Magnetic Field and Plasma Scaling Laws: Their Implications for Coronal Heating Models

2000 ◽  
Vol 530 (2) ◽  
pp. 999-1015 ◽  
Author(s):  
C. H. Mandrini ◽  
P. Demoulin ◽  
J. A. Klimchuk
Keyword(s):  
Magnetic Field ◽  
Scaling Laws ◽  
Coronal Heating

scholarly journals Empirical Scaling Laws for Coronal Heating

1983 ◽  
Vol 102 ◽  
pp. 345-361
Author(s):  
Leon Golub
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Solar Corona ◽  
Magnetic Field Strength ◽  
Scaling Laws ◽  
Coronal Heating ◽  
Coronal Loops ◽  
The Sun ◽  
Single Loop

We review the origins and uses of scaling laws in studies of stellar outer atmospheres, with particular emphasis on the properties of coronal loops. The evidence for a fundamental structuring of the Solar corona is reviewed and a discussion of thermodynamic scaling laws is presented. In order to intercompare different theories for coronal formation and heating, it is necessary to recast the theories in terms of observable quantities. As an example, we present a discussion of magnetic field-related heating and scaling laws which can be obtained relating coronal pressure, temperature and magnetic field strength; available data are shown to be consistent with scaling laws obtained in this way. However, some parameters of the theory must be treated as adjustable at the present time and it is necessary to examine data from other stars in order to determine whether these are true parameters in coronal heating. We examine some of the difficulties involved in using unresolved stellar data when dealing with loop atmospheres, by first treating the Sun as an unresolved source. Using the detailed observations now available we examine the limits of applicability of single-loop models. The possibilities and limits of stellar data are then discussed.

scholarly journals Planetary Magnetic Fields and Habitability in Super Earths

2018 ◽  
Vol 27 (1) ◽  
pp. 183-231 ◽  
Author(s):  
Pablo Cuartas-Restrepo
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Scaling Laws ◽  
Thermal Evolution ◽  
Solid Core ◽  
Direct Influence ◽  
Physical Processes ◽  
Planetary Magnetic Fields ◽  
Planetary Magnetic Field ◽  
Planetary Dynamos

Abstract This work seeks to summarize some special aspects of a type of exoplanets known as super-Earths (SE), and the direct influence of these aspects in their habitability. Physical processes like the internal thermal evolution and the generation of a protective Planetary Magnetic Field (PMF) are directly related with habitability. Other aspects such as rotation and the formation of a solid core are fundamental when analyzing the possibilities that a SE would have to be habitable. This work analyzes the fundamental theoretical aspects on which the models of thermal evolution and the scaling laws of the planetary dynamos are based. These theoretical aspects allow to develop models of the magnetic evolution of the planets and the role played by the PMF in the protection of the atmosphere and the habitability of the planet.

scholarly journals Flux expulsion with dynamics

2016 ◽  
Vol 791 ◽  
pp. 568-588 ◽  
Author(s):  
Andrew D. Gilbert ◽  
Joanne Mason ◽  
Steven M. Tobias
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Lorentz Force ◽  
Differential Rotation ◽  
Time Scale ◽  
Scaling Laws ◽  
Dynamical Regime ◽  
Kinematic Evolution ◽  
Flux Expulsion ◽  
The Magnetic Field

In the process of flux expulsion, a magnetic field is expelled from a region of closed streamlines on a $TR_{m}^{1/3}$ time scale, for magnetic Reynolds number $R_{m}\gg 1$ ($T$ being the turnover time of the flow). This classic result applies in the kinematic regime where the flow field is specified independently of the magnetic field. A weak magnetic ‘core’ is left at the centre of a closed region of streamlines, and this decays exponentially on the $TR_{m}^{1/2}$ time scale. The present paper extends these results to the dynamical regime, where there is competition between the process of flux expulsion and the Lorentz force, which suppresses the differential rotation. This competition is studied using a quasi-linear model in which the flow is constrained to be axisymmetric. The magnetic Prandtl number $R_{m}/R_{e}$ is taken to be small, with $R_{m}$ large, and a range of initial field strengths $b_{0}$ is considered. Two scaling laws are proposed and confirmed numerically. For initial magnetic fields below the threshold $b_{core}=O(UR_{m}^{-1/3})$, flux expulsion operates despite the Lorentz force, cutting through field lines to result in the formation of a central core of magnetic field. Here $U$ is a velocity scale of the flow and magnetic fields are measured in Alfvén units. For larger initial fields the Lorentz force is dominant and the flow creates Alfvén waves that propagate away. The second threshold is $b_{dynam}=O(UR_{m}^{-3/4})$, below which the field follows the kinematic evolution and decays rapidly. Between these two thresholds the magnetic field is strong enough to suppress differential rotation, leaving a magnetically controlled core spinning in solid body motion, which then decays slowly on a time scale of order $TR_{m}$.

scholarly journals Coronal Heating, Weak MHD Turbulence, and Scaling Laws

2007 ◽  
Vol 657 (1) ◽  
pp. L47-L51 ◽  
Author(s):  
A. F. Rappazzo ◽  
M. Velli ◽  
G. Einaudi ◽  
R. B. Dahlburg
Keyword(s):  
Scaling Laws ◽  
Coronal Heating ◽  
Mhd Turbulence

scholarly journals Magnetic Topology and Current Sheet Formation

1989 ◽  
Vol 104 (2) ◽  
pp. 277-280
Author(s):  
Spiro K. Antiochos
Keyword(s):  
Magnetic Field ◽  
Current Sheet ◽  
Field Line ◽  
Complex Network ◽  
Rapid Heating ◽  
Negative Polarity ◽  
Coronal Magnetic Field ◽  
Coronal Heating ◽  
Magnetic Topology ◽  
Magnetic Null

AbstractWe describe a mechanism for coronal heating. The basic idea is that since the photospheric flux is observed to consist of a complex pattern of positive and negative polarity regions, the topology of the coronal magnetic field (in particular the connectivity) must be discontinuous over a complex network of surfaces and magnetic null points in the corona. Consequently, photospheric motions of the field line footpoints, even if arbitrarily smooth, result in discontinuous stressing of the field. This produces coronal current sheets, reconnection at the null points, and rapid heating.

scholarly journals A contemporary view of coronal heating

2012 ◽  
Vol 370 (1970) ◽  
pp. 3217-3240 ◽  
Author(s):  
Clare E. Parnell ◽  
Ineke De Moortel
Keyword(s):  
Magnetic Field ◽  
Recent Progress ◽  
Coupled System ◽  
Coronal Heating ◽  
The Sun ◽  
Key Factors ◽  
Computing Power ◽  
Heating Mechanism ◽  
Outer Atmosphere ◽  
The Magnetic Field

Determining the heating mechanism (or mechanisms) that causes the outer atmosphere of the Sun, and many other stars, to reach temperatures orders of magnitude higher than their surface temperatures has long been a key problem. For decades, the problem has been known as the coronal heating problem, but it is now clear that ‘coronal heating’ cannot be treated or explained in isolation and that the heating of the whole solar atmosphere must be studied as a highly coupled system. The magnetic field of the star is known to play a key role, but, despite significant advancements in solar telescopes, computing power and much greater understanding of theoretical mechanisms, the question of which mechanism or mechanisms are the dominant supplier of energy to the chromosphere and corona is still open. Following substantial recent progress, we consider the most likely contenders and discuss the key factors that have made, and still make, determining the actual (coronal) heating mechanism (or mechanisms) so difficult.

Zur Begrenzung der radial en Ausdehnung des Li chtbogenstromes durch ein axiales Magnetfeld. II. Skalengesetze und Vergleich mit Experimenten / On Limitation of the Radial Extent of the Arc Current by Means of an Axial Magnetic Field. II. Scaling Laws and Comparison with Experimental Results

1972 ◽  
Vol 27 (4) ◽  
pp. 652-670
Author(s):  
O. Klüber
Keyword(s):  
Magnetic Field ◽  
Cross Sections ◽  
Scaling Laws ◽  
Axial Magnetic Field ◽  
Angular Frequency ◽  
Model Calculations ◽  
Simple Geometry ◽  
Radial Extent ◽  
Arc Current ◽  
Field Lines

Abstract In an arc with superimposed axial magnetic field, radial current components cause a rotational motion of the plasma column and produce azimuthal Hall currents and hence electromotive forces such that the arc current is guided by the magnetic field lines. In the first part of this paper the steady-state plasma equations have been solved for a homogeneous plasma in simple geometry, allowance being made for finite viscosity. Here, scaling laws giving the radial extent of the arc current are obtained. In addition, electrodes with finite cross sections are treated. The results of model calculations agree well with experimental data. Generally, the model is applicable, if the angular frequency of the plasma is small compared with the ion gyration frequency.

Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 2. Magnetohydrodynamic flow

2011 ◽  
Vol 674 ◽  
pp. 132-162 ◽  
Author(s):  
C. MISTRANGELO
Keyword(s):  
Magnetic Field ◽  
Liquid Metal ◽  
Scaling Laws ◽  
Numerical Study ◽  
Topological Analysis ◽  
Metal Flow ◽  
Magnetohydrodynamic Flow ◽  
Sudden Expansion ◽  
Internal Layers ◽  
Flow Topology

A numerical study has been carried out to analyse liquid metal flows in a sudden expansion of electrically conducting rectangular ducts under the influence of an imposed uniform magnetic field. Separation phenomena are investigated by selecting a reference Reynolds number and by increasing progressively the applied magnetic field. The magnetic effects leading to the reduction of the size of separation zones that form behind the cross-section enlargement are studied by considering modifications of flow topology, streamline patterns and electric current density distribution. In the range of parameters investigated, the magnetohydrodynamic flow undergoes substantial transitions from a hydrodynamic-like flow to one dominated by electromagnetic forces, where the influence of inertia and viscous forces is confined to thin internal layers aligned with the magnetic field and to boundary layers that form along the walls. Scaling laws describing the reattachment length and the pressure drop in the sudden expansion are derived for intense magnetic fields.

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