arXiv:0710.4972v1 [physics.plasm-ph] 26 Oct 2007 Nonlinear polarisation and dissipative correspondence between low frequency fluid and gyrofluid equations Bruce D. Scott ∗ Max-Planck-Institut f¨ ur Plasmaphysik, Euratom Association, D-85748 Garching, Germany (Dated: February 2, 2008) Abstract The correspondence between gyrofluid and low frequency fluid equations is examined. The lowest order conservative effects in ExB advection, parallel dynamics, and curvature match trivially. The principal concerns are polarisation fluxes, and dissipative parallel viscosity and parallel heat fluxes. The emergence of the polarisation heat flux in the fluid model and its contribution to the energy theorem is reviewed. It is shown that gyroviscosity and the polarisation fluxes are matched by the finite gyroradius corrections to advection in the long wavelength limit, provided that the differences between gyrocenter and particle representations is taken into account. The dissipative parallel viscosity is matched by the residual thermal anisotropy in the gyrofluid model in the collision dominated limit. The dissipative parallel heat flux is matched by the gyrofluid parallel heat flux variables in the collision dominated limit. Hence, the gyrofluid equations are a complete superset of the low frequency fluid equations. PACS numbers: 52.65.Tt, 52.35.Ra, 52.30.-q, 52.25.Fi * email: bds@ipp.mpg.de; URL: http://www.rzg.mpg.de/ ∼ bds/ 1