Drift kinetic equation in the moving reference frame and reduced magnetohydrodynamic equations

Smolyakov, A. I.; Garbet, X.
April 2010
Physics of Plasmas;Apr2010, Vol. 17 Issue 4, p042105
Academic Journal
The drift kinetic equation is formulated by using the phase space conservation law and drift equations of particle motion in the reference frame moving with plasma fluid velocity. The latter includes the parallel and ExB drift, diamagnetic velocity, and diamagnetic velocity due to the parallel viscosity tensor (anisotropic pressure). It is shown explicitly that the particle drift equations conserve the adiabatic invariant and kinetic equation conserves the phase space volume. The resulting drift kinetic equation is used to obtain a set of moment equations corresponding to the conservation laws for plasma density, momentum, and energy. These equations are compared with reduced equations obtained from hierarchy of extended magnetohydrodynamic equations including the evolution equation for the heat flux (Grad hydrodynamics). The reduction is done in the drift limit by using 1/B as an expansion parameter. We demonstrate that reduced moment equations derived from our drift kinetic equation are identical to the reduced equations obtained from extended magnetohydrodynamic equations. The structure of the reduced equations and implications for the closure problem, including neoclassical effects, are discussed.


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