Unexpanded nonlinear electromagnetic gyrokinetic equations for magnetized plasmas

Nonlinear electromagnetic gyrokinetic equations have been constructed without expanding the field variables into background and finite but small-amplitude fluctuating components. At the long-wavelength limit, these unexpanded nonlinear gyrokinetic equations recover the well-known drift-kinetic equations. At the expanded limit, they recover the usual nonlinear gyrokinetic equations. These equations can therefore be applied to long-term simulations covering from microscopic to macroscopic spatial scales.