Plasma Position Constrained Free-Boundary MHD Equilibrium in Tokamaks using pyIPREQ

TL;DR

pyIPREQ addresses the challenge of reconstructing free-boundary MHD equilibria in Tokamaks by solving the Grad-Shafranov equation on a poloidal plane with Green's function boundary contributions and finite-difference interiors. It extends prior work by incorporating a magnetic axis position constraint and a vertical-stability mechanism, and it validates the approach against ITER, IPREQ, and FREEGS benchmarks. The paper demonstrates ADITYA-U applications with axis-informed reconstructions and uses the framework to generate SST-1 upgrade scenarios and ADITYA-U divertor-coil predictions. While effective, the method relies on careful initial guesses for profile parameters and incurs computational costs due to Python implementation, suggesting avenues for performance optimization and integration with broader diagnostics.

Abstract

A free-boundary, axisymmetric magnetohydrodynamic (MHD) equilibrium code, pyIPREQ, has been developed for Tokamak plasmas using finite difference and Green's function approach. The code builds upon the foundational frameworks of the PEST and IPREQ codes, introducing several enhancements and new capabilities. Notably, pyIPREQ supports the specification of limiter boundaries and enables the computation of key physical quantities. The code has also been extended to compute equilibria constrained by a prescribed magnetic axis position, which is particularly useful when such information can be inferred from the diagnostics data. In addition, pyIPREQ includes functionality to address vertical instabilities, a requirement for accurately modeling elongated plasma configurations. Benchmarking has been carried out against published results and the original IPREQ code. Applications are demonstrated for ADITYA-U Tokamak experiments, where magnetic axis measurements are available, and predictions are also made for SST-1 and ADITYA-U Tokamaks under various operational scenarios.

Figures (21)

• Figure 1: Comparison of $\psi$ contours from pyIPREQ (dashed lines) with 2004Portone (solid lines), using Method-1 (left) and Method-2 (right).
• Figure 2: $\psi$ for ITER with Method-2 on a larger grid.
• Figure 3: Comparison of $J_\phi$ and $\psi$ from IPREQ (---) and pyIPREQ (- -) for ADITYA-U case.
• Figure 4: $\log_{10}$ of absolute relative error in $J_\phi$ and $\psi$ from IPREQ and pyIPREQ for ADITYA-U case.
• Figure 5: Comparison of $J_\phi$ and $\psi$ from IPREQ (---) and pyIPREQ (- -) for SST-1 case.