Complementary Variational Principles on Electrical Conductivities of a Plasma in a Uniform Magnetic Field

摘要

Several functionals, whose Euler-Lagrange equations are the kinetic equations for the velocity-distribution functions, are derived. The extremal values of these functionals are proved to be proportional to the Ohm conductivity exp + sup( i) or to the Hall conductivity exp + sup( i i). The complementary variational principles for exp + sup( i) and exp + sup( i i), 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. (Atomindex citation 10:489217)