scholarly journals Magnetic Equilibria and Instabilities

1989 ◽  
Vol 104 (1) ◽  
pp. 347-360
Author(s):  
Takashi Sakurai
Keyword(s):  
Solar Flares ◽  
Multiple Solutions ◽  
Magnetic Energy ◽  
Slow Phase ◽  
Two Dimensional ◽  
Explosive Energy ◽  
Mhd Instabilities ◽  
Ideal Mhd ◽  
Slow Evolution ◽  
Equilibrium Sequence

AbstractSolar flares are understood as a process of explosive liberation of magnetic energy, coming after a slow phase of energy build-up. The slow evolution of magnetic equilibria may end up with (a) the termination of an equilibrium sequence, or (b) an instability. The distinction between the two can be made by drawing schematic potential curves. Case (a) has been extensively studied in two-dimensional models. The appearance of multiple solutions, or disappearance of a solution takes place as the system evolves away from the current-free configuration. Case (b) can be discussed in terms of ideal MHD or resistive MHD instabilities. A possible route to explosive energy release is suggested by combining these two cases.

The Energy Release in Solar Flares: Implications of a Constant-Current Model

1990 ◽  
Vol 8 (3) ◽  
pp. 286-288 ◽  
Author(s):  
D. B. Melrose
Keyword(s):  
Energy Release ◽  
Solar Flares ◽  
Magnetic Energy ◽  
Current Model ◽  
Rate Of Change ◽  
Constant Current ◽  
Rapid Rise ◽  
Explosive Energy ◽  
Large Flare ◽  
A Current

AbstractA model is explored for energy release in solar flares that involves a constant coronal current. An emerging flux tube is assumed to carry a current I≲1012 A, and this current is assumed not to change during flare. Using a circuit model, explosive energy release is attributed to a rapid rise in the coronal resistance Rc, which must adjust to Rc = − Lc, with Lc the rate of change of the coronal inductance Lc, to ensure I = constant. In this model the total energy released in the corona is twice the change in the magnetic energy stored in the corona. It is argued that this energy is inadequate to power a large flare and the implications of this conclusion are discussed.

scholarly journals Can Multi-threaded Flux Tubes in Coronal Arcades Support a Magnetohydrodynamic Avalanche?

Solar Physics ◽  
2021 ◽  
Vol 296 (8) ◽  
Author(s):  
J. Threlfall ◽  
J. Reid ◽  
A. W. Hood
Keyword(s):  
Magnetic Fields ◽  
Three Dimensional ◽  
Coronal Loops ◽  
Flux Tubes ◽  
Single Thread ◽  
Mhd Instabilities ◽  
Mhd Instability ◽  
Mhd Simulations ◽  
Ideal Mhd ◽  
Model Geometry

AbstractMagnetohydrodynamic (MHD) instabilities allow energy to be released from stressed magnetic fields, commonly modelled in cylindrical flux tubes linking parallel planes, but, more recently, also in curved arcades containing flux tubes with both footpoints in the same photospheric plane. Uncurved cylindrical flux tubes containing multiple individual threads have been shown to be capable of sustaining an MHD avalanche, whereby a single unstable thread can destabilise many. We examine the properties of multi-threaded coronal loops, wherein each thread is created by photospheric driving in a realistic, curved coronal arcade structure (with both footpoints of each thread in the same plane). We use three-dimensional MHD simulations to study the evolution of single- and multi-threaded coronal loops, which become unstable and reconnect, while varying the driving velocity of individual threads. Experiments containing a single thread destabilise in a manner indicative of an ideal MHD instability and consistent with previous examples in the literature. The introduction of additional threads modifies this picture, with aspects of the model geometry and relative driving speeds of individual threads affecting the ability of any thread to destabilise others. In both single- and multi-threaded cases, continuous driving of the remnants of disrupted threads produces secondary, aperiodic bursts of energetic release.

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

MAGNETIC FIELD AMPLIFICATION BY RELATIVISTIC SHOCKS IN AN INHOMOGENEOUS MEDIUM

2012 ◽  
Vol 08 ◽  
pp. 364-367
Author(s):  
YOSUKE MIZUNO ◽  
MARTIN POHL ◽  
JACEK NIEMIEC ◽  
BING ZHANG ◽  
KEN-ICHI NISHIKAWA ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Inhomogeneous Medium ◽  
Magnetic Energy ◽  
Small Scale ◽  
Two Dimensional ◽  
Filamentary Structure ◽  
Field Amplification ◽  
Relativistic Shocks ◽  
Field Lines ◽  
Magnetohydrodynamic Simulations

We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneity, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in two-dimensional simulations. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that the so-called small-scale dynamo is occurring in the postshock region. We also find that the amplitude of magnetic-field amplification depends on the direction of the mean preshock magnetic field.

scholarly journals A Two-Dimensional Coupled Atmosphere-Ice-Sheet-Continent Model Designed for Paleoclimatic Simulations

1990 ◽  
Vol 14 ◽  
pp. 55-57 ◽  
Author(s):  
M.B. Esch ◽  
K. Herterich
Keyword(s):  
Climate Model ◽  
Hydrological Cycle ◽  
Vertical Plane ◽  
Ice Sheet ◽  
Ice Age ◽  
Balance Model ◽  
Two Dimensional ◽  
Geothermal Heat ◽  
The North ◽  
Slow Evolution

We present a two-dimensional climate model to be used for basic dynamic studies on ice-age time scales (103 to 106 years). The model contains an ice sheet, where flow and temperature are calculated in a vertical plane, oriented in the north-south direction. The model ice sheet is forced by a zonally-averaged atmospheric energy-balance model, including a seasonal cycle and a simplified hydrological cycle, which specifies ice temperature and the mass balance at the ice-sheet surface. At the bottom of the ice sheet, the geothermal heat flux is prescribed. In addition, delayed bedrock sinking (or bedrock rising) is assumed.A stationary state is achieved after 200 000 model years. This long time scale is introduced by the slow evolution of the temperature field within the ice sheet. Using reasonable parameter values and presently observed precipitation patterns, modified by ice-sheet orography, the observed thickness to length ratio (4 km/3300 km) of the Laurentide ice sheet can be simulated within a realistic build-up time (40 000 years). Near the ice bottom, temperate regions developed. They may have had an important effect on ice-sheet build-up and ice-sheet decay.

Plasma Diagnostics of Microflares observed by STIX and AIA

2021 ◽  
Author(s):  
Jonas Saqri ◽  
Astrid Veronig ◽  
Ewan Dickson ◽  
Säm Krucker ◽  
Andrea Francesco Battaglia ◽  
...  
Keyword(s):  
Solar Flares ◽  
Magnetic Energy ◽  
Emission Measure ◽  
Transport Processes ◽  
X Rays ◽  
Solar Dynamics Observatory ◽  
Energy Bands ◽  
Accurate Analysis ◽  
Great Opportunity ◽  
Wide Range

<p>Solar flares are generally thought to be the impulsive release of magnetic energy giving rise to a wide range of solar phenomena that influence the heliosphere and in some cases even conditions of earth. Part of this liberated energy is used for particle acceleration and to heat up the solar plasma. The Spectrometer/Telescope for Imaging X-rays (STIX) instrument onboard the Solar Orbiter mission launched on February 10th 2020 promises advances in the study of solar flares of various sizes. It is capable of measuring X-ray spectra from 4 to 150 keV with 1 keV resolution binned into 32 energy bins before downlinking. With this energy range and sensitivity, STIX is capable of sampling thermal plasma with temperatures of≳10 MK, and to diagnose the nonthermal bremsstrahlung emission of flare-accelerated electrons. During the spacecraft commissioning phase in the first half of the year 2020, STIX observed 68 microflares. Of this set, 26 events could clearly be identified in at least two energy channels, all of which originated in an active region that was also visible from earth. These events provided a great opportunity to combine the STIX observations with the multi-band EUV imagery from the Atmospheric Imaging Assembly (AIA) instrument on board the earth orbiting Solar Dynamics Observatory (SDO). For the microflares that could be identified in two STIX science energy bands, it was possible to derive the temperature and emission measure (EM) of the flaring plasma assuming an isothermal source. For larger events where more detailed spectra could be derived, a more accurate analysis was performed by fitting the spectra assuming various thermal and nonthermal sources. These results are compared to the diagnostics derived from AIA images. To this aim, the Differential EmissionMeasure (DEM) was reconstructed from AIA observations to infer plasma temperatures and EM in the flaring regions. Combined with the the relative timing between the emission seen by STIX and AIA, this allows us to get deeper insight into the flare energy release and transport processes.</p>

scholarly journals Particle Orbits, Trapping, and Acceleration in a Filamentary Current Sheet Model

1994 ◽  
Vol 142 ◽  
pp. 719-728
Author(s):  
Bernhard Kliem
Keyword(s):  
Particle Acceleration ◽  
Electric Field ◽  
Test Particle ◽  
Solar Flares ◽  
Acceleration Of Particles ◽  
Acceleration Process ◽  
Two Dimensional ◽  
Magnetic Island ◽  
Particle Orbits ◽  
Island Dynamics

AbstractTest particle orbits in the two-dimensional Fadeev equilibrium with a perpendicular electric field added are analyzed to show that impulsive bursty reconnection, which has been proposed as a model for fragmentary energy release in solar flares, may account also for particle acceleration to (near) relativistic energies within a fraction of a second. The convective electric field connected with magnetic island dynamics can play an important role in the acceleration process.Subject headings: acceleration of particles — MHD — plasmas — Sun: corona — Sun: flares

scholarly journals On energetics and inertial-range scaling laws of two-dimensional magnetohydrodynamic turbulence

2012 ◽  
Vol 703 ◽  
pp. 238-254 ◽  
Author(s):  
Luke A. K. Blackbourn ◽  
Chuong V. Tran
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Energy Flux ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Inertial Range ◽  
Two Dimensional ◽  
Magnetohydrodynamic Turbulence ◽  
Direct Energy ◽  
Energy Equipartition

AbstractWe study two-dimensional magnetohydrodynamic turbulence, with an emphasis on its energetics and inertial-range scaling laws. A detailed spectral analysis shows that dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo inverse flux partially neutralizes the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. This result is consistent with a qualitative prediction of energy transfer reduction due to Alfvén wave effects by the Iroshnikov–Kraichnan theory (which was originally formulated for magnetohydrodynamic turbulence in three dimensions). We numerically confirm the correlation between dynamo action and direct magnetic energy flux and investigate the applicability of quantitative aspects of the Iroshnikov–Kraichnan theory to the present case, particularly its predictions of energy equipartition and ${k}^{\ensuremath{-} 3/ 2} $ spectra in the energy inertial range. It is found that for turbulence satisfying the Kraichnan condition of magnetic energy at large scales exceeding total energy in the inertial range, the kinetic energy spectrum, which is significantly shallower than ${k}^{\ensuremath{-} 3/ 2} $, is shallower than its magnetic counterpart. This result suggests no energy equipartition. The total energy spectrum appears to depend on the energy composition of the turbulence but is clearly shallower than ${k}^{\ensuremath{-} 3/ 2} $ for $r\approx 2$, even at moderate resolutions. Here $r\approx 2$ is the magnetic-to-kinetic energy ratio during the stage when the turbulence can be considered fully developed. The implication of the present findings is discussed in conjunction with further numerical results on the dependence of the energy dissipation rate on resolution.

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