plasma-boundaries
This code computes and plots analytical solutions of the Grad-Shafranov (GS) equation for studying plasma equilibrium, stability and transport in fusion reactors based on the work of A. Cerfon and J. Freidberg. Details on the method can be found in "One size fits all" analytical solutions to the Grad-Shafranov equation, Physics of Plasmas 17 (2010)
Documentation can be found here.
Installation
You can install plasma-boundaries using Pip by running:
pip install plasmaboundaries
Alternatively you can clone the repository:
git clone https://github.com/RemiTheWarrior/plasma-boundaries
Install the dependencies
pip install -r requirements.txt
Usage
First compute the magnetic flux from plasma-boundaries based on a specific set of parameters.
In this example, the built-in ITER plasma parameters will be used:
import plasmaboundaries
# plasma parameters
params = plasmaboundaries.ITER
# compute magnetic flux psi(R, z)
psi = plasmaboundaries.compute_psi(params, config='double-null')The magnetic flux can now be calculated for any coordinates and plotted with matplotlib:
print(psi(1.0, 0))
# plot the results
import matplotlib.pyplot as plt
import numpy as np
rmin, rmax = 0.6, 1.4
zmin, zmax = -0.6, 0.6
r = np.arange(rmin, rmax, step=0.01)
z = np.arange(zmin, zmax, step=0.01)
R, Z = np.meshgrid(r, z)
PSI = psi(R, Z) # compute magnetic flux
levels = np.linspace(PSI.min(), 0, num=25)
CS = plt.contourf(R, Z, PSI, levels=levels, vmax=0)
plt.contour(R, Z, PSI, levels=[0], colors="black") # display the separatrix
plt.colorbar(CS, label="Magnetic flux $\Psi$")
plt.xlabel('Radius $R/R_0$')
plt.ylabel('Height $z/R_0$')
plt.gca().set_aspect("equal")
plt.show()In compute_psi, the argument config can also be set to 'single-null' or 'non-null' for other plasma shapes.
Custom plasma parameters
Parameters can also be defined by creating the parameters dictionary:
params = {
"A": -0.155,
"aspect_ratio": 0.32,
"elongation": 1.7,
"triangularity": 0.33,
}Run the tests
You can run the tests with:
pytest tests/