Exact momentum conservation laws for gyrofluid and gyrokinetic models*

Exact momentum conservation laws for gyrofluid and gyrokinetic models are derived by Noether method applied to the gyrofluid [1] and gyrokinetic [2,3] action functionals, respectively. As a result of the separation of a nonuniform (and time-independent) background magnetic field from the time-dependent dynamical fields, the gyrofluid and gyrokinetic momentum-stress tensors are asymmetric, which implies transport of angular momentum. The nature of the momentum-stress asymmetry for the gyrofluid model [1] is discussed in terms of reduced polarization and magnetization effects. The conservation of momentum for the gyrokinetic model [4], on the other hand, involves the Hamiltonian dynamics of the gyrocenter canonical momentum. \\[4pt] [1] A. J. Brizard, R. E. Denton, B. Rogers, and W. Lotko, Phys. Plasmas {\bf 15}, 082302 (2008). \newline \noindent [2] A. J. Brizard, Phys. Plasmas {\bf 7}, 4816 (2000). \newline \noindent [3] A. J. Brizard, Phys. Plasmas {\bf 17}, 042303 (2010). \newline \noindent [4] A. J. Brizard and N. Tronko, in preparation (2010).