Nonlinear gyrokinetic equation

Youjun Hu1
Institute of Plasma Physics, Chinese Academy of Sciences
Email: yjhu@ipp.cas.cn
Abstract. The nonlinear δf gyrokinetic equation in Frieman-Chen’s paper[3] is re-derived, with more details provided. All formulas are in SI units. Numerical implementation of the gyrokinetic model using the PIC method is also discussed. A gyrokinetic PIC code called TEK was developed using the formulas given in this document. TEK has been benchmarked with GENE code in the DIII-D cyclone base case for both ITG-KBM transition and ITG-TEM transition.
1 Introduction
2 Transform Vlasov equation from particle coordinates to guiding-center coordinates
3 δf form of Vlasov equation in guiding-center variables
4 Gyrokinetic equation suitable for numerical simulation
5 Poisson’s equation and polarization density
6 Polarization density matrix
7 TEK benchmarking with GENE in DIII-D cyclone base case
8 Heat diffusivity
A Adiabatic electron response
B Characteristic curves of Frieman-Chen gyrokinetic equation
C From (δΦ,δA) to (δE,δB)
D Coordinate system and grid in TEK code
E Implementation of gyrokinetics in particle-in-cell (PIC) codes
F Diamagnetic flow **check**
G Transform gyrokinetic equation from (X,μ,𝜀,α) to (X,μ,v∥,α) coordinates
H Drift-kinetic limit
I Derivation of Eq. (122), not finished
J Modern gyrokinetic formulation
K About this document
References