coil.s.plot(figure=f, contours=20) shieldcoil.s.plot(figure=f, contours=20) #%% # Compute the field and scalar potential on an XY-plane x = y = np.linspace(-8, 8, 150) X, Y = np.meshgrid(x, y, indexing="ij") points = np.zeros((X.flatten().shape[0], 3)) points[:, 0] = X.flatten() points[:, 1] = Y.flatten() CB1 = coil.B_coupling(points) CB2 = shieldcoil.B_coupling(points) CU1 = coil.U_coupling(points) CU2 = shieldcoil.U_coupling(points) B1 = CB1 @ coil.s B2 = CB2 @ shieldcoil.s U1 = CU1 @ coil.s U2 = CU2 @ shieldcoil.s #%% # Now, plot the field streamlines and scalar potential from bfieldtools.contour import scalar_contour cc1 = scalar_contour(mesh1, mesh1.vertices[:, 2], contours=[-0.001]) cc2 = scalar_contour(mesh2, mesh2.vertices[:, 2], contours=[-0.001])
# A1, Beta1 = compute_sphcoeffs_mesh(mesh1, 5, normalization='energy', R=1) # A2, Beta2 = compute_sphcoeffs_mesh(mesh2, 5, normalization='energy', R=1) # Beta1 = Beta1[:, coil1.inner_vertices] # Beta2 = Beta2[:, coil2.inner_vertices] x = y = np.linspace(-0.8, 0.8, 50) # 150) X, Y = np.meshgrid(x, y, indexing="ij") points = np.zeros((X.flatten().shape[0], 3)) points[:, 0] = X.flatten() points[:, 1] = Y.flatten() CB1 = coil1.B_coupling(points) CB2 = coil2.B_coupling(points) CU1 = coil1.U_coupling(points) CU2 = coil2.U_coupling(points) #%% Precalculations for the solution # alpha[15] = 1 # Minimization of magnetic energy with spherical harmonic constraint C = Beta1 + Beta2 @ P M = M11 + M21.T @ P from scipy.linalg import eigvalsh ssmax = eigvalsh(C.T @ C, M, eigvals=[M.shape[1] - 1, M.shape[1] - 1]) #%% Specify spherical harmonic and calculate corresponding shielded field beta = np.zeros(Beta1.shape[0]) beta[7] = 1 # Gradient
f.scene.isometric_view()
f.scene.camera.zoom(0.95)
#%%
# Now, let's compute the effect of the shield on the field produced by the coil
# Points slightly inside the shield
d = (np.mean(np.diff(shield.mesh.vertices[shield.mesh.faces[:, 0:2]], axis=1),
axis=0) / 10)
points = shield.mesh.vertices - d * shield.mesh.vertex_normals
# Solve equivalent stream function for the perfect linear mu-metal layer.
# This is the equivalent surface current in the shield that would cause its
# scalar magnetic potential to be constant
shield.s = StreamFunction(
np.linalg.solve(shield.U_coupling(points),
coil.U_coupling(points) @ coil.s), shield)
#%%
# Plot the difference in field when taking the shield into account
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
mlab.clf()
B_target = coil.B_coupling(target_points) @ coil.s
B_target_w_shield = (coil.B_coupling(target_points) @ coil.s +
shield.B_coupling(target_points) @ shield.s)
#%% interpolate data on planar mesh
from bfieldtools.utils import load_example_mesh
from bfieldtools.mesh_calculus import gradient
plane = load_example_mesh("10x10_plane_hires")
scaling_factor = 0.03
plane.apply_scale(scaling_factor)
# Rotate to x-plane
t = np.eye(4)
theta = np.pi / 2 * 1.2
t[1:3, 1:3] = np.array([[np.cos(theta), np.sin(theta)],
[-np.sin(theta), np.cos(theta)]])
plane.apply_transform(t)
c.U_coupling.reset()
U_suh = c.U_coupling(plane.vertices) @ a
# Adapt mesh to the function and calculate new points
for i in range(2):
g = np.linalg.norm(gradient(U_suh, plane), axis=0)
face_ind = np.flatnonzero(g > g.max() * 0.05)
plane = plane.subdivide(face_ind)
U_suh = c.U_coupling(plane.vertices) @ a
U_sph = potential(plane.vertices,
alpha,
np.zeros(alpha.shape),
lmax=lmax,
normalization="energy",
R=R)
#%%
]
scene.scene.camera.view_angle = 30.0
scene.scene.camera.view_up = [
-0.28276020498745635,
0.33658483701858727,
0.898196701154387,
]
scene.scene.camera.clipping_range = [16.139073445910277, 116.31572537292347]
scene.scene.camera.compute_view_plane_normal()
scene.scene.render()
#%%
#%% Calculate primary potential matrix
# Compute slightly inside
d = 1e-3
P_prim = coil.U_coupling(shieldmesh.vertices - d * shieldmesh.vertex_normals)
#%% Plot the resulting primary potential
mlab.figure()
s = mlab.triangular_mesh(*shieldmesh.vertices.T,
shieldmesh.faces,
scalars=P_prim @ sprim,
opacity=1.0)
s.enable_contours = True
s.contour.filled_contours = True
s.contour.number_of_contours = 30
#%%
#%% Calculate linear collocation BEM matrix
P_shield = shield.U_coupling(shieldmesh.vertices -
d * shieldmesh.vertex_normals)