This vertical stability analysis is carried out on a tokamak plasma for nuclear fusion, where plasma is confined through magnetic flux surfaces that are analytically described as constant u surfaces. The first magnetic surface where plasma is contained is the elliptical surface u = u_b, which is then surrounded by a vacuum region, where a magnetic separatrix, u = u_X, is present. This latter is a magnetic flux surface with two magnetic X-points produced by additional external currents (divertor tokamak configuration), that also cause a vertical elongation of the confined plasma. Everything is then confined inside a toroidal containment chamber, that in our case study will be assumed to stand sufficiently far away from the plasma’s boundary, so that it does not interfere with plasma stability.