Spatial covariance of disc thermal noise

Compute the spatial covariance of thermal magnetic noise above a conducting disc at several frequencies.

import pyvista as pv

pv.set_plot_theme("document")

import numpy as np
import matplotlib.pyplot as plt
import trimesh
from bfieldtools.thermal_noise import (
    compute_current_modes,
    noise_covar,
    noise_covar_dir,
    noise_var,
    visualize_current_modes,
)
from bfieldtools.mesh_magnetics import magnetic_field_coupling

from bfieldtools import resources


font = {"family": "normal", "weight": "normal", "size": 18}
plt.rc("font", **font)

# Fix the simulation parameters
d = 1e-3
sigma = 3.8e7
T = 293
kB = 1.38064852e-23
mu0 = 4 * np.pi * 1e-7


# freqs = np.array((0,100, 1000, 10000))
freqs = np.array((0, 50, 100, 500))

Np = 121

z = 0.1
x = np.linspace(-1.25, 1.25, Np)
fp = np.array((x, np.zeros(x.shape), z * np.ones(x.shape))).T

ind_orig = 60

Nchunks = 4
quad_degree = 2

mesh = trimesh.load(
    resources.files("bfieldtools", "example_meshes/unitdisc_extremelyfine.stl")
)

B_coupling = magnetic_field_coupling(mesh, fp, analytic=True)

vl = compute_current_modes(
    obj=mesh,
    T=T,
    resistivity=1 / sigma,
    thickness=d,
    mode="AC",
    freqs=freqs,
    return_eigenvals=False,
)


Bcov = noise_covar(B_coupling, vl) * (1e30)

Bdircov = noise_covar_dir(B_coupling, vl) * (1e30)

Computing magnetic field coupling matrix analytically, 2790 vertices by 121 target points... took 0.20 seconds.
No component count given, computing all components.
Calculating surface harmonics expansion...
Computing the resistance matrix...
Computing the inductance matrix...
Computing self-inductance matrix using rough quadrature (degree=2).              For higher accuracy, set quad_degree to 4 or more.
Estimating 27858 MiB required for 2790 by 2790 vertices...
Computing inductance matrix in 60 chunks (13898 MiB memory free),              when approx_far=True using more chunks is faster...
Computing triangle-coupling matrix
Inductance matrix computation took 20.37 seconds.

plt.figure(figsize=(5, 5))
plt.plot(x, np.diag(Bcov[:, :, 0, 0]), linewidth=2, label="$B_x$")
plt.plot(x, np.diag(Bcov[:, :, 1, 0]), linewidth=2, label="$B_y$")
plt.plot(x, np.diag(Bcov[:, :, 2, 0]), linewidth=2, label="$B_z$")
plt.grid()
plt.gca().spines["right"].set_visible(False)
plt.gca().spines["top"].set_visible(False)
plt.legend(frameon=False)
plt.xlabel("x (m)")
plt.ylabel("Noise variance (fT$^2$/Hz)")
plt.tight_layout()

plt.figure(figsize=(5, 5))
plt.plot(x, Bcov[ind_orig, :, 0, 0], linewidth=2, label="$B_x$")
plt.plot(x, Bcov[ind_orig, :, 1, 0], linewidth=2, label="$B_y$")
plt.plot(x, Bcov[ind_orig, :, 2, 0], linewidth=2, label="$B_z$")
plt.grid()
plt.gca().spines["right"].set_visible(False)
plt.gca().spines["top"].set_visible(False)
plt.legend(frameon=False)
plt.xlabel("x (m)")
plt.ylabel("Noise covariance (fT$^2$/Hz)")
plt.tight_layout()

plt.figure(figsize=(5, 5))
plt.plot(x, Bcov[ind_orig, :, 2, 0], linewidth=2, label="DC")
plt.plot(x, Bcov[ind_orig, :, 2, 1], linewidth=2, label="50 Hz")
plt.plot(x, Bcov[ind_orig, :, 2, 2], linewidth=2, label="100 Hz")
plt.plot(x, Bcov[ind_orig, :, 2, 3], linewidth=2, label="500 Hz")
plt.grid()
plt.gca().spines["right"].set_visible(False)
plt.gca().spines["top"].set_visible(False)
plt.legend(frameon=False)
plt.xlabel("x (m)")
plt.ylabel(r"$B_z$ covariance (fT$^2$/Hz)")
plt.tight_layout()


plt.figure(figsize=(3, 3))
plt.plot(x, Bcov[ind_orig, :, 2, 0] / np.max(Bcov[ind_orig, :, 2, 0]), linewidth=2)
plt.plot(x, Bcov[ind_orig, :, 2, 1] / np.max(Bcov[ind_orig, :, 2, 1]), linewidth=2)
plt.plot(x, Bcov[ind_orig, :, 2, 2] / np.max(Bcov[ind_orig, :, 2, 2]), linewidth=2)
plt.plot(x, Bcov[ind_orig, :, 2, 3] / np.max(Bcov[ind_orig, :, 2, 3]), linewidth=2)
plt.gca().tick_params(labelbottom=False, labelleft=False)
plt.gca().spines["right"].set_visible(False)
plt.gca().spines["top"].set_visible(False)
plt.axis("off")
plt.tight_layout()


plt.figure(figsize=(5, 5))
plt.plot(x, Bdircov[:, 0, 1, 0], linewidth=2, label=r"$B_x$$-$$B_y$")
plt.plot(x, Bdircov[:, 0, 2, 0], linewidth=2, label=r"$B_x$$-$$B_z$")
plt.plot(x, Bdircov[:, 1, 2, 0], linewidth=2, label=r"$B_y$$-$$B_z$")
plt.grid()
plt.gca().spines["right"].set_visible(False)
plt.gca().spines["top"].set_visible(False)
plt.legend(frameon=False)
plt.xlabel("x (m)")
plt.ylabel("Noise covariance (fT$^2$/Hz)")
plt.tight_layout()

# Display the assembled scene (Sphinx-Gallery captures it during docs builds).
if "plotter" in globals() and not plotter._closed:
    plotter.show()

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