freegs-plasma/freegs: Free boundary Grad-Shafranov solver

This Python module calculates plasma equilibria for tokamak fusion experiments, by solving the Grad-Shafranov equation with free boundaries. Given a set of coils, plasma profiles and shape, FreeGS finds the currents in the coils which produce a steady-state solution in force balance.

Note This is a work in progress, and probably contains bugs. There is a feature wishlist in issues, suggestions and contributions welcome!

Installing ----------

FreeGS is available on PyPI

$ pip install --user freegs

or clone/download this repository and run setup:

$ git clone https://github.com/freegs-plasma/freegs.git $ cd freegs $ python setup.py install --user

Documentation -------------

• MAST-example.ipynb

$ python 01-freeboundary.py

This solves a free boundary problem, specifying the desired location of two X-points. Writes the equilibrium to a G-EQDSK file "lsn.geqdsk"

$ python 02-read-geqdsk.py

Reads in the file "lsn.geqdsk", inferring the coil currents from the plasma boundary and profiles in the G-EQDSK file.

$ python 03-mast.py

Calculates a double-null (CDND) equilibrium for MAST from scratch. Writes solution to G-EQDSK file "mast.geqdsk"

$ python 04-read-mast-geqdsk.py

Reads the file "mast.geqdsk", inferring the coil currents.

$ python 05-fixed-boundary.py

This example solves a fixed boundary problem, in which the square edges of the domain are fixed. The plasma pressure on axis and plasma current are fixed.

$ python 06-xpoints.py

This demonstrates the coil current control code, finding X-points, and marking core region These routines are used inside the free boundary solver

Files -----

The "freegs" module consists of the following files:

• boundary.py - Operators for applying boundary conditions to plasma psi
• control.py - Routines for controlling coil currents based on constraints
• critical.py - Finds critical points (O- and X-points)
• equilibrium.py - Represents the plasma equilibrium state
• gradshafranov.py - Greens functions and operators for the Grad-Shafranov equation
• jtor.py - Routines for calculating toroidal current density (profiles)
• machine.py - Represents the coils and power supply circuits
• multigrid.py - The multigrid solver for the linear elliptic operator
• picard.py - Nonlinear solver, iterating the profiles and constraints
• plotting.py - Plotting routines using matplotlib

Copyright 2016-2022 Ben Dudson, University of York, and other contributors. Email: [email protected]

This program is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with this program. If not, see .

References ----------