Analysis of the polarization effects in the gyrokinetic theory of magnetized plasmas

By adopting the hybrid coordinates, in which the nonlinearity of polarization displacement is included in the configuration space variables compared to the conventional gyrocenter coordinates, the polarization effects are analyzed by using the modern gyrokinetic (GK) theory of magnetized plasmas. Based on the invariant property, the velocity transformation between the gyrocenter and hybrid coordinates is calculated, and the phase-space velocity in terms of the hybrid coordinates is obtained. The linear and nonlinear polarization distribution functions are defined, and the evolutions for the polarization distribution functions are derived. It is well known that the polarization density is important in the GK calculation of particle density. Analogously, it is shown that the polarization current should be considered in the GK calculation of current density. In the case with electrostatic fluctuations, the roles of the polarization current are illustrated in the derivations of the Hasegawa-Mima equation and the dispersion relation for geodesic acoustic mode. In the case with magnetic fluctuations, the procedure for the GK calculation of perpendicular current is clarified, the dispersion relation for compressional Alfven wave is derived, in which the effect of polarization current is discussed.

Automated summary

This study analyzes the polarization effects in magnetized plasmas using modern gyrokinetic theory by adopting hybrid coordinates, and derives the evolution of polarization distribution functions while discussing the role of polarization current in current density calculations. It clarifies the procedures for GK calculations of perpendicular current in the presence of magnetic fluctuations and discusses the impact of polarization current on dispersion relations for compressional Alfven waves.