LAUSR

The use of gyrokinetics, wherein phase-space coordinate transformations result in a phase-space dimensionality reduction as well as the removal of fast time scales, has enabled the simulation of microturbulence in fusion devices. The state-of-the-art gyrokinetic models used in practice are parallel-only models wherein the perpendicular part of the vector potential is neglected. Such models are inherently not gauge-invariant. We generalise the work of Burby & Brizard (2019 Phys. Lett. A vol. 383, no. 18, pp. 2172–2175) by deriving a sufficient condition on the gyrocentre coordinate transformation that ensures gauge invariance. This leads to a parametrised family of gyrokinetic models for which we motivate a specific choice of parameters that results in the smallest gyrocentre coordinate transformation for which the resulting gyrokinetic model is consistent, gyro-phase independent, gauge-invariant and has an invariant magnetic moment. Due to gauge invariance, this model can be expressed directly in terms of the electromagnetic fields rather than the potentials, and the gyrokinetic model thereby results in the macroscopic Maxwell’s equations. For the linearised model, it is demonstrated that the shear and compressional Alfvén waves are present with the correct frequencies. The fast compressional Alfvén wave can be removed by making use of a Darwin approximation. This approximation retains the gauge invariance of the proposed model.