4.2 Solving by using integral form of the GS equation

The Green’s function method of calculating Ψ from Jϕ via Eq. (72) can be considered as the integral form of the GS equation. Re-examing the previous subsection, we find, instead of inverting the Laplace operator to solve for Ψ at the interior points, we can just use Eq. (72) to calculate them. The plasma toroidal current Jϕ is calculated through Eq. (67). In this case, we only have two levels of iteration: 1. interation over the rhd of GS equation, 2. iteration over the free parameters (αn, βn, PF coil currents). The iteration over the value of Ψ on the boundary is not needed. So, this is a more straightforward method.