Applications of Lie groups to the theory of equilibrium of cylindrically symmetric magnetic flux tubes
Abstract
A group analysis of differential equations for the selfconsistent equilibrium of cylindrically symmetric magnetic flux tubes is presented. The existence of nonMaxwellian distribution functions, which make it possible to find analytical expressions for magnetic field and plasma density, is proved. The distribution functions are assumed to depend only on constants of motion, which makes it possible to formulate and solve the group classification problem for nonlinear thirdorder differential equations. Analytical solutions to differential equations with a nontrivial symmetry group are calculated. The results can be used to analyze fractal properties of plasma configurations in solar and stellar atmospheres for different distribution functions.
 Publication:

Astronomicheskii Zhurnal
 Pub Date:
 February 1992
 Bibcode:
 1992AZh....69..147Z
 Keywords:

 Lie Groups;
 Magnetic Flux;
 Plasma Density;
 PlasmaElectromagnetic Interaction;
 Solar Atmosphere;
 Stellar Atmospheres;
 Distribution Functions;
 Equilibrium Equations;
 Magnetic Field Configurations;
 Self Consistent Fields;
 Astrophysics