Transport processes: Perturbations propagation, the local time concept and experimental data for perturbations propagation in plasma

Classical equations for transport processes predict infinite speed of the perturbations propagation. From molecular point of view, this feature is rather doubtful, because, for instance in gas or plasma, any perturbation propagates as a result of molecules or charged particles (ions, electrons) interaction. In the present work, exact statistical description of the perturbations propagation in gas and plasma is presented based on the Boltzmann equation written in the most general form. As a result of statistical analysis, for transport processes in the systems with zero or small hydrodynamic velocity, the local time concept and the eikonal type equation for 3D propagation of the perturbations with varying speed are formulated. The local time concept shows how classical transport equations predicting infinite speed of the perturbations propagation, must be modified in order to describe transport processes with finite speed of the perturbations propagation. I also determine conditions, when solutions of classical transport governing equations are accurate enough in the case of finite speed of the perturbations propagation. Three dimensional heat conduction governing equation with finite speed of heat propagation is derived, and illustrative examples of its analytical solutions are obtained and analyzed. Three dimensional governing equation for non-compressible viscous fluid with finite speed of the perturbations propagation is formulated, and its particular analytical solution is derived and studied. Experimental data for thermal perturbations propagation in magnetically confined fusion plasma is compared with the theoretical predictions.