Equivalence of measures and stochastic equations of hydrodynamic theory of plasma

Abstract

Stochastic equations of hydrodynamic theory of plasma are presened. The article shows that for transfer processes in liquid and gas, on the one hand, and in plasma, on the other hand, there exist sets of stochastic differential equations for substantial quantities based on the equality of measures between deterministic motion and random motion. It is shown that the application of these stochastic equations makes it possible to obtain new theoretical solutions for the occurrence of turbulence also for a plasma as a result of its heating in an external electric field instead of only for a classical gas, as it was proved previously. Theoretical solutions for the conductivity of turbulent plasma during its heating in an external electric field are considered. At a first time taking into account the turbulence parameters theoretical relations for the electron drift velocity and corresponding relations for electron mobility, for the frequency of electron collisions, and for the Coulomb integral are obtained. All theoretical relations are applied to calculate the conductivity during the turbulent heating of plasma in an electric field. Here experiments with hydrogen plasma are being considered. The theoretical explanation of the cause for the existence of a constant conductivity in the field of strength \(E = 0.6-19\) V/cm and its fall at \(19<E<100\) V/cm is given. The calculated dependences of plasma conductivity are in satisfactory agreement with experimental data at the electric-field strength in the turbulent region \(E = 0.6-100\) V/cm and in the region \(E < 0.6\) V/cm.The equation for the critical electric-field strength is presented.