Classification of Orbits in Poincar\'e Maps using Machine Learning

The quest for low-cost fusion power has led to the construction of experimental devices such as the DIII-D[8], an operational device for conducting magnetic fusion research, and ITER [16], an international project to help make the transition from studies of plasma physics to electricity-generating fusion power plants. These devices, called tokamaks, use magnetic fields to confine the fusion fuel in the form of a plasma, enabling physicists to perform experiments to determine the best shape for the hot reacting plasma and the magnetic fields necessary to hold it in place. To complement the experiments, computer simulations are used to gain an understanding of the complex physics of the plasmas, design new reactors, and select the parameters to be used in experiments. Data from both the experiments and the simulations are analyzed to provide the insights that will contribute to achieving the goal of fusion power. In this paper, we focus on a specific analysis problem that arises in both simulation and experimental data, namely, the classification of orbits in a Poincaré map, also called a Poincaré plot. These two-dimensional plots are obtained for planes, called poloidal planes, which intersect the torus-shaped tokamak perpendicular to the magnetic axis, as shown in Figure 1(a). A plot consists of several orbits, each composed of a number of points (Figure 1(b)). For a given orbit, these points are the intersections of a field line (the solid lines in Figure 1(a)) with a poloidal plane, as the field line is followed around the torus. There are four distinct shapes traced out by these points, leading to four classes of orbits: quasi-periodic, separatrix, island chain, and stochastic, as shown in Figure 2. In some cases, the orbit shows its distinctive shape with just a few points, corresponding to the first few intersections of the field line with the poloidal plane.