plasmaboundaries¶
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 [1].
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 \(\Psi\) 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 ploted 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,
}
References¶
| [1] | “One size fits all” analytical solutions to the Grad-Shafranov equation, Physics of Plasmas 17 (2010) https://doi.org/10.1063/1.3328818 |