Finding Magnetic Surfaces via a Single Trajectory

Many important qualities of nuclear plasma confinement devices can be determined via the Poincare plot of the magnetic field return map. These qualities include the locations of the invariant circles (magnetic flux surfaces), chaotic regions, and magnetic islands. The convergence rate of ergodic averages has been shown to successfully categorize these orbits, but many iterations of the return map are needed to implement this directly. Recently, it has been shown that a weighted average can be used to accelerate the convergence, resulting in a useful method for categorizing trajectories.

In this poster, we will show how a technique from sequence extrapolation, the reduced rank extrapolation method (RRE), can also be used to classify trajectories with a single linear least-squares solve. For the islands and invariant circles, a subsequent eigenvalue problem gives the number of islands, the rotation number, and the Fourier coefficients of the trajectory. We will show examples of this method on the standard map and a candidate stellarator configuration.