Polarization and magnetization laws in collisional and turbulent transport processes

Global simulations of collisional and turbulent plasma transport are now vigorously conducted based on gyrokinetic equations using the gyrocenter coordinates that are derived from the Lie transformation method. Such gyrokinetic equations possess conservation properties which are suitable for global and long-time transport simulations. It is well-known that the finite distance between particle and gyrocenter positions generates so-called polarization and magnetization laws, which relate the density and mean velocity of particles to those of gyrocenters, respectively. These relations are important for using gyrokinetic simulation results to correctly evaluate particle transport as well as to accurately calculate the charge density and the electric current in Poisson and Ampère equations which are required to self-consistently determine electromagnetic fields in the simulation. In the present study, expressions of polarization and magnetization laws including effects of collisions and gyroradius scale electromagnetic turbulence are presented. It is shown that collisional effects appear in the magnetization law as an additional term representing the classical particle flux of second order in the normalized gyroradius parameter which becomes influential in transport time scale. The turbulent parts of Poisson and Ampère equations obtained here are verified to agree with the gyrokinetic Poisson and Ampère equations derived in earlier works using the WKB representation.