TCV equilibrium reconstruction using a quasi-Newton method with the LIUQE code from the MEQ suite

Equilibrium reconstruction is ubiquitous in the analysis and control of tokamak discharges, providing information about global parameters such as the total plasma current or plasma stored energy as well as the position of different flux surfaces. Many equilibrium reconstruction codes such as the LIUQE code [1, 2], inspired by early work on the EFIT code [3] use the Picard iteration method to reach convergence. One drawback of this method is the requirement to add some artificial stabilization mechanism which usually leads to small violations of the free-boundary Grad-Shafranov equation. Another approach is to use a quasi-Newton method such as the one implemented in the NICE code [4] which is intrinsically stable.

This work reports on the implementation of a quasi-Newton method similar to the one described in [4] for equilibrium reconstruction in the LIUQE code from the MEQ suite. The Picard iteration method can be expressed as this same quasi-Newton method with an approximate expression of the Jacobian which allows detailed comparison of the two methods. This comparison is performed over a diverse database of past TCV discharges using magnetic measurements only. It is shown that the reconstructions using Picard and quasi-Newton methods are generally very close in terms of plasma position, global parameters, shaping parameters and divertor geometry. In addition to the absence of an artificial vertical stabilisation mechanism another advantage of the quasi-Newton method is the reduced number of iterations required to reach convergence which is offset by the greater computational cost of each iteration. Additionally uncertainty quantification of the equilibrium reconstructions will be assessed extending the approach of [4] by including terms stemming from the hessian of the Grad-Shafranov equation residual.

References

[1] F. Hofmann et. al, Nucl. Fusion, vol. 28, 1871 (1988)

[2] J.-M. Moret et. al, Fusion Eng. and Design, vol. 91, 1-15 (2015)

[3] L.L. Lao et. al, Nucl. Fusion, vol. 25, 1611 (1985)

[4] B. Faugeras, Fusion Eng. and Design, vol. 160, 112020 (2020)