A new approach to static force-free electromagnetic fields

In the early 1950s, Lundquist showed the significance of electromagnetic fields with a vanishing Lorentz force density to magnetohydrostatic fluids. Today, these fields are known as force-free electromagnetic fields. Later that decade, Lüst and Schlüter demonstrated that cosmic magnetic fields are force-free and Chandrasekhar and Kendall then constructed a large class of force-free fields whose electric charge density field is also vanishing. In this article, we constructed force-free fields without assuming that the electric charge density vanishes, and in some cases we established a connection between force-free fields and nonlinear Schrödinger equations.