422 research outputs found
Three-dimensional analytical magnetohydrostatic equilibria of rigidly rotating magnetospheres in cylindrical geometry
We present three-dimensional solutions of the magnetohydrostatic equations in
the co-rotating frame of reference outside a magnetized rigidly rotating
cylinder. We make no symmetry assumption for the magnetic field, but to be able
to make analytical progress we neglect outflows and specify a particular form
for the current density. The magnetohydrostatic equations can then be reduced
to a single linear partial differential equation for a pseudo-potential ,
from which the magnetic field can be calculated by differentiation. The
equation for can be solved by standard methods. The solutions can also be
used to determine the plasma pressure, density and temperature as functions of
all three spatial coordinates. Despite the obvious limitations of this
approach, it can for example be used as a simple tool to create
three-dimensional models for the closed field line regions of rotating
magnetospheres without rotational symmetry.Comment: 13 pages, 2 figures, accepted for publication by Geophysical and
Astrophysical Fluid Dynamic
Collisionless distribution function for the relativistic force-free Harris sheet
A self-consistent collisionless distribution function for the relativistic analogue of the force-free Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the non-relativistic collisionless force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3677268]PostprintPeer reviewe
Particle energisation in a collapsing magnetic trap model : the relativistic regime
The authors acknowledge financial support by the UK’s Science and Technology Facilities Council through a Doctoral Training Grant (SEO) and Consolidated Grant ST/K000950/1 (SEO and TN).Context. In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation. Aims. In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the non-relativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Methods. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the non-relativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and non-relativistic particle orbits mainly agree well, but clear deviations are seen for higher energies. In particular, the final particle energies obtained from the relativistic calculations are systematically lower than the energies reached from the corresponding non-relativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding non-relativistic orbits. Conclusions. While the overall behaviour of particle orbits in CMTs does not differ qualitatively when using the relativistic guiding centre equations, there are a few systematic quantitative differences between relativistic and non-relativistic particle dynamics.Publisher PDFPeer reviewe
Singular inextensible limit in the vibrations of post-buckled rods: analytical derivation and role of boundary conditions
In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load
Computing nonlinear force free coronal magnetic fields
International audienceKnowledge of the structure of the coronal magnetic field is important for our understanding of many solar activity phenomena, e.g. flares and CMEs. However, the direct measurement of coronal magnetic fields is not possible with present methods, and therefore the coronal field has to be extrapolated from photospheric measurements. Due to the low plasma beta the coronal magnetic field can usually be assumed to be approximately force free, with electric currents flowing along the magnetic field lines. There are both observational and theoretical reasons which suggest that at least prior to an eruption the coronal magnetic field is in a nonlinear force free state. Unfortunately the computation of nonlinear force free fields is way more difficult than potential or linear force free fields and analytic solutions are not generally available. We discuss several methods which have been proposed to compute nonlinear force free fields and focus particularly on an optimization method which has been suggested recently. We compare the numerical performance of a newly developed numerical code based on the optimization method with the performance of another code based on an MHD relaxation method if both codes are applied to the reconstruction of a semi-analytic nonlinear force-free solution. The optimization method has also been tested for cases where we add random noise to the perfect boundary conditions of the analytic solution, in this way mimicking the more realistic case where the boundary conditions are given by vector magnetogram data. We find that the convergence properties of the optimization method are affected by adding noise to the boundary data and we discuss possibilities to overcome this difficulty
Including stereoscopic information in the reconstruction of coronal magnetic fields
We present a method to include stereoscopic information about the three
dimensional structure of flux tubes into the reconstruction of the coronal
magnetic field. Due to the low plasma beta in the corona we can assume a force
free magnetic field, with the current density parallel to the magnetic field
lines. Here we use linear force free fields for simplicity. The method uses the
line of sight magnetic field on the photosphere as observational input. The
value of is determined iteratively by comparing the reconstructed
magnetic field with the observed structures. The final configuration is the
optimal linear force solution constrained by both the photospheric magnetogram
and the observed plasma structures. As an example we apply our method to SOHO
MDI/EIT data of an active region. In the future it is planned to apply the
method to analyse data from the SECCHI instrument aboard the STEREO mission.Comment: 18 pages, 7 figure
Negative Specific Heat of a Magnetically Self-Confined Plasma Torus
It is shown that the thermodynamic maximum entropy principle predicts
negative specific heat for a stationary magnetically self-confined
current-carrying plasma torus. Implications for the magnetic self-confinement
of fusion plasma are considered.Comment: 10p., LaTeX, 2 eps figure file
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