scholarly journals Linear Force-free Magnetic Fields and Coronal Models

1990 ◽  
Vol 43 (6) ◽  
pp. 813
Author(s):  
CJ Durrant
Keyword(s):  
Magnetic Fields ◽  
Helmholtz Equation ◽  
Bessel Functions ◽  
Spherical Geometry ◽  
Radius Vector ◽  
Basis Vector ◽  
Radial Dependence ◽  
Unit Radius ◽  
Linear Force

I am grateful to Dr N. Seehafer for drawing attention to the fact that the basis vector for writing linear force-free solutions in spherical geometry is the radius vector r and not the unit radius vector r. In order to correct the results given in Section 3 of Durrant (1989). it suffices to replace the spherical Bessel functions iI. ni, hI by riI. rnI. rhI. The only effect of this replacement is to change the radial dependence of B8 and Bef> in the limit of large r to eiOCr fr. Thus the total magnetic density for the exterior volume r> R is unbounded. This result is now consistent with the fact that the cartesian components of B satisfy the Helmholtz equation.

scholarly journals Linear Force-free Magnetic Fields and Coronal Models

1989 ◽  
Vol 42 (3) ◽  
pp. 317 ◽  
Author(s):  
CJ Durrant
Keyword(s):  
Boundary Condition ◽  
Magnetic Fields ◽  
Helmholtz Equation ◽  
Normal Component ◽  
Coordinate Systems ◽  
Mathematical Properties ◽  
Cylindrical Coordinate ◽  
Linear Force ◽  
Free Fields

The mathematical properties of linear force-free fields generated by the Helmholtz equation are reviewed, and the solutions in terms of spherical, cartesian and cylindrical coordinate systems are discussed. When only the normal component of the field on a single (photospheric) surface is available as a boundary condition, the solutions are not niquely determined. If further conditions are imposed, solutions may be unique or multiple or may not exist. The

A Test on Two Codes for Extrapolating Solar Linear Force-free Magnetic Fields

Solar Physics ◽  
2009 ◽  
Vol 260 (1) ◽  
pp. 109-124 ◽  
Author(s):  
Yiwei Li ◽  
Guoxiang Song ◽  
Junlin Li
Keyword(s):  
Magnetic Fields ◽  
Linear Force

scholarly journals On the stability of a general magnetic field topology in stellar radiative zones

2019 ◽  
Vol 82 ◽  
pp. 365-371
Author(s):  
K. Augustson ◽  
S. Mathis ◽  
A. Strugarek
Keyword(s):  
Magnetic Field ◽  
Global Change ◽  
Magnetic Fields ◽  
Potential Energy ◽  
Massive Stars ◽  
Spherical Geometry ◽  
Stable Region ◽  
Magnetic Field Topology ◽  
The Stability ◽  
The Magnetic Field

This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. One such instability is the purely magnetic Tayler instability, which can occur for poloidal, toroidal, and mixed poloidal-toroidal axisymmetric magnetic field configurations. However, most of the magnetic field configurations observed at the surface of massive stars are non-axisymmetric. Thus, extending earlier studies in spherical geometry, we introduce a formulation for the global change in the potential energy contained in a convectively-stable region for both axisymmetric and non-axisymmetric magnetic fields.

scholarly journals Topological study of active region 11158

2013 ◽  
Vol 8 (S300) ◽  
pp. 479-480
Author(s):  
Jie Zhao ◽  
Hui Li ◽  
Etienne Pariat ◽  
Brigitte Schmieder ◽  
Yang Guo ◽  
...  
Keyword(s):  
Active Region ◽  
Magnetic Fields ◽  
Free Field ◽  
Three Dimensional ◽  
Projection Data ◽  
Solar Dynamics Observatory ◽  
Equal Area ◽  
Linear Force ◽  
Solar Dynamics ◽  
Force Free Field

AbstractWith the cylindrical equal area (CEA) projection data from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO), we reconstructed the three-dimensional (3D) magnetic fields in the corona, using a non-linear force-free field (NLFFF) extrapolation method every 12 minutes during five days, to calculate the squashing degree factor Q in the volume. The results show that this AR has an hyperbolic flux tube (HFT) configuration, a typical topology of quadrupole, which is stable even during the two large flares (M6.6 and X2.2 class flares).

scholarly journals Exact solutions of asymmetric baroclinic quasi-geostrophic dipoles with distributed potential vorticity

2019 ◽  
Vol 868 ◽  
Author(s):  
A. Viúdez
Keyword(s):  
Exact Solution ◽  
Velocity Field ◽  
Potential Vorticity ◽  
Bessel Functions ◽  
Three Dimensional ◽  
Geophysical Flows ◽  
Radial Dependence ◽  
Vortex Dipole ◽  
Second Mode ◽  
Vorticity Anomaly

An exact solution of a baroclinic three-dimensional vortex dipole in geophysical flows with constant background rotation and constant background stratification is provided under the quasi-geostrophic (QG) approximation. The motion of the dipole is unsteady but the potential vorticity contours move rigidly. The vortex comprises three potential vorticity anomaly modes, with a radial dependence given by the spherical Bessel functions and with azimuthal and polar dependences given by the spherical harmonics. The first mode, or spherical mode, accounts for the horizontal asymmetry of the vortex dipole and curvature of the dipole’s horizontal trajectory. The second mode, or dipolar mode, accounts for the speed of displacement of the vortex dipole. A third mode, or vertical tilting mode, accounts for the dipole’s vertical asymmetry. The QG vertical velocity field has two contributions: the first one is octupolar and depends entirely on the dipolar mode, and the second one is dipolar and depends on the nonlinear interaction between dipolar and vertical tilting modes.

scholarly journals Force-Free Models of Filament Channels

1998 ◽  
Vol 167 ◽  
pp. 274-277
Author(s):  
A.W. Longbottom
Keyword(s):  
Magnetic Fields ◽  
Multigrid Method ◽  
Flux Distribution ◽  
Free Field ◽  
Idealized Model ◽  
System A ◽  
Filament Channel ◽  
Linear Force ◽  
Field Lines ◽  
Force Free Field

AbstractA fast multigrid method to calculate the linear force-free field for a prescribed photospheric flux distribution is outlined. This is used to examine an idealized model of a filament channel. The magnetic fields, for a number of different field strengths and positions, are calculated and the height up to which field lines connect along the channel is examined. This is shown to strongly depend on the value of the helicity of the system. A possible explanation, in terms of the global helicity of the system, is suggested for the dextral/sinistral hemispheric pattern observed in filament channels.

Sign in / Sign up

Export Citation Format

Share Document