Implementation of higher-order velocity mapping between marker particles and grid in the particle-in-cell code XGC

TL;DR

This paper introduces a new higher-order velocity mapping technique using pseudo-inverse in the XGC code, significantly reducing interpolation errors and improving conservation of moments in gyrokinetic plasma simulations.

Contribution

The paper presents a novel higher-order mapping method based on pseudo-inverse calculation for particle-to-grid transfer in XGC, enhancing conservation properties.

Findings

Reduced interpolation error with higher-order elements

Exact preservation of moments up to discretization order

Improved accuracy in neoclassical tokamak test case

Abstract

The global total-$f$ gyrokinetic particle-in-cell code XGC, used to study transport in magnetic fusion plasmas, implements a continuum grid to perform the dissipative operations, such as plasma collisions. To transfer the distribution function between marker particles and a rectangular velocity-space grid, XGC employs a bilinear mapping. The conservation of particle density and momentum is accurate enough in this bilinear operation, but the error in the particle energy conservation can become undesirably large in special conditions. In the present work we update XGC to use a novel mapping technique, based on the calculation of a pseudo-inverse, to exactly preserve moments up to the order of the discretization space. We describe the details of the implementation and we demonstrate the reduced interpolation error for a neoclassical tokamak test case by using $1^{\mathrm{st}}$- and $2^{\mathrm{nd}}$-order elements with the pseudo-inverse method and comparing to the bilinear mapping.