Physics
Scientific paper
Aug 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986soph..106..287w&link_type=abstract
Solar Physics (ISSN 0038-0938), vol. 106, Aug. 1986, p. 287-313.
Physics
10
Conservation Laws, Magnetic Field Configurations, Magnetohydrodynamic Stability, Magnetohydrostatics, Similarity Theorem, Solar Atmosphere, Elliptic Differential Equations, Gas Pressure, Liouville Equations, Nonlinear Equations, Solar Physics
Scientific paper
The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.
No associations
LandOfFree
Similarity considerations and conservation laws for magneto-static atmospheres does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Similarity considerations and conservation laws for magneto-static atmospheres, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Similarity considerations and conservation laws for magneto-static atmospheres will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-895548