Nonlinear gyrokinetics of high   axisymmetric plasmas

The authors derive the nonlinear gyrokinetic equation for axisymmetric plasmas in its most general form, i.e. including finite beta , collisions, driving toroidal electric field, and, accordingly, non-Maxwellian, poloidally dependent unperturbed distribution functions. The authors note the relation between the assumption of radial periodicity of the linear eigenfunction-the period being a multiple of the distance between rational surfaces-and the ballooning representation. They remark that this assumption is not justified in the presence of nonlinear interactions, and, from there, suggest a possible saturation mechanism of the potentially dangerous toroidicity induced modes.