Conservation equations and calculation of mean flows in gyrokinetics

Conservation equations are derived for the gyrocenter toroidal momentum density and the polarization field. These equations are derived from the gyrokinetic model as it is implemented in simulation codes. In view of predicting the toroidal rotation in future fusion devices such as ITER, where external momentum input will be small, accurate simulations of momentum transport are crucial. The evolution equation for gyrocenter toroidal momentum density involves the divergence of the off-diagonal components of the Reynolds and generalized Maxwell stress, while the source term is the radial current of gyrocenters. The time evolution of the polarization field is the opposite of the gyrocenter current. Hence, an evolution equation for the total momentum density, i.e., the sum of gyrocenter and polarization field toroidal momentum density can be written. The force balance equation and the toroidal momentum conservation equations have been numerically tested with the gysela code. They are satisfied with a high level of accuracy. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3620407]