Oberseminar Wissenschaftliches Rechnen (Dr. Florian Wechsung, Courant Institute of Mathematical Sciences New York University)

Abstract:

When designing a new Stellarator fusion reactor, the design of the coils that generate the magnetic
eld used to contain the plasma is a crucial step. Once designed, building these coils is extremely
expensive and tight manufacturing tolerances only increase the cost further. The classical way
of designing coils is a two-stage approach in which rst a magnetic con guration with desirable
physics properties is found, and then coils that aim at realizing this magnetic con guration are
designed.
Recently, a single-stage approach was introduced that directly optimises coils for their physics
properties. We combine this approach with a model for coil manufacturing errors to nd coil
designs that are robust with respect to small perturbations of the coils.
The corresponding stochastic optimization problems are formulated using a risk-neutral or risk-
averse approach. We present an ecient, gradient-based descent algorithm which relies on ana-
lytical derivatives to solve these problems. In a comprehensive numerical study, we compare the
coil designs resulting from deterministic and risk-neutral stochastic optimization and nd that
the risk-neutral formulation results in more robust con gurations and reduces the number of local
minima of the optimization problem. We also compare deterministic and risk-neutral approaches
in terms of quasi-symmetry on and away from the magnetic axis, and in terms of the con nement
of particles released close to the axis.

via Zoom video conference (request the Zoom link from frank.werner@mathematik.uni-wuerzburg.de)
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