Stochastic Equations of Hydrodynamic Theory of Plasma

Abstract

Stochastic equations of the hydrodynamic theory of plasma are presented in relation to strong external fields. It is shown that the use of these stochastic equations makes it possible to obtain new theoretical solutions for plasma as a result of its heating in a strong external electric field. Theoretical solutions for the conductivity of turbulent plasma when heated in an external electric field of 100 V/cm are considered. Calculated values for the electron drift velocity, electron mobility, electron collision frequency, and the Coulomb logarithm in the region of strong electric fields are obtained. Here we consider experiments on turbulent heating of hydrogen plasma in the range of electric field strength of 100 < E < 1000. The calculated dependences of plasma conductivity are in satisfactory agreement with experimental data for heating plasma in a strong electric field. It is shown that the plasma turbulence in the region of strong electric fields E ~1000 V/cm is close to 100%. For the first time, it is confirmed that the derived dependences for collision frequency, drift velocity, and other values include the degree of turbulence of plasma, which makes it possible to correctly describe experimental data for heating plasma even with strong electric fields. In addition, it was determined that the scatter of experimental data may be associated with the variability of the function in the expression for the heat flux density. For the first time, it is shown theoretically that the experimentally determined fact of the possibility of the existence of an approximate constancy of plasma conductivity in the region E = 100–1000 V/cm can occur with an error of ~30%. The results show significant advantages of the stochastic hydrodynamic plasma theory over other methods that are not yet able to satisfactorily as well as qualitatively and quantitatively predict long-known experimental data while taking into account the degree of turbulence.

Keywords

• stochastic equations
• equivalence of measures
• hydrodynamic theory of plasma