A drift-kinetic perturbed Lagrangian for low-frequency nonideal MHD applications

We find that the perturbed Lagrangian derived from the drift-kinetic equation in Porcelli F et al 1994 Phys. Plasmas 1 470 is inconsistent with the ordering for the low-frequency large-scale magnetohydrodynamic (MHD). Here, we rederive the expression for the perturbed Lagrangian within the framework of nonideal MHD using the ordering system for the low-frequency large-scale MHD in a low-beta plasma. The obtained perturbed Lagrangian is consistent with Chen's gyrokinetic theory Chen L and Zonca F 2016 Rev. Mod. Phys. 88 015008, where the terms related to the field curvature and gradient are small quantities of higher order and thus negligible. As the perturbed Lagrangian has been widely used in the literature to calculate the plasma nonadiabatic response in low-frequency MHD applications, this finding may have a significant impact on the understanding of the kinetic driving and dissipative mechanisms of MHD instabilities and the plasma response to electromagnetic perturbations in fusion plasmas.