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## Section: New Results

### An Automated Approach to Plasma Breakdown Design

Participants : Holger Heumann, Eric Nardon.

Plasma breakdown in a tokamak requires a large toroidal electric field ${E}_{\phi }$ and a low poloidal magnetic field ${B}_{p}$, i.e. a so-called field null region. The latter should remain as extended as possible for a sufficient duration (typically a few tens of $ms$), all the more if one operates at low ${E}_{\phi }$ (e.g. in ITER where ${E}_{\phi }=0.3V/m$). Finding appropriate settings (i.e. premagnetization coils currents and voltage waveforms) to produce and maintain a good field null region is not a trivial task, in particular in the presence of highly conducting passive structures which make the problem dynamic. WEST is a good example of this situation, due to two toroidally continuous copper plates which have been added for vertical stabilization: indeed, the current in the plates ramps up fast when ${E}_{\phi }$ is applied, which tends to degrade the field null region.

Our automated approach to determining appropriate breakdown settings relies on a precise electromagnetic model of the machine (including the iron core) and solves a constrained optimization problem, where the objective function to be minimized quantifies the design goal: the averaged magnitude of ${B}_{p}$. After discretization we end up with finite dimensional convex constrained optimization problem, that can be solved efficiently with Sequential Quadratic Programming. The approach follows the lines of optimal control methods for plasma equilibria in [35] and [36].

The automated approach was already beneficial for obtaining first breakdowns in WEST during the initial launch in December 2016. The data collected during these breakdowns allowed for improving the electromagnetic model and the simulations reproduce now very well magnetic measurements and the shapes observed on the fast camera during the experiments.