Gyroaveraged equations for both the gyrokinetic and drift-kinetic regimes

The regime of validity of nonlinear gyrokinetic equations is extended to cover uniformly both the usual drift-kinetic and gyrokinetic regimes through the use of an expansion in the parameter ε∼(ρ/λ⊥)e(φ−v∥ Az/c)/T. Here, ρ is the gyroradius, λ⊥ is the scale length of the electrostatic and parallel magnetic potentials φ and Az, c is the speed of light, and T is the temperature. This is made possible by a preparatory split of the potentials into gyrophase-dependent and independent parts. For nonlinear fluctuations saturated at mixing-length levels (e.g., with eφ/T∼λ⊥ /L, where L is the equilibrium scale length), ε is of order ρ/L for all scales λ⊥ ranging from ρ to L, and is therefore small in plasmas of fusion interest.