-178
Author(s):  
Toshifumi Shimizu ◽  
Satoshi Inoue ◽  
Yusuke Kawabata
Keyword(s):  
Magnetic Field ◽  
Free Field ◽  
Coronal Magnetic Field ◽  
Field Configuration ◽  
Optical Telescope ◽  
Magnetic Field Data ◽  
Trigger Mechanisms ◽  
The Magnetic Field ◽  
Force Free Field ◽  
Chromospheric Flare

AbstractThe spectro-polarimeter in the Hinode Solar Optical Telescope (SOT) is one of the powerful instruments for the most accurate measurements of vector magnetic fields on the solar surface. The magnetic field configuration and possible candidates for flare trigger are briefly discussed with some SOT observations of solar flare events, which include X5.4/X1.3 flares on 7 March 2012, X1.2 flare on 7 January 2014 and two M-class flares on 2 February 2014. Especially, using an unique set of the Hinode and SDO data for the X5.4/X1.3 flares on 7 March 2012, we briefly reviewed remarkable properties observed in the spatial distribution of the photospheric magnetic flux, chromospheric flare ribbons, and the 3D coronal magnetic field structure inferred by non-linear force-free field modeling with the Hinode photospheric magnetic field data.

scholarly journals CME–HSS Interaction and Characteristics Tracked from Sun to Earth

Solar Physics ◽  
2019 ◽  
Vol 294 (9) ◽  
Author(s):  
Stephan G. Heinemann ◽  
Manuela Temmer ◽  
Charles J. Farrugia ◽  
Karin Dissauer ◽  
Christina Kay ◽  
...  
Keyword(s):  
Magnetic Field ◽  
High Speed ◽  
Free Field ◽  
Field Configuration ◽  
Solar Dynamics Observatory ◽  
Magnetic Field Configuration ◽  
Launch Site ◽  
Nonlinear Force ◽  
Solar Dynamics

Abstract In a thorough study, we investigate the origin of a remarkable plasma and magnetic field configuration observed in situ on June 22, 2011, near L1, which appears to be a magnetic ejecta (ME) and a shock signature engulfed by a solar wind high-speed stream (HSS). We identify the signatures as an Earth-directed coronal mass ejection (CME), associated with a C7.7 flare on June 21, 2011, and its interaction with a HSS, which emanates from a coronal hole (CH) close to the launch site of the CME. The results indicate that the major interaction between the CME and the HSS starts at a height of $1.3~\mbox{R}_{\odot }$ 1.3 R ⊙ up to $3~\mbox{R}_{\odot }$ 3 R ⊙ . Over that distance range, the CME undergoes a strong north-eastward deflection of at least $30^{\circ }$ 30 ∘ due to the open magnetic field configuration of the CH. We perform a comprehensive analysis for the CME–HSS event using multi-viewpoint data (from the Solar TErrestrial RElations Observatories, the Solar and Heliospheric Observatory and the Solar Dynamics Observatory), and combined modeling efforts (nonlinear force-free field modeling, Graduated Cylindrical Shell CME modeling, and the Forecasting a CME’s Altered Trajectory – ForeCAT model). We aim at better understanding its early evolution and interaction process as well as its interplanetary propagation and related in situ signatures, and finally the resulting impact on the Earth’s magnetosphere.

scholarly journals Simulating the Coronal Evolution of Bipolar Active Regions to Investigate the Formation of Flux Ropes

Solar Physics ◽  
2021 ◽  
Vol 296 (1) ◽  
Author(s):  
S. L. Yardley ◽  
D. H. Mackay ◽  
L. M. Green
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Initial Conditions ◽  
Free Field ◽  
Active Regions ◽  
Coronal Magnetic Field ◽  
Solar Dynamics Observatory ◽  
Horizontal Magnetic Field ◽  
Nonlinear Force ◽  
Force Free Field

AbstractThe coronal magnetic field evolution of 20 bipolar active regions (ARs) is simulated from their emergence to decay using the time-dependent nonlinear force-free field method of Mackay, Green, and van Ballegooijen (Astrophys. J. 729, 97, 2011). A time sequence of cleaned photospheric line-of-sight magnetograms, which covers the entire evolution of each AR, is used to drive the simulation. A comparison of the simulated coronal magnetic field with the 171 and 193 Å observations obtained by the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA), is made for each AR by manual inspection. The results show that it is possible to reproduce the evolution of the main coronal features such as small- and large-scale coronal loops, filaments and sheared structures for 80% of the ARs. Varying the boundary and initial conditions, along with the addition of physical effects such as Ohmic diffusion, hyperdiffusion and a horizontal magnetic field injection at the photosphere, improves the match between the observations and simulated coronal evolution by 20%. The simulations were able to reproduce the build-up to eruption for 50% of the observed eruptions associated with the ARs. The mean unsigned time difference between the eruptions occurring in the observations compared to the time of eruption onset in the simulations was found to be ≈5 hrs. The simulations were particularly successful in capturing the build-up to eruption for all four eruptions that originated from the internal polarity inversion line of the ARs. The technique was less successful in reproducing the onset of eruptions that originated from the periphery of ARs and large-scale coronal structures. For these cases global, rather than local, nonlinear force-free field models must be used. While the technique has shown some success, eruptions that occur in quick succession are difficult to reproduce by this method and future iterations of the model need to address this.

scholarly journals An optimization principle for computing stationary MHD equilibria with solar wind flow

2020 ◽  
Author(s):  
Thomas Wiegelmann ◽  
Thomas Neukirch ◽  
Dieter Nickeler ◽  
Iulia Chifu
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Coronal Magnetic Field ◽  
Field Vector ◽  
Source Surface ◽  
Solar Chromosphere ◽  
Wind Flow ◽  
Solar Wind Flow ◽  
Nonlinear Force ◽  
The Magnetic Field

<p>Knowledge about the magnetic field and plasma environment is important<br>for almost all physical processes in the solar atmosphere. Precise<br>measurements of the magnetic field vector are done routinely only in<br>the photosphere, e.g. by SDO/HMI. These measurements are used as<br>boundary condition for modelling the solar chromosphere and corona,<br>whereas some model assumptions have to be made. In the low-plasma-beta<br>corona the Lorentz-force vanishes and the magnetic field<br>is reconstructed with a nonlinear force-free model. In the mixed-beta<br>chromosphere plasma forces have to be taken into account with the<br>help of a magnetostatic model. And finally for modelling the global<br>corona far beyond the source surface the solar wind flow has to<br>be incorporated within a stationary MHD model.<br>To do so, we generalize a nonlinear force-free and magneto-static optimization<br>code by the inclusion of a field aligned compressible plasma flow.<br>Applications are the implementation of the solar wind on<br>global scale. This allows to reconstruct the coronal magnetic field further<br>outwards than with potential field, nonlinear force-free and magneto-static models.<br>This way the model might help in future to provide the magnetic connectivity<br>for joint observations of remote sensing and in-situ instruments on Solar<br>Orbiter and Parker Solar Probe.</p>

scholarly journals Testing magnetohydrostatic extrapolation with radiative MHD simulation of a solar flare

2019 ◽  
Vol 631 ◽  
pp. A162 ◽  
Author(s):  
X. Zhu ◽  
T. Wiegelmann
Keyword(s):  
Magnetic Field ◽  
Solar Flare ◽  
Initial Conditions ◽  
Free Field ◽  
Optimization Method ◽  
Field Vector ◽  
Plasma Pressure ◽  
Nonlinear Force ◽  
The Magnetic Field ◽  
Force Free Field

Context. On the sun, the magnetic field vector is measured routinely solely in the photosphere. By using these photospheric measurements as a boundary condition, we developed magnetohydrostatic (MHS) extrapolation to model the solar atmosphere. The model makes assumptions about the relative importance of magnetic and non-magnetic forces. While the solar corona is force-free, this is not the case with regard to the photosphere and chromosphere. Aims. The model has previously been tested with an exact equilibria. Here we present a more challenging and more realistic test of our model with the radiative magnetohydrodynamic simulation of a solar flare. Methods. By using the optimization method, the MHS model computes the magnetic field, plasma pressure and density self-consistently. The nonlinear force-free field (NLFFF) and gravity-stratified atmosphere along the field line are assumed as the initial conditions for optimization. Results. Compared with the NLFFF, the MHS model provides an improved magnetic field not only in magnitude and direction, but also in magnetic connectivity. In addition, the MHS model is capable of recovering the main structure of plasma in the photosphere and chromosphere.

Studying Magnetic Field Variations Accompanying the 2011 June 7 Eruptive Event, by Using Nonlinear Force-Free Field Modeling

Solar Physics ◽  
2020 ◽  
Vol 295 (4) ◽  
Author(s):  
Y. I. Egorov ◽  
V. G. Fainshtein ◽  
I. I. Myshyakov ◽  
S. A. Anfinogentov ◽  
G. V. Rudenko
Keyword(s):  
Magnetic Field ◽  
Free Field ◽  
Eruptive Event ◽  
Field Modeling ◽  
Nonlinear Force ◽  
Magnetic Field Variations ◽  
Force Free Field
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