Second order Gyrokinetic theory for Particle-In-Cell codes

TL;DR

This paper derives a second order gyrokinetic Maxwell-Vlasov system from first principles, clarifies its connection to the ORB5 Particle-In-Cell code, and verifies energy conservation diagnostics within a code verification project.

Contribution

It explicitly links the modern second order gyrokinetic theory with the implementation in the ORB5 code and verifies energy conservation diagnostics.

Findings

Derived the second order gyrokinetic Maxwell-Vlasov equations from first principles.

Connected the theoretical model with the ORB5 code implementation.

Verified energy conservation diagnostics in the ORB5 code.

Abstract

The main idea of Gyrokinetic dynamical reduction consists in systematical removing of fastest scale of motion (the gyro motion) from plasma's dynamics, resulting in a considerable model simplification and gain of computing time. Gyrokinetic Maxwell-Vlasov system is broadly implemented in nowadays numerical experiments for modeling strongly magnetized plasma (both laboratory and astrophysical). Different versions of reduced set of equations exist depending on the construction of the Gyrokinetic reduction procedure and approximations assumed while their derivation. The purpose of this paper is to explicitly show the connection between the general second order gyrokinetic Maxwell-Vlasov system issued from the Modern Gyrokinetic theory derivation and the model currently implemented in global electromagnetic Particle in Cell code ORB5. Strictly necessary information about the Modern Gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell-Vlasov equations from the first principle of dynamics. Variational formulation of dynamics is also used for simultaneously obtaining the corresponding exact energy conservation law. The result of that explicit derivation is used for verification of the energy conservation diagnostics currently implemented in ORB5 code. This work subscribes into the context of codes verification project VeriGyro currently run in IPP Max Planck Institut in collaboration with others European institutions.