Fluid equations for temperature anisotropy based on kinetic drifts

Moments of the Boltzmann equations describing transport of plasma and anisotropic forms of energy are derived for ions and/or electrons. Formal closure of the moment equations is obtained by a standard reduction technique applied to the fourth moment. It is shown how the heat-flow tensor can be decomposed into four separate tensors describing the flows of parallel and perpendicular energy in the directions parallel and perpendicular to the magnetic field; the solutions for these tensors are obtained from ten coupled equations. The transport of plasma density n and perpendicular and parallel temperatures T-parallel to and T-perpendicular to can be described by three strongly coupled nonlinear differential equations characterized by an advective velocity which is the fluid analogue of the guiding centre drift velocity. The transport equations show how specific kinetic drift mechanisms contribute to transport driven by gradients in n, T-parallel to and T-perpendicular to and by gradients in the electric and magnetic fields; collisional effects are included and involve separate calculations of collision integrals. Finite-Larmor-radius, 'gyro-fluid' or micro-turbulence effects cannot be described by the equations derived.