An overview of kinetic theory in plasma physics to obtain a specific form of the Grad-Shafranov equation

This article aims to present a theoretical formulation in the area of plasma physics to obtain a specific form of the Grad-Shafranov equation, in other words, to obtain the Ampère-Maxwell law as a function of the magnetic vector potential and current density. We seek to better understand some phenomena that occur in interplanetary plasma. Another objective is to present this theme in a didactic way as clearly and concisely as possible. In particular, a mathematical development takes place as an introduction to the work, showing the equations we want to deduce, with each section we build a theoretical basis in plasma physics, using concepts of thermodynamics and the universal laws of physics, as well as mathematics, culminating in the Grad-Shafranov specific equation. Finally, we present one of the best known solutions for the Grad-Shafranov equation, as well as references for those who want to delve into the subject.

Keywords
Ideal Magnetohydrodynamics; Kinetic theory; Current sheet; Grad-Shafranov equation.