Semi-analytical Methods for Analysis of Tokamak Plasma Equilibrium and Magnetic Field Perturbations

This thesis develops semi-analytical tools to analyse tokamak equilibria and quantify the effects of magnetic perturbations. An open-source Python package, PLEQUE, is introduced as an equilibrium and field-line analysis framework that simplifies tasks such as coordinate system handling, flux-function mapping, flux-expansion metric evaluation, and 3D field-line tracing. The Melnikov-type formalism, derived for the tokamak topology, predicts magnetic footprints formation due to the separatrix splitting in real geometry; its linearity enables efficient optimisation of resonant magnetic perturbation coil currents, as illustrated for ITER. Finally, the analysis of the 3D magnetic field of the toroidal field coil system for the future COMPASS Upgrade tokamak is conducted to ensure that the coil design does not exceed the toroidal ripple design target.