Equivalence of two independent calculations of the higher order guiding center Lagrangian

TL;DR

This paper demonstrates that the difference between two higher order guiding center Lagrangians arises from different definitions of guiding center coordinates, providing an explicit calculation of this coordinate difference.

Contribution

It explicitly calculates the difference in guiding center coordinates used in two independent derivations of the higher order guiding center Lagrangian.

Findings

The difference is due to coordinate definition choices.

Explicit calculation of coordinate differences clarifies the equivalence.

Reconciles two previously separate formulations.

Abstract

The difference between the guiding center phase-space Lagrangians derived in [J.W. Burby, J. Squire, and H. Qin, Phys. Plasmas {\bf 20}, 072105 (2013)] and [F.I. Parra, and I. Calvo, Plasma Phys. Control. Fusion {\bf 53}, 045001 (2011)] is due to a different definition of the guiding center coordinates. In this brief communication the difference between the guiding center coordinates is calculated explicitly.