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!
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
The manual is in the docs subdirectory, and hosted here on readthedocs.
Unit tests use pytest so after installing, run with:
$ pytest
The tests are in the src/ subdirectory.
A convergence test is described in the manual. To run:
$ python test-convergence.py
The Jupyter notebooks contain examples with additional notes
- MAST-example.ipynb
There are also some Python scripts to run short tests and examples
$ 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
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
- newtonk.py - Nonlinear solver, iterating the profiles
- 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 <http://www.gnu.org/licenses/>.
- YoungMu Jeon, Development of a free boundary Tokamak Equlibrium Solver arXiv:1503.03135
- S.Jardin "Computational Methods in Plasma Physics" CRC Press
0.7.1 17th August 2022
- Precalculation of green functions for freeboundary
- Implementation of Newton Krylov non linear solver
- Separation of forward and inverse GS problems
0.7.0 16th August 2022
- Fixes and additional features for equilibrium measurements
- Limited plasma detection and handling throughout code
- Optional adittional constraints on coil currents
- Constraints on coil currents when reading geqdsks
- Replacement of MultiCoil with FilamentCoil
- Addition of PreCalcCoil
0.6.1 11th February 2021
- Fixes for HDF5 reading and writing
- Fix Numpy deprecations
- Catch errors in optimisation measures, making that more robust
- Fix core mask in geqdsk file reading
- Flake8 fixes
- Move to Github actions
0.6.0 29th January 2021
- Improve separatrix finding (Pablo Rodriguez-Fernandez)
- Update MAST-U machine description (James Harrison)
- Updated documentation
- Add tests for critical point finding
- Black format all library code
- Fix wall intersection calculation in optimisation
- Fix factor of pi in effectiveElongation (Chris Winnard)
- Miscellaneous fixes and tidying (Chris Winnard)
- Fix psi_bndry test in critical.core_mask
- Fix comments in Greens functions (James Morris)
0.5.0 25th March 2020
- More tests, thanks to @ZedThree.
- Added more flexible coil types, thanks to Chris Marsden. Includes support for shaped coils, multi-strand coils, and up-down mirrored coils.
- Basic support for reading and writing AEQDSK files
- Added h5py to requirements, fixes for latest NumPy
0.4.0 10th November 2019
- Add optimisation with Differential Evolution
- More unit testing, documentation
0.3.0 28th July 2019
- Add 4th-order solver for potential
- Add convergence test
0.2.0 12th March 2019
- Add field line tracer,
freegs.fieldtracer - Add Equilibrium.Btor toroidal field calculation
- Add Equilibrium.plasmaVolume
- Fix rlim, zlim saved into GEQDSK files