# Create bfield specifications used when optimizing the coil geometry
from bfieldtools import sphtools
lmax = 4
alm = np.zeros((lmax * (lmax + 2), ))
blm = np.zeros((lmax * (lmax + 2), ))
# Set one specific component to one
blm[16] += 1
sphfield = sphtools.field(target_points, alm, blm, lmax)
target_field = sphfield / np.max(sphfield[:, 0])
coil.plot_mesh(opacity=0.2)
mlab.quiver3d(*target_points.T, *sphfield.T)
target_spec = {
"coupling": coil.B_coupling(target_points),
"abs_error": 0.1,
"target": target_field,
}
#%%
# Run QP solver
import mosek
coil.s, prob = optimize_streamfunctions(
coil,
[target_spec],
stray_points_mesh = trimesh.creation.icosphere(subdivisions=3,
radius=stray_radius)
stray_points = stray_points_mesh.vertices + center
n_stray_points = len(stray_points)
#%%
# Plot geometry
if PLOT:
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
coil.plot_mesh(representation="wireframe",
opacity=0.1,
color=(0, 0, 0),
figure=f)
coil.plot_mesh(representation="surface",
opacity=0.1,
color=(0, 0, 0),
figure=f)
mlab.points3d(*target_points.T, color=(0, 0, 1))
mlab.points3d(*stray_points.T, scale_factor=0.3, color=(1, 0, 0))
f.scene.isometric_view()
f.scene.camera.zoom(1.5)
if SAVE_FIGURES:
mlab.savefig(
SAVE_DIR + "biplanar_geometry.png",
figure=f,
process=False)
mesh1 = combine_meshes((coil_plus, coil_minus))
mesh2 = mesh1.copy()
mesh2.apply_scale(1.4)
coil = MeshConductor(mesh_obj=mesh1, basis_name="inner", N_sph=4)
shieldcoil = MeshConductor(mesh_obj=mesh2, basis_name="inner", N_sph=4)
#%%
# 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
if SAVE:
mlab.savefig(
SAVE_DIR + "surface_harmonics.png",
figure=f,
magnification=4,
)
mlab.close()
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(750, 600))
c.plot_mesh(representation="wireframe", figure=f)
c.plot_mesh(opacity=0.2, figure=f)
#
# f.scene.camera.parallel_projection=1
# mlab.view(0,160)
f.scene.camera.zoom(1.5)
f.scene.z_plus_view()
# f.scene.camera.roll(270)
if SAVE:
mlab.savefig(
SAVE_DIR + "suhmesh.png",
figure=f,
magnification=6,
)
mlab.close()
import mosek
coil.s, prob = optimize_streamfunctions(
coil,
[target_spec],
objective="minimum_ohmic_power",
solver="MOSEK",
solver_opts={"mosek_params": {
mosek.iparam.num_threads: 8
}},
)
#%%
# Plot coil windings
f = coil.plot_mesh(opacity=0.2)
loops = coil.s.discretize(N_contours=6)
loops.plot_loops(figure=f)
#%%
# Now, let's change the spherical harmonics inner expansion radius (i.e. the target region radius)
# and optimize a new coil (with the same target sph component)
coil.set_sph_options(sph_radius=1.4)
target_spec = {
"coupling": coil.sph_couplings[1],
"abs_error": 0.01,
"target": target_blms,
# s[63] += 2
s = StreamFunction(s, c)
from mayavi import mlab
from mayavi.api import Engine
engine = Engine()
engine.start()
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(800, 700))
s.plot(figure=f, ncolors=256)
c.plot_mesh(representation="wireframe", figure=f)
j = gradient(s.vert, c.mesh, rotated=True)
Len = np.log(np.linalg.norm(j, axis=0))
vectors = mlab.quiver3d(*c.mesh.triangles_center.T,
*j,
mode="arrow",
colormap="Greens",
scalars=Len)
# vectors = engine.scenes[0].children[2].children[0].children[0]
vectors.glyph.glyph.scale_mode = "scale_by_scalar"
vectors.glyph.glyph.scale_factor = 0.6
f.scene.z_plus_view()
z = Z.ravel()
target_points = np.array([x, y, z]).T
# Turn cube into sphere by rejecting points "in the corners"
target_points = (
target_points[np.linalg.norm(target_points, axis=1) < sidelength / 2] +
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
#%%
target_points = np.array([x, y, z]).T
# Turn cube into sphere by rejecting points "in the corners"
target_points = (
target_points[np.linalg.norm(target_points, axis=1) < sidelength / 2] +
center)
# Plot coil, shield and target points
f = mlab.figure(None,
bgcolor=(1, 1, 1),
fgcolor=(0.5, 0.5, 0.5),
size=(800, 800))
coil.plot_mesh(representation="surface", figure=f, opacity=0.5)
shield.plot_mesh(representation="surface", opacity=0.2, figure=f)
mlab.points3d(*target_points.T)
f.scene.isometric_view()
f.scene.camera.zoom(1.1)
#%%
# Let's design a coil without taking the magnetic shield into account
# 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[:, 0] = target_field[:, 0] + 1 # Homogeneous Y-field
target_abs_error = np.zeros_like(target_field)