Simons Collaboration on Hidden Symmetries and Fusion Energy Annual Meeting

The most compelling transformational use of magnetically confined, high-temperature plasma is to realize sustained fusion energy. Despite impressive progress, net energy production has not yet been achieved. The tokamak, which is the leading magnetic confinement concept in the world today, has the topology of a torus and continuous symmetry with respect to the toroidal angle, giving it good confinement properties. In the stellarator, which is the leading alternative to the tokamak, the confining magnetic field is mostly produced by external current-carrying coils. In contrast to the tokamak, stellarators rely on symmetry breaking to realize the magnetic field needed to confine particles.

Over the last few decades, a new concept has emerged in the design of stellarators, giving rise to a renaissance—the remarkable discovery that it is possible to design 3-D magnetic confinement devices with hidden symmetries that can have the same virtues as tokamaks while overcoming some of the inherent drawbacks of the latter. An example of a hidden symmetry, known as “quasi-symmetry,” is that the magnitude B of the magnetic vector field B has a negligible coordinate dependence (in a special curvilinear coordinate system) even though B does not. The primary purpose of this Simons Collaboration in Mathematical and Physical Sciences is to create and exploit an effective mathematical and computational framework for the design of stellarators with hidden symmetries.

The challenge of finding 3D optimum magnetic fields with hidden symmetries encompasses mathematical and computational problems of great subtlety, straddling optimization theory, plasma physics, dynamical systems, and the analysis of partial differential equations. In this Workshop, we are bringing together a diverse interdisciplinary group of applied mathematicians, computer scientists, and plasma physicists to discuss the fundamental challenges and transformational potential of the stellarator approach to magnetic confinement. Presentations at the Annual Meeting, which is by invitation only, include eight plenary lectures, a poster session, and ample time for discussion.

Collaboration website