EQDSK Equilibrium Files

The eqdsk_file class provides tools for reading G-EQDSK equilibrium files and converting between cylindrical (R, Z) coordinates and flux coordinates.

Reading EQDSK Files

from libneo import eqdsk_file

eq = eqdsk_file('equilibrium.geqdsk')

# Access grid data
print(f"R range: {eq.R.min():.2f} - {eq.R.max():.2f} m")
print(f"Z range: {eq.Z.min():.2f} - {eq.Z.max():.2f} m")
print(f"Magnetic axis: R={eq.Rpsi0:.3f} m, Z={eq.Zpsi0:.3f} m")

Coordinate Conversion

Converting (R, Z) to Flux Coordinates

The most common use case is converting arbitrary (R, Z) measurement points to normalized poloidal flux coordinates for radial profile analysis:

import numpy as np
from libneo import eqdsk_file

eq = eqdsk_file('equilibrium.geqdsk')

# Single point
R, Z = 1.8, 0.1
s_pol, theta = eq.rz_to_flux_coords(R, Z)
print(f"s_pol = {s_pol:.3f}, theta = {theta:.3f} rad")

# Array of measurement points
R_data = np.array([1.7, 1.8, 1.9, 2.0])
Z_data = np.array([0.0, 0.1, -0.1, 0.0])
s_pol, theta = eq.rz_to_flux_coords(R_data, Z_data)

Interpolating Poloidal Flux

Get the raw poloidal flux values at arbitrary (R, Z) points:

# Scalar
psi = eq.psi_at_rz(1.8, 0.1)

# Vectorized
psi = eq.psi_at_rz(R_data, Z_data)

# On a 2D grid (for contour plots)
R_grid = np.linspace(1.5, 2.2, 50)
Z_grid = np.linspace(-0.5, 0.5, 50)
psi_2d = eq.psi_at_rz(R_grid, Z_grid, grid=True)

Plotting Scalar Data vs Flux Coordinate

A typical workflow for plotting diagnostic data against normalized flux:

import numpy as np
import matplotlib.pyplot as plt
from libneo import eqdsk_file

# Load equilibrium
eq = eqdsk_file('equilibrium.geqdsk')

# Your measurement data at (R, Z) locations
R_meas = np.array([1.65, 1.70, 1.75, 1.80, 1.85, 1.90])
Z_meas = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.0])
temperature = np.array([3.2, 2.8, 2.3, 1.7, 1.1, 0.5])  # keV

# Convert to flux coordinates
s_pol, theta = eq.rz_to_flux_coords(R_meas, Z_meas)
rho_pol = np.sqrt(s_pol)  # sqrt(s_pol) is common radial coordinate

# Plot
plt.figure()
plt.plot(rho_pol, temperature, 'o-')
plt.xlabel(r'$\\rho_{pol}$')
plt.ylabel('Temperature [keV]')
plt.title('Temperature Profile')
plt.show()

Flux Coordinate Definitions

Normalized Poloidal Flux (s_pol)

The normalized poloidal flux is defined as:

\[\begin{split}s_{pol} = \\frac{\\psi - \\psi_{axis}}{\\psi_{edge} - \\psi_{axis}}\end{split}\]

where:

\(s_{pol} = 0\) at the magnetic axis
\(s_{pol} = 1\) at the last closed flux surface (LCFS/separatrix)

Geometric Poloidal Angle (theta)

The geometric poloidal angle is defined as:

\[\begin{split}\\theta = \\arctan2(Z - Z_{axis}, R - R_{axis})\end{split}\]