Using Permanent Magnets for Near Perfect Quasi-Symmetry in a Stellarator

  • Awardees
  • Elizabeth Paul, Ph.D. Columbia University
Year Awarded


Stellarators are very promising magnetic fusion energy confinement devices. Recent developments in stellarator theory, computational methods and the identification of the possibility of using permanent magnets for field shaping in stellarators have enabled a solution for confining energetic particles in stellarator geometry. This project uses tools developed for a recent ARPA-E project to verify that attractive magnet geometries exist.

Sufficient fast particle confinement has been identified as a key research need for stellarators in a recent paper from the National Stellarator Coordinating Committee. In a recent publication, Landreman and Paul demonstrated that a 2-period QA device could confine fast particles efficiently. In fact, good fast particle confinement was demonstrated over a range of magnetic equilibria. These configurations were identified using the newly developed SIMSOPT code. The key to achieving good confinement was the application of precise constraints on the degree of quasi-symmetry.

This work was done using an equilibrium solution constraint called “fixed-boundary mode.” In this solution mode, external field sources are assumed to exist that provide the appropriate three- dimensional magnetic field. It is now crucial to demonstrate that these assumed highly-precise magnetic fields can be created using realistic field sources. The project will design such sources. This magnetic configuration could be used as the basis for a future experiment.

Elizabeth Paul is currently an assistant professor of applied physics at Columbia University. She uses theoretical and computational methods to study the magnetic confinement of plasmas for fusion energy sciences. Controlled fusion holds promise of providing a carbon-neutral, safe and sustainable energy source. Her work focuses on the advancement of the stellarator magnetic confinement concept, a complex toroidal device which enjoys enhanced stability properties.

Dr. Paul’s research integrates applied mathematical techniques to improve the design of stellarator configurations through numerical optimization. She studies the rich behavior present in three-dimensional magnetic confinement devices, including the nonlinear dynamics of fast particle populations.

Dr. Paul received her A. B. in Astrophysical Sciences with concentrations in applied and computational mathematics and applications of computing from Princeton University in 2015. In 2020, she received her Ph.D. in Physics from the University of Maryland, College Park. In 2021, Dr. Paul received the Marshall N. Rosenbluth Award from the American Physical Society in recognition of her doctoral work, “For pioneering the development of adjoint methods and application of shape calculus for fusion plasmas, enabling a new derivative-based method of stellarator design.” Prior to joining Columbia University, Dr. Paul was a Presidential Postdoctoral Research Fellow at Princeton University.

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