86 research outputs found
An Iterative Method for Solving Non-Linear Hydromagnetic Equations
We propose an iterative finite element method for solving non-linear
hydromagnetic and steady Euler's equations. Some three-dimensional
computational tests are given to confirm the convergence and the high
efficiency of the method
Computing Beltrami Fields
International audienceFor solving the nonlinear equations governing force-free fields, an iterative methodology based on the splitting of the problem is described. On the basis of this splitting, three families of subproblems have to be solved numerically. The first problem consists to find a potential field. A mixed hybrid method is used to solve it. The second problem, which is a curl-div system, is solved by means of a mixed method. The last problem is a transport equation which is approximated using a streamline diffusion technique. Numerical three-dimensional experiments and results are given to illustrate the efficiency of the method
Nonlinear force-free magnetic field extrapolations: comparison of the Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithm
We compare the performance of two alternative algorithms which aim to
construct a force-free magnetic field given suitable boundary conditions. For
this comparison, we have implemented both algorithms on the same finite element
grid which uses Whitney forms to describe the fields within the grid cells. The
additional use of conjugate gradient and multigrid iterations result in quite
effective codes. The Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithms
both perform well for the reconstruction of a known analytic force-free field.
For more arbitrary boundary conditions the Wheatland-Sturrock-Roumeliotis
approach has some difficulties because it requires overdetermined boundary
information which may include inconsistencies. The Grad-Rubin code on the other
hand loses convergence for strong current densities. For the example we have
investigated, however, the maximum possible current density seems to be not far
from the limit beyond which a force free field cannot exist anymore for a given
normal magnetic field intensity on the boundary.Comment: 21 pages, 13 figure
Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Application to Discrete Data
We investigate how the divergence-free property of magnetic fields can be
exploited to resolve the azimuthal ambiguity present in solar vector
magnetogram data, by using line-of-sight and horizontal heliographic derivative
information as approximated from discrete measurements. Using synthetic data we
test several methods that each make different assumptions about how the
divergence-free property can be used to resolve the ambiguity. We find that the
most robust algorithm involves the minimisation of the absolute value of the
divergence summed over the entire field of view. Away from disk centre this
method requires the sign and magnitude of the line-of-sight derivatives of all
three components of the magnetic field vector.Comment: Solar Physics, in press, 20 pages, 11 figure
Nonlinear force-free and potential field models of active-region and global coronal fields during the Whole Heliospheric Interval
Between 2008/3/24 and 2008/4/2, the three active regions NOAA active regions
10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term
Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they
traversed the solar disk. We use these measurements and the nonlinear
force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic
field for each active region and compare model field lines with images from the
Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope
(XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global
Oscillations Network Group (GONG) magnetograms provide information on the
global photospheric field and potential-field source-surface models based on
these maps describe the global coronal field during the Whole Heliospheric
Interval (WHI) and its neighboring rotations. Features of the modeled global
field, such as the coronal holes and streamer belt locations, are discussed in
comparison with extreme ultra-violet and coronagraph observations from STEREO.
The global field is found to be far from a minimum, dipolar state. From the
nonlinear models we compute physical quantities for the active regions such as
the photospheric magnetic and electric current fluxes, the free magnetic energy
and the relative helicity for each region each day where observations permit.
The interconnectivity of the three regions is addressed in the context of the
potential-field source-surface model. Using local and global quantities derived
from the models, we briefly discuss the different observed activity levels of
the regions.Comment: Accepted for publication in the Solar Physics Whole Heliospheric
Interval (WHI) topical issue. We had difficulty squeezing this paper into
arXiv's 15 Mb limit. The full paper is available here
ftp://gong2.nso.edu/dsds_user/petrie/PetrieCanouAmari.pd
How to optimize nonlinear force-free coronal magnetic field extrapolations from SDO/HMI vector magnetograms?
The SDO/HMI instruments provide photospheric vector magnetograms with a high
spatial and temporal resolution. Our intention is to model the coronal magnetic
field above active regions with the help of a nonlinear force-free
extrapolation code. Our code is based on an optimization principle and has been
tested extensively with semi-analytic and numeric equilibria and been applied
before to vector magnetograms from Hinode and ground based observations.
Recently we implemented a new version which takes measurement errors in
photospheric vector magnetograms into account. Photospheric field measurements
are often due to measurement errors and finite nonmagnetic forces inconsistent
as a boundary for a force-free field in the corona. In order to deal with these
uncertainties, we developed two improvements: 1.) Preprocessing of the surface
measurements in order to make them compatible with a force-free field 2.) The
new code keeps a balance between the force-free constraint and deviation from
the photospheric field measurements. Both methods contain free parameters,
which have to be optimized for use with data from SDO/HMI. Within this work we
describe the corresponding analysis method and evaluate the force-free
equilibria by means of how well force-freeness and solenoidal conditions are
fulfilled, the angle between magnetic field and electric current and by
comparing projections of magnetic field lines with coronal images from SDO/AIA.
We also compute the available free magnetic energy and discuss the potential
influence of control parameters.Comment: 17 Pages, 6 Figures, Sol. Phys., accepte
Nonlinear force-free modeling of the solar coronal magnetic field
The coronal magnetic field is an important quantity because the magnetic
field dominates the structure of the solar corona. Unfortunately direct
measurements of coronal magnetic fields are usually not available. The
photospheric magnetic field is measured routinely with vector magnetographs.
These photospheric measurements are extrapolated into the solar corona. The
extrapolated coronal magnetic field depends on assumptions regarding the
coronal plasma, e.g. force-freeness. Force-free means that all non-magnetic
forces like pressure gradients and gravity are neglected. This approach is well
justified in the solar corona due to the low plasma beta. One has to take care,
however, about ambiguities, noise and non-magnetic forces in the photosphere,
where the magnetic field vector is measured. Here we review different numerical
methods for a nonlinear force-free coronal magnetic field extrapolation:
Grad-Rubin codes, upward integration method, MHD-relaxation, optimization and
the boundary element approach. We briefly discuss the main features of the
different methods and concentrate mainly on recently developed new codes.Comment: 33 pages, 3 figures, Review articl
The spectrum of a weighted Laplacian in the half-space
J. Banasiak In this paper, we deal with spectral properties of a weighted Laplacian in the half-space when a Dirichlet or a Neumann boundary condition is imposed. After proving that the spectrum is discrete under suitable assumptions, we give explicit formulae of eigenvalues and eigenfunctions in a specific case. In particular, the obtained eigenfunctions are rational or pseudo-rational and have remarkable orthogonality properties. These results suggest the use of the discovered functions for approximating solutions of elliptic problems in the half-space. Copyright (c) 2015John Wiley and Sons, Ltd
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