Complementary Variational Principles on Electrical Conductivities of a Plasma in a Unifrom Magnetic Field
Abstract
Several functionals, whose EulerLagrange equations are the kinetic equations for the velocitydistribution functions, are derived. The extremal values of these functionals are proved to be proportional to the Ohm conductivity σ^{I} or to the Hall conductivity σ^{II}. The complementary variational principles for σ^{I} and σ^{II}, which give both lower and upper bounds, are derived by use of these functionals. These principles are applied to a plasma composed of electrons and singly charged positive ions. The results of computations by use of simple trial functions show that the complementary variational principles derived in this paper are very useful.
 Publication:

Journal of the Physical Society of Japan
 Pub Date:
 March 1979
 DOI:
 10.1143/JPSJ.46.975
 Bibcode:
 1979JPSJ...46..975K
 Keywords:

 Electrical Resistivity;
 Magnetic Fields;
 Plasma Conductivity;
 Variational Principles;
 Collisional Plasmas;
 Functionals;
 Hall Effect;
 Kinetic Equations;
 Plasma Physics