Created: 2019-03-07
Author: Christopher Albert [email protected]

This directory collects the original Python proof-of-concept scripts for guiding-center symplectic integrators described in [1]. The examples implement axisymmetric guiding-center motion in canonicalized flux coordinates and were the foundation for the production SIMPLE code.

• common.py – derivative computation and Newton iteration helpers
• field_test.py – simple magnetic configuration for testing
• plotting.py – helper routines for plotting

• expl_impl_euler.py – explicit-implicit Euler method
• expl_impl_euler_optim.py – optimized explicit-implicit Euler method with user-supplied Jacobian
• expl_impl_euler_r_theta.py – explicit-implicit Euler in (r, theta) coordinates
• impl_expl_euler.py – implicit-explicit Euler method
• impl_midpoint.py – implicit midpoint rule
• impl_pendulum.py – nonlinear pendulum example
• verlet.py – Stoermer-Verlet / leap-frog method
• rk.py – adaptive Runge-Kutta 4/5 reference implementation (SciPy)
• pauli_particle.py – Pauli particle dynamics example
• discrete_variational.py – discrete variational integrator notebook helpers

• exportfig.py – export utilities for the published figures
• simple.in – sample SIMPLE configuration used by the prototypes
• iaea2019/ – scripts and notebooks prepared for the 2019 IAEA meeting

[1] C. G. Albert, S. V. Kasilov, and W. Kernbichler, Symplectic integration with non-canonical quadrature for guiding-center orbits in magnetic confinement devices, Mar. 2019, arXiv:1903.06885. Submitted to J. Comput. Phys.