process=False)
coil_minus = trimesh.Trimesh(planemesh.vertices + center_offset - standoff,
planemesh.faces,
process=False)
mesh1 = combine_meshes((coil_minus, coil_plus))
mesh2 = mesh1.copy()
mesh2.apply_scale(1.4)
coil1 = MeshConductor(mesh_obj=mesh1, basis_name="inner", N_sph=4)
coil2 = MeshConductor(mesh_obj=mesh2, basis_name="inner", N_sph=4)
M11 = coil1.inductance
M22 = coil2.inductance
M21 = coil2.mutual_inductance(coil1)
# Mapping from I1 to I2, constraining flux through mesh2 to zero
P = -np.linalg.solve(M22, M21)
A1, Beta1 = coil1.sph_couplings
A2, Beta2 = coil2.sph_couplings
# Use lines below to get coulings with different normalization
# from bfieldtools.sphtools import compute_sphcoeffs_mesh
# 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)
#%%
# Plot geometry
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
coil.plot_mesh(opacity=0.2, figure=f)
shieldcoil.plot_mesh(opacity=0.2, figure=f)
#%%
# Compute inductances and coupling
M11 = coil.inductance
M22 = shieldcoil.inductance
M21 = shieldcoil.mutual_inductance(coil)
# Mapping from I1 to I2, constraining flux through shieldcoil to zero
P = -np.linalg.solve(M22, M21)
A1, Beta1 = coil.sph_couplings
A2, Beta2 = shieldcoil.sph_couplings
#%%
# Precalculations for the solution
# Minimization of magnetic energy with spherical harmonic constraint
C = Beta1 + Beta2 @ P
M = M11 + M21.T @ P
# Regularization
center)
# Plot coil, shield and target points
if PLOT:
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
coil.plot_mesh(figure=f, opacity=0.2)
shield.plot_mesh(figure=f, opacity=0.2)
mlab.points3d(*target_points.T)
#%%
# Compute C matrices that are used to compute the generated magnetic field
mutual_inductance = coil.mutual_inductance(shield)
# Take into account the field produced by currents induced into the shield
# NB! This expression is for instantaneous step-function switching of coil current, see Eq. 18 in G.N. Peeren, 2003.
shield.M_coupling = np.linalg.solve(-shield.inductance, mutual_inductance.T)
secondary_C = shield.B_coupling(target_points) @ -shield.M_coupling
#%%
# Create bfield specifications used when optimizing the coil geometry
# The absolute target field amplitude is not of importance,
# and it is scaled to match the C matrix in the optimization function
target_field = np.zeros(target_points.shape)
target_field[:, 1] = target_field[:, 1] + 1