The circuit dynamics of plasma

Equations applicable to the behaviour of plasma in bulk are derived and discussed. Starting with the equations of plasma dynamics the total and thermal energy equations are integrated over all space. Certain bulk variables such as the geometrical dimensions of a conductor and the total charge in a circuit are then introduced. Subsequent definition of various circuit parameters and the introduction of generalized e.m.f.´s permit the integrated equations to be expressed in terms of the bulk variables. Using the fact that the total energy is constant, it is possible to obtain the equations of circuit dynamics, applicable to a plasma, in Lagrangian form. The derivation is not rigorous, relying for its validity on physical arguments and the consistency of the final equations with those of plasma dynamics. Again, the proof is confined to cases in which the nature of the functions determining the distribution of mass, current and charge density throughout the volume of a conductor are time-independent. The generalized e.m.f. concept is unfamiliar; it mainly arises from coupling between the electrical and thermal properties of a plasma. It is shown that these e.m.f.´s lead to a form of magneto-resistive coupling and, even in the absence of Hall currents, an apparent anisotropic resistivity. A general proof of the equivalent transformer circuit is given.