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/bendudson/freegs.git
$ cd freegs
$ python setup.py install --user
The manual is in the docs subdirectory, and hosted here on readthedocs.
The Jupyter notebooks contain examples wuth 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
- plotting.py - Plotting routines using matplotlib
Copyright 2016-2018 Ben Dudson, University of York. 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