The component development status of HL-2M tokamak

Automating the design of tokamak experiment scenarios

“…Repeating the same test for the implementation for FBEE problem (13), based on the discretization and linarization described in Section 3.1 and 3.3 we observe the expected second order convergence (see Table 1, 8th and 9th column). This reassures that the implementation in FEEQS.M is correct.…”

“…We present di↵erent numerical tests, that verify that the implementation of derivatives of the non-linear constraints (13) in FEEQS.M is correct. These derivatives are the cornerstone of the proposed optimal control approach and appear through b y (y, u) in SQP (see Algorithm 1).…”

“…SQP Formulation. Combining the discretized free-boundary plasma equilibrium evolution (13) with discretized objective and regularization functionals we arrive at discretized versions of the optimal control formulation (1) that is of the general form (13). The control variable u contains a subset of the expansion coe cients V ij , 1  i  n, 1  j  N c for the voltages.…”

“…But, as we presented in Sections 3.1 and 3.2 explicit expressions for b(y, u) and J(y, u) that are algebraic in u and y, we can also provide explicit expressions for the first and second order derivatives. An inspection of (13) shows that the constraint b(y, u) is a ne in the control unknown u, hence has vanishing second order derivatives. Moreover, to avoid the expensive assembling of second order derivatives of b(y, u) we neglect those in the SQP iterations.…”

“…FEEQS.M is publicly available 1 and a forthcoming release will contain the methods introduced 1 http://www-sop.inria.fr/members/Holger.Heumann/Software.html in this work. The Section 4 contains validation and verification results for these new developments and the Section 5 presents applications for the tokamaks WEST [5] in Cadarache, France and HL-2M [13] in Chengdu, China. We can also refer the related [14], where the same approach was used to identify for WEST configurations with regions of low magnetic fields as it is required for a successful start-up.…”