The Transport Coefficients Of Power-law Distributed Nonequilibrium Plasmas In Nonextensive Statistics

Statistical mechanics is a foundational theory to describe the properties of complex systems.However,the traditional Boltzmann-Gibbs statistical mechanics cannot describe the nonequilibrium state of the system.In recent years,the power-law velocity kappa long tail distribution has successfully fitted the astronomical observation data,The power-law velocity q-distribution function is derived from the nonextensive statistical mechanics.However,the physical meaning of the parameters in the power-law distribution is not clear.In order to understand the nonextensibility of the system,the nonextensive statistical theory of plasma transport process is studied in this paper,namely,in the framework of nonextensive statistical mechanics,the power-law velocity q-distribution function is used to study the diffusion flux and heat flux caused by the particle number gradient,temperature gradient and electric potential gradient,as well as the momentum flux caused by bulk velocity gradient in the nonequilibrium plasma under the conditions of the weakly ionized unmagnetized,weakly ionized magnetized and fully ionized strong magnetic field.Then the transport coefficients describing the linear relationship between "flux" and "force" are obtained,and the physical significance of the nonextensive q-parameter in the transport coefficients is analyzed by drawing.This paper mainly discusses the following contents.Firstly,we study the momentum flux caused by the bulk velocity gradient in the weakly ionized q-distributed unmagnetized plasma.The Krook collision term under the nonextensive dynamics is used to describe the collision processes between charged particles and neutral particles in the plasma.The matrix elements of momentum flux tensor of the plasma under the nonextensive statistical mechanics are calculated.Combined with the Navier-Stokes equation,the first viscosity coefficient,second viscosity coefficient and pressure dependent on q-parameter are derived.Secondly,we study the effect of the magnetic field on the momentum flux of the weakly ionized q-distributed magnetized plasma.The momentum flux tensor of the magnetized plasma under the nonextensive statistical mechanics is calculated by using the nonextensive dynamic equation with the magnetic field term.Combined with the macroscopic law of viscosity stress tensor,six viscosity coefficients dependent on q-parameter are derived,including five first viscosity coefficients and the second viscosity coefficient.Thirdly,we study the diffusion flux and heat flux caused by the particle number gradient,temperature gradient and electric potential gradient in the weakly ionized q-distributed magnetized plasma.The diffusion flux and heat flux of the plasma under the nonextensive statistical mechanics are calculated.Combined with the macroscopic law of diffusion flux and the generalized Fourier law,the diffusion,thermal diffusion coefficient,thermal conductivity tensor dependent on q-parameter,as well as mobility tensor independent of q-parameter are derived.The matrix elements of the above transport coefficients include longitudinal,transverse and Hall transport coefficients respectively.Fourthly,we study the current caused by temperature gradient and electric potential gradient in the fully ionized q-distributed magnetized plasma.The Fokker-Planck collision term under the nonextensive dynamics is used to describe the electron-ion collision process in the magnetized plasma,and the transverse current in the plasma under nonextensive statistical mechanics is calculated.Combined with the generalized Ohm law,the transverse conductivity,transverse thermoelectric coefficient,and Nernst coefficient dependent on q-parameter,as well as Hall coefficient independent of q-parameter are derived.Fifthly,we study the average collision frequencies of the weakly and highly ionized q-distributed plasma.For weakly and highly ionized plasmas,the rigid sphere collision model and Coulomb scattering model are used respectively,the average collision frequencies of electron-neutral particle,ion-neutral particle,neutral-neutral particle,electron-ion,electron-electron and ion-ion collisions are calculated in the frame of the nonextensive statistical mechanics,where the influence of q-parameter on the average collision frequencies of weakly ionized and highly ionized plasmas is different.