Accuracy of momentum and gyrodensity transport in global gyrokinetic particle-in-cell simulations

Gyrokinetic Particle-In-Cell (PIC) simulations based on conservative Lagrangian formalisms admit transport equations for conserved quantities such as gyrodensity and toroidal momentum, and these can be derived for arbitrary wavelength, even though previous applications have used the long-wavelength approximation. In control-variate PIC simulations, a consequence of the different treatment of the background (f0) and perturbed parts (δf), when a splitting f = f0 + δf is performed, is that analytical transport relations for the relevant fluxes and moments are only reproduced in the large marker number limit. The transport equations for f can be used to write the inconsistency in the perturbed quantities explicitly in terms of the sampling of the background distribution f0. This immediately allows estimates of the error in consistency of momentum transport in control-variate PIC simulations. This inconsistency tends to accumulate secularly and is not directly affected by the sources and noise control in the s...