Nonlocal Nonlinear Electrostatic Gyrofluid Equations: A four-moment   model
  Extending a previous single-temperature model, an electrostatic gyrofluid model that includes anisotropic temperatures (parallel and perpendicular) and can treat general nonlinear situations is constructed. The model is based on a Lagrangian formulation of gyrofluid dynamics, which leads to an exact energy conservation law. Diamagnetic cancelations are inserted manually in such a way that energy conservation is preserved. Comparison with previous models shows a very good agreement for zero-Larmor-radius terms in the gyrofluid equations of motion. 
D. Strintzi, B. D. Scott and A. J. Brizard