These notes were initially written when I visited University of Colorado at Boulder (Sept.-Nov. 2016), where I worked with Yang Chen, who said that most gyrokinetic simulations essentially employ Frieman-Chen’s equation. So a careful re-derivation of the equation is highly helpful for one who is interested in implementing gyrokinetic models in codes, which motivated me to write this document.
After the visit, I went to CUB again, working with Yang Chen and Scott Parker as a postdoc researcher for two years, during which I tried to develop a fully kinetic code (including gyromotion of ions and drift-kinetic electrons) for electromagnetic turbulence simulation. I got an electrostatic version (fully kinetic ions with adiabatic electrons) work[5], but failed to deliver a working electromagnetic version. After coming back to ASIPP, I transformed that code to a gyrokinetic code (gyrokinetic ions with drift-kinetic electrosn), which can handle electromagnetic perturbations (using the mixed-variable pull-back method). That is the TEK code discussed in the main text.
This document was written by using TeXmacs[9], a structured wysiwyw (what you see is what you want) editor for scientists. The HTML version of this document was generated by using TeXmacs’ HTML converter (or sometinmes by first converting the TeXmacs ∖le to TeX format and then using htlatex to convert the TeX ∖le to HTML).