Elliptical corrections to the gyroaveraging operation in gyrokinetic simulations in high E-field-gradients

In gyrokinetic Particle-in-Cell codes, a particle is treated as a charged "ring" subject to a force from the effective potential representing the averaged value over the ring. Thanks to gyroaveraging, a particle's charge is split into N portions and projected onto a circular gyro-ring of size equal to one Larmor radius at equidistant gyro angles. However, in a region with large electric field gradients, like plasma quasi-neutral sheath and steep edge pedestal, the particle orbit departs from being circular, deformed by the presence of the electric field and of the E-field shear. At those locations, the use of circular ring may not be accurate assumption, and elliptical corrections may be applied. In this work, we quantify the deviation from circular orbits by analyzing the full-orbit trajectory of particles inside the quasi-neutral sheath using the hPIC code, a full-orbit Particle-in-Cell code developed at Illinois. The orbit ellipticity is then obtained by fitting the particle trajectory to an ellipse after projection onto the plane perpendicular to the B-field in the moving ExB frame. The ellipse parameters (eccentricity, minor and major axes) are characterized under a range of plasma conditions spanning over the conditions normally encountered in the near-surface region of tokamaks. The correction factors are tabulated in a form convenient for implementations in gyrokinetic PIC codes such as XGC.