Rotating Gyrokinetics with Poloidal and Toroidal Rotation

A canonical transformation was found in Ref. [1] that includes poloidal and toroidal rotation in a Vlasov equilibrium distribution function. The magnetic field is required to have closed nested flux surfaces but does not need to be axisymmetric. This starting point is extended to a gyro-kinetic equation in the transformed Lagrangian phase space. It is found to be much easier to include rotation first into the Vlasov equation and then gyro-average to obtain a reduced gyro-kinetic equation than it is to try and add rotation to the gyrokinetic equation directly. The contribution to the gyrokinetic equation obtained has a simple form in vector notation. There are velocity shear and Coriolis terms for both the toroidal and poloidal rotation components. Higher order ``obit squeezing'' terms are also found from the canonical transformation. Similarities and differences with previous work will be presented. \vskip6pt \noindent [1] G.M. Staebler, Phys. Plasmas 11, 1064 (2004).