Implement space-charge initialization (non-relativistic, single-level)

1 files changed, 85 insertions, 0 deletions

diff --git a/Examples/Modules/space_charge_initialization/analysis.py b/Examples/Modules/space_charge_initialization/analysis.py
new file mode 100755
index 000000000..30954c41d
--- /dev/null
+++ b/Examples/Modules/space_charge_initialization/analysis.py
@@ -0,0 +1,85 @@
+#! /usr/bin/env python
+"""
+This script checks the space-charge initialization routine, by
+verifying that the space-charge field of a Gaussian beam corresponds to
+the expected theoretical field.
+"""
+import sys
+import yt
+import numpy as np
+import matplotlib.pyplot as plt
+import scipy.constants as scc
+from scipy.special import gammainc
+yt.funcs.mylog.setLevel(0)
+
+# Parameters from the Simulation
+Qtot = -1.e-20
+r0 = 2.e-6
+
+# Open data file
+filename = sys.argv[1]
+ds = yt.load( filename )
+# Extract data
+ad0 = ds.covering_grid(level=0, left_edge=ds.domain_left_edge, dims=ds.domain_dimensions)
+Ex_array = ad0['Ex'].to_ndarray().squeeze()
+if ds.dimensionality == 2:
+    # Rename the z dimension as y, so as to make this script work for 2d and 3d
+    Ey_array = ad0['Ez'].to_ndarray().squeeze()
+elif ds.dimensionality == 3:
+    Ey_array = ad0['Ey'].to_ndarray()
+    Ez_array = ad0['Ez'].to_ndarray()
+
+# Extract grid coordinates
+Nx, Ny, Nz =  ds.domain_dimensions
+xmin, ymin, zmin = ds.domain_left_edge.v
+Lx, Ly, Lz = ds.domain_width.v
+x = xmin + Lx/Nx*(0.5+np.arange(Nx))
+y = ymin + Ly/Ny*(0.5+np.arange(Ny))
+z = zmin + Lz/Nz*(0.5+np.arange(Nz))
+
+# Compute theoretical field
+if ds.dimensionality == 2:
+    x_2d, y_2d = np.meshgrid(x, y, indexing='ij')
+    r2 = x_2d**2 + y_2d**2
+    factor = (Qtot/r0)/(2*np.pi*scc.epsilon_0*r2) * (1-np.exp(-r2/(2*r0**2)))
+    Ex_th = x_2d * factor
+    Ey_th = y_2d * factor
+elif ds.dimensionality == 3:
+    x_2d, y_2d, z_2d = np.meshgrid(x, y, z, indexing='ij')
+    r2 = x_2d**2 + y_2d**2 + z_2d**2
+    factor = Qtot/(4*np.pi*scc.epsilon_0*r2**1.5) * gammainc(3./2, r2/(2.*r0**2))
+    Ex_th = factor*x_2d
+    Ey_th = factor*y_2d
+    Ez_th = factor*z_2d
+
+# Plot theory and data
+def make_2d(arr):
+    if arr.ndim == 3:
+        return arr[:,:,Nz//2]
+    else:
+        return arr
+plt.figure(figsize=(10,10))
+plt.subplot(221)
+plt.title('Ex: Theory')
+plt.imshow(make_2d(Ex_th))
+plt.colorbar()
+plt.subplot(222)
+plt.title('Ex: Simulation')
+plt.imshow(make_2d(Ex_array))
+plt.colorbar()
+plt.subplot(223)
+plt.title('Ey: Theory')
+plt.imshow(make_2d(Ey_th))
+plt.colorbar()
+plt.subplot(224)
+plt.title('Ey: Simulation')
+plt.imshow(make_2d(Ey_array))
+plt.colorbar()
+plt.savefig('Comparison.png')
+
+# Automatically check the results
+print( 'Relative error in Ex: %.3f'%(abs(Ex_array-Ex_th).max()/Ex_th.max()))
+assert np.allclose( Ex_array, Ex_th, atol=0.15*Ex_th.max() )
+assert np.allclose( Ey_array, Ey_th, atol=0.15*Ey_th.max() )
+if ds.dimensionality == 3:
+    assert np.allclose( Ez_array, Ez_th, atol=0.15*Ez_th.max() )