def test_vs_analytic():
obj = _fake_mesh_conductor("unit_disc")
mesh = obj.mesh
mesh.vertices, mesh.faces = trimesh.remesh.subdivide(mesh.vertices, mesh.faces)
# Fix the simulation parameters
d = 100e-6 # thickness
sigma = 3.7e7 # conductivity
res = 1 / sigma # resistivity
T = 300 # temperature
kB = 1.38064852e-23 # Boltz
mu0 = 4 * np.pi * 1e-7 # permeability of freespace
# Compute the AC-current modes and visualize them
vl, u = thermal_noise.compute_current_modes(
obj=mesh, T=T, resistivity=res, thickness=d, mode="AC", return_eigenvals=True
)
# Define field points on z axis
Np = 10
z = np.linspace(0.2, 1, Np)
fp = np.array((np.zeros(z.shape), np.zeros(z.shape), z)).T
B_coupling = magnetic_field_coupling(
mesh, fp, analytic=True
) # field coupling matrix
# Compute noise variance
B = np.sqrt(thermal_noise.noise_var(B_coupling, vl))
# Next, we compute the DC noise without reference to the inductance
vl_dc, u_dc = thermal_noise.compute_current_modes(
obj=mesh, T=T, resistivity=res, thickness=d, mode="DC", return_eigenvals=True
)
# Compute noise variance
B_dc = np.sqrt(thermal_noise.noise_var(B_coupling, vl_dc))
# Calculate Bz noise using analytical formula and plot the results
r = 1
Ban = (
mu0
* np.sqrt(sigma * d * kB * T / (8 * np.pi * z ** 2))
* (1 / (1 + z ** 2 / r ** 2))
)
assert_allclose(B_dc[:, 2], B[:, 2, 0])
assert_allclose(Ban, B[:, 2, 0], rtol=5e-2)
def test_magnetic_field_coupling():
mesh = load_example_mesh("unit_disc")
points = mesh.vertices + np.array([0, 0, 20])
B_1_chunk = mesh_magnetics.magnetic_field_coupling(mesh, points, Nchunks=1)
B_2_chunk = mesh_magnetics.magnetic_field_coupling(mesh, points, Nchunks=2)
assert_allclose(B_1_chunk, B_2_chunk, atol=1e-16)
B_q_1 = mesh_magnetics.magnetic_field_coupling(mesh, points, quad_degree=1)
B_q_2 = mesh_magnetics.magnetic_field_coupling(mesh, points, quad_degree=2)
B_q_3 = mesh_magnetics.magnetic_field_coupling(mesh, points, quad_degree=3)
assert_allclose(B_q_1, B_q_2, atol=1e-3 * np.mean(np.abs(B_q_2)))
assert_allclose(B_q_2, B_q_3, atol=1e-3 * np.mean(np.abs(B_q_2)))
B_a = mesh_magnetics.magnetic_field_coupling(mesh, points, analytic=True)
assert_allclose(B_a, B_q_1, atol=1e-3 * np.mean(np.abs(B_a)))
assert_allclose(B_a, B_q_2, atol=1e-3 * np.mean(np.abs(B_a)))
assert_allclose(B_a, B_q_3, atol=1e-3 * np.mean(np.abs(B_a)))
# Stream functions
s = disc.vertices[:, 0]**2 + disc.vertices[:, 1]**2
#%% Create evaluation points and plot them
Np = 50
z = np.linspace(-1, 10, Np) + 0.001
points = np.zeros((Np, 3))
points[:, 2] = z
mlab.triangular_mesh(*disc.vertices.T,
disc.faces,
scalars=s,
colormap="viridis")
mlab.points3d(*points.T, scale_factor=0.1)
bfield_mesh = magnetic_field_coupling(disc, points, analytic=True) @ s
#%% Plot asymptotic error with different radii
Nr = 100
drs = np.linspace(-0.0035, -0.0034, Nr)
from matplotlib import cm
colors = cm.viridis(np.linspace(0, 1, Nr))
err = []
for c, dr in zip(colors, drs):
err.append((abs((bfield_mesh[:, 2] - field_disc(z, 1 + dr)) /
field_disc(z, 1 + dr)))[-1])
plt.plot(1 + drs, err)
plt.ylabel("error")
plt.xlabel("disc radius")
#%% Determine the "most fit" radius and compare
# Unit sphere
# ------------
Np = 10
radius = np.linspace(0.1, 1, Np)
fp = np.zeros((1, 3))
B = np.zeros((Np, 3))
for i in range(Np):
mesh = trimesh.load(
pkg_resources.resource_filename("bfieldtools", "example_meshes/unit_sphere.stl")
)
mesh.apply_scale(radius[i])
B_coupling = magnetic_field_coupling(mesh, fp, analytic=True)
vl = compute_current_modes(
obj=mesh,
T=T,
resistivity=1 / sigma,
thickness=d,
mode="AC",
return_eigenvals=False,
)
# scene = mlab.figure(None, bgcolor=(1, 1, 1), fgcolor=(0.5, 0.5, 0.5),
# size=(800, 800))
# visualize_current_modes(mesh,vl[:,:,0], 8, 1)
vl[:, 0] = np.zeros(vl[:, 0].shape) # fix DC-component
mesh, plane.vertices, multiply_coeff=False, approx_far=True
)
uprim = phi0x(plane.vertices)
usec = (mu_r - 1) / (4 * np.pi) * Uplane @ u
uplane = uprim + usec
# Meshgrid on the same plane for the bfield
X, Y = np.meshgrid(
np.linspace(-1.5, 1.5, 50), np.linspace(-1.5, 1.5, 50), indexing="ij"
)
pp = np.zeros((50 * 50, 3))
pp[:, 0] = X.flatten()
pp[:, 1] = Y.flatten()
Bplane = magnetic_field_coupling(mesh, pp, analytic=True)
bprim = pp * 0 # copy pp
# add x directional field
mu0 = 1e-7 * 4 * np.pi
bprim[:, 0] = -1
# In this simulation mu0==1 is assumed
# magnetic_field_coupling uses mu0 in SI units
bplane = (mu_r - 1) / (4 * np.pi) / mu0 * Bplane @ u + bprim
# uplane[Uplane.sum(axis=1)]
#%% Plot the results
mlab.figure("Potential for B", bgcolor=(1, 1, 1), size=(1000, 1000))
m = mlab.triangular_mesh(*plane.vertices.T, plane.faces, scalars=uplane, colormap="bwr")
m.actor.mapper.interpolate_scalars_before_mapping = True
m.module_manager.scalar_lut_manager.number_of_colors = 32
# vectors = mlab.quiver3d(*(plane.triangles_center + np.array([0,0,0.001])).T,
from bfieldtools.mesh_conductor import MeshConductor
import pkg_resources
# Load simple plane mesh that is centered on the origin
file_obj = pkg_resources.resource_filename(
"bfieldtools", "example_meshes/10x10_plane.obj"
)
coilmesh = trimesh.load(file_obj, process=False)
coil = MeshConductor(mesh_obj=coilmesh)
weights = np.zeros(coilmesh.vertices.shape[0])
weights[coil.inner_vertices] = 1
test_points = coilmesh.vertices + np.array([0, 1, 0])
B0 = magnetic_field_coupling(coilmesh, test_points) @ weights
B1 = magnetic_field_coupling_analytic(coilmesh, test_points) @ weights
f = mlab.figure(None, bgcolor=(1, 1, 1), fgcolor=(0.5, 0.5, 0.5), size=(800, 800))
s = mlab.triangular_mesh(
*coilmesh.vertices.T, coilmesh.faces, scalars=weights, colormap="viridis"
)
s.enable_contours = True
s.actor.property.render_lines_as_tubes = True
s.actor.property.line_width = 3.0
mlab.quiver3d(*test_points.T, *B0.T, color=(1, 0, 0))
mlab.quiver3d(*test_points.T, *B1.T, color=(0, 0, 1))
thickness=d,
mode="AC",
return_eigenvals=True)
scene = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
visualize_current_modes(mesh, vl[:, :, 0], 42, 5, contours=True)
# Define field points on z axis
Np = 30
z = np.linspace(0.1, 1, Np)
fp = np.array((np.zeros(z.shape), np.zeros(z.shape), z)).T
B_coupling = magnetic_field_coupling(mesh, fp,
analytic=True) # field coupling matrix
# Compute noise variance
B = np.sqrt(noise_var(B_coupling, vl))
# Calculate Bz noise using analytical formula and plot the results
r = 1
Ban = (mu0 * np.sqrt(sigma * d * kB * T / (8 * np.pi * z**2)) *
(1 / (1 + z**2 / r**2)))
plt.figure()
plt.subplot(2, 1, 1)
plt.semilogy(z, Ban, label="Analytic")
plt.semilogy(z, B[:, 2, 0], "x", label="Numerical")
plt.legend(frameon=False)
plt.xlabel("Distance d/R")
