SOLUTIONS TO THE FORCE-FREE FIELD EQUATIONS

1996 ◽  
pp. 17-55
Keyword(s):  
Free Field ◽  
Field Equations ◽  
Force Free Field

Various Barbs in Solar Filaments

2017 ◽  
Vol 34 ◽  
Author(s):  
Boris Filippov
Keyword(s):  
Free Field ◽  
Flux Rope ◽  
Lateral Extension ◽  
Solar Filaments ◽  
Solar Filament ◽  
Field Lines ◽  
The Magnetic Field ◽  
Narrow Structure ◽  
Force Free Field ◽  
Helical Field

AbstractInterest to lateral details of the solar filament shape named barbs, motivated by their relationship to filament chirality and helicity, showed their different orientation relative to the expected direction of the magnetic field. While the majority of barbs are stretched along the field, some barbs seem to be transversal to it and are referred to as anomalous barbs. We analyse the deformation of helical field lines by a small parasitic polarity using a simple flux rope model with a force-free field. A rather small and distant source of parasitic polarity stretches the bottom parts of the helical lines in its direction creating a lateral extension of dips below the flux-rope axis. They can be considered as normal barbs of the filament. A stronger and closer source of parasitic polarity makes the flux-rope field lines to be convex below its axis and creates narrow and deep dips near its position. As a result, the narrow structure, with thin threads across it, is formed whose axis is nearly perpendicular to the field. The structure resembles an anomalous barb. Hence, the presence of anomalous barbs does not contradict the flux-rope structure of a filament.

scholarly journals Particle Acceleration Driven by Null Electromagnetic Fields Near a Kerr Black Hole

Universe ◽  
2020 ◽  
Vol 7 (1) ◽  
pp. 1
Author(s):  
Yasufumi Kojima ◽  
Yuto Kimura
Keyword(s):  
Black Hole ◽  
Particle Acceleration ◽  
Free Field ◽  
Kerr Black Hole ◽  
High Energy ◽  
Maximum Energy ◽  
Dimensionless Number ◽  
Massive Black Hole ◽  
Relativistic Regime ◽  
Force Free Field

Short timescale variability is often associated with a black hole system. The consequence of an electromagnetic outflow suddenly generated near a Kerr black hole is considered assuming that it is described by a solution of a force-free field with a null electric current. We compute charged particle acceleration induced by the burst field. We show that the particle is instantaneously accelerated to the relativistic regime by the field with a very large amplitude, which is characterized by a dimensionless number κ. Our numerical calculation demonstrates how the trajectory of the particle changes with κ. We also show that the maximum energy increases with κ2/3. The typical maximum energy attained by a proton for an event near a super massive black hole is Emax∼100 TeV, which is enough observed high-energy flares.

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 Quasi–Static Evolution of Force–Free Magnetic Fields and a Model for Two–Ribbon Solar Flares

1985 ◽  
Vol 107 ◽  
pp. 221-224
Author(s):  
J. J. Aly
Keyword(s):  
Magnetic Fields ◽  
Solar Flares ◽  
Free Field ◽  
Qualitative Theory ◽  
Force Free Field ◽  
Open Configuration

We show that a sheared 2–D force–free field can evolve in a quasi–static way towards an open configuration, and apply this result to a qualitative theory of two–ribbon solar flares.

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