On the gyrokinetic equilibrium

Recent developments in gyrokinetic-magnetohydrodynamics (MHD) theory and in electromagnetic gyrokinetic particle simulations raise the question of con sistency between the gyrokinetic model and the fluid model. Due to the spec ial characteristics of the guiding center coordinates, it is a nontrivial e xercise to show this consistency. In this paper it is shown, in a very gene ral setting, that the gyrokinetic theory and the fluid equations do give an equivalent description of plasma equilibrium (partial derivative/partial d erivative t = 0). The fluid continuity equation and momentum equation for e quilibrium plasmas are recovered entirely from the gyrokinetic theory. Howe ver, it was Spitzer who first realized the importance of consistency betwee n guiding-center motion and fluid equations. In particular, he studied the "apparent paradoxical result" regarding the difference between perpendicula r particle flow and guiding-center flow, which will be referred to as the S pitzer paradox in this paper. By recovering the fluid equations from the gy rokinetic theory, we automatically resolve the Spitzer paradox, whose essen ce is how the perpendicular current and flow are microscopically generated from particles' guiding-center motion. The mathematical construction in the gyrokinetic theory which relates observable quantities in the laboratory f rame to the distribution function in the guiding-center coordinates is cons istent with Spitzer's original physical picture, while today's gyrokinetic- MHD theory covers a much wider range of problems in a much more general and quantitative way. (C) 2000 American Institute of Physics. [S1070-664X(00)0 5202-2].