The Grad–Shafranov (GS) equation is a nonlinear elliptic partial differential equation that governs the ideal magnetohydrodynamic equilibrium of a tokamak plasma. Previous studies have demonstrated the existence of multiple solutions to the GS equation when solved in idealistic geometries with simplified plasma current density profiles and bounda…
Collisions between particles in a low density plasma are described by the Fokker–Planck collision operator. In applications, this nonlinear integro-differential operator is often approximated by linearised or ad-hoc model operators due to computational cost and complexity. In this work, we present an implementation of the nonlinea…
The Grad–Shafranov equation for axisymmetric MHD equilibria is a nonlinear, scalar PDE which in principle can have zero, one or more non-trivial solutions. The conditions for the existence of multiple solutions has been little explored in the literature so far. We develop a simple analytic model to calculate multiple solutions in the large asp…
