mbkumar / SIMPLE

Symplectic Integration Methods for Particle Loss Estimation

SIMPLE

Symplectic Integration Methods for Particle Loss Estimation

SIMPLE computes statistical losses of guiding-center orbits for particles of given mass, charge and energy from the volume of 3D magnetic configurations. Orbits are traced via a symplectic integrator [1,2] that guarantees conservation of invariants of motion within fixed bounds over long integration periods. A classifier based on Poincarè plots [1] allows for accelerated prediction for confinement of regular (non-chaotic) orbits.

The main focus of SIMPLE is to make computation of fusion alpha particle losses fast enough to be used directly in stellarator optimization codes. For that reason currently 3D configurations with nested magnetic flux surfaces are supported based on a VMEC equilibrium file in NetCDF format, and orbits are computed without taking collisions into account.

The code is free to use and modify under the MIT License and links to Runge-Kutta-Fehlberg routines in SRC/contrib/rkf45.f90 from https://people.sc.fsu.edu/~jburkardt/f_src/rkf45/rkf45.html under the GNU LGPL License.

Building

The build system for SIMPLE is CMake.

Required libraries:

• NetCDF
• LAPACK/BLAS

Supported compilers:

• GNU Fortan
• Intel Fortran

Building:

cd /path/to/SIMPLE
mkdir build; cd build
cmake ..
make

This will produce libsimple.so and simple.x required to run the code.

Usage

SIMPLE currently runs on a single node with OpenMP shared memory parallelization with one particle per thread and background fields residing in main memory.

The main executable is simple.x. As an input it takes

• simple.in
• a VMEC NetCDF equlibrium (wout.nc) file with name specified in simple.in

An example input file with explanation of each parameter can be found in examples/simple.in. An example wout.nc can be obtained by

wget https://github.com/hiddenSymmetries/simsopt/raw/master/tests/test_files/wout_LandremanPaul2021_QA_reactorScale_lowres_reference.nc -O wout.nc

The main output is confined_fraction.dat, containing four columns:

1. Physical time
2. Confined fraction of passing particles
3. Confined fraction of trapped particles
4. Total number of particles

The sum of 2. and 3. yields the overall confined fraction at each time.

In addition start.dat is either an input for given or an output for randomly generated initial conditions. Diagnostics for slow convergence of Newton iterations are written in fort.6601.

References

When using this code for scientific publications, please cite the according references:

[1] C. G. Albert, S. V. Kasilov, and W. Kernbichler, Accelerated methods for direct computation of fusion alpha particle losses within stellarator optimization. J. Plasma Phys 86, 815860201 (2020), https://doi.org/10.1017/S0022377820000203

[2] C. G. Albert, S. V. Kasilov, and W. Kernbichler, Symplectic integration with non-canonical quadrature for guiding-center orbits in magnetic confinement devices. J. Comp. Phys 403, 109065 (2020), https://doi.org/10.1016/j.jcp.2019.109065, preprint on https://arxiv.org/abs/1903.06885