Unsupervised machine-learning algorithm for Orbit classification of electron trajectory under magnetic island

Abstract

The tearing mode in fusion reactor is one of the instabilities which tears and reconnects magnetic field lines forming a topological object, so-called ‘Magnetic Island’ on the current sheet where the magnetic field lines of opposing directions are close to each other[1]. In the magnetic island structure, particles, such as electrons, are expected to exhibit different trajectories with those in the absence of the magnetic island structure. In this work, the differences between particles’ trajectories in the presence / absence of magnetic island were simulated in Tokamak geometry by a passive particle code, named Particle Around Magnetic Island(PAMI), which has been developed on C++ and parallelized with Message Passing Interface(MPI). The simulation results calculated by PAMI were classified using unsupervised machine-learning(ML) algorithms, such as Self-Organizing Map(SOM)[2], Hierarchical Cluster Analysis(HCA)[3], and K-mean clustering.

In order to scan various particle trajectories near magnetic island structures, the code PAMI has been executed with inputs sampled based on initial speed, pitch-angle, and initial position of particles. The simulation results, which are stored in 3D positions on cylindrical coordinates of each time step, were transformed into parameters by Fourier Transforms, Chebyshev Polynomial, and Least Square Polynomials, in order to be dealt with by the ML algorithms for clustering.