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

Abstract

We find that the perturbed Lagrangian derived from the drift-kinetic equation in the paper [Porcelli F et al 1994 Phys. Plasmas 1 470] is inconsistent with the ordering for the low-frequency large-scale MHD. Here, we rederive the expression for the perturbed Lagrangian in the framework of nonideal MHD by 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 field curvature and gradient are small quantities of higher order and thus negligible. As the perturbed Lagrangian has been widely used in literatures to calculate the plasma nonadiabatic response in low-frequency MHD applications, this finding may have 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.

The magnetic coherent mode with shifted Alfvén gap frequency destabilized by the thermal trapped electron resonance in the pedestal of high-confinement tokamak plasmas

“…For the ordering system for low-frequency largescale MHD (i.e. the radial mode structure is relatively large in comparison with the ion gyro-radius ρ s k ⊥ ≪ 1, and the mode frequency is much smaller than the ion cyclotron frequency ω/ ω ci ≪ 1) [52,53], the drift-kinetic theory is valid for this study. Then, based on the linear analysis of driftkinetic theory [53], the total distribution function of thermal electrons could be expressed as f = f 0 + fadi + h including the equilibrium term f 0 , the adiabatic perturbation term fadi and the non-adiabatic perturbation term h. It should be pointed out that the perturbed physical quantities in the previous fluid module could be exactly obtained by taking moments of the adiabatic perturbation term fadi [34], which will not be discussed in this drift kinetic module.…”

“…l = 1 for resonance with a single bounce). Furthermore, via a systematic ordering analysis [52], the revised perturbation of Lagrangian L to the leading order for the low-frequency dynamics is adopted in this model as follows, which is consistent with the gyrokinetic form [10],…”

Role of electrostatic perturbation on kinetic resistive wall mode with application to spherical tokamak

“…We make two remarks here on the above form of the particle Lagrangian, which was also derived by Littlejohn [24] and Antonsen [25] assuming ideal MHD. First, a recent work [26] derived another form of Lagrangian assuming resistive MHD. Whilst the new form can be useful in describing the particle dynamics within the resistive layer, the drift kinetic effects that we consider here are due to the mode-particle resonances in global regions, in particular in those regions outside the resistive layer where the plasma can be regarded as ideal (note that we solve the ideal MHD equation ( 3) in this work).…”