FieldMesh Conversion¶

In [1]:

from beamphysics import FieldMesh

import numpy as np
import matplotlib.pyplot as plt

from beamphysics import FieldMesh import numpy as np import matplotlib.pyplot as plt

2D cylindrically symmetric RF gun FieldMesh¶

This data was originally generated using Superfish.

In [2]:

FM1 = FieldMesh("../data/rfgun.h5")
FM1.plot("re_E", aspect="equal", figsize=(12, 4))

FM1 = FieldMesh("../data/rfgun.h5") FM1.plot("re_E", aspect="equal", figsize=(12, 4))

3D rectangular field from ANSYS¶

In [3]:

FM3D = FieldMesh.from_ansys_ascii_3d(
    efile="../data/ansys_rfgun_2856MHz_E.dat",
    hfile="../data/ansys_rfgun_2856MHz_H.dat",
    frequency=2856e6,
)


FM3D

FM3D = FieldMesh.from_ansys_ascii_3d( efile="../data/ansys_rfgun_2856MHz_E.dat", hfile="../data/ansys_rfgun_2856MHz_H.dat", frequency=2856e6, ) FM3D

Out[3]:

<FieldMesh with rectangular geometry and (3, 3, 457) shape at 0x7f2186df2990>

This will convert to 2D cylindrical:

In [4]:

FM2 = FM3D.to_cylindrical()
FM2

FM2 = FM3D.to_cylindrical() FM2

Out[4]:

<FieldMesh with cylindrical geometry and (2, 1, 457) shape at 0x7f2186df2ad0>

Spacing is different:

In [5]:

FM1.dr, FM2.dr

FM1.dr, FM2.dr

Out[5]:

(np.float64(0.00025), np.float64(0.001))

Set a scale to rotate and normalize Ez to be mostly real

In [6]:

E0 = FM2.components["electricField/z"][0, 0, 0]
FM2.scale = -np.exp(-1j * np.angle(E0)) / np.abs(E0)  # - sign to agree with FM1

FM2.Ez[0, 0, 0]

E0 = FM2.components["electricField/z"][0, 0, 0] FM2.scale = -np.exp(-1j * np.angle(E0)) / np.abs(E0) # - sign to agree with FM1 FM2.Ez[0, 0, 0]

Out[6]:

np.complex128(-1-1.890985933883628e-16j)

In [7]:

z1 = FM1.coord_vec("z")
z2 = FM2.coord_vec("z")


fig, ax = plt.subplots()
ax.plot(z1, np.real(FM1.Ez[0, 0, :]), label="Superfish")
ax.plot(z2, np.real(FM2.Ez[0, 0, :]), label="ANSYS")
ax.set_xlabel(r"$z$ (m)")
ax.set_ylabel(r"$E_z$ (V/m)")
plt.legend()

z1 = FM1.coord_vec("z") z2 = FM2.coord_vec("z") fig, ax = plt.subplots() ax.plot(z1, np.real(FM1.Ez[0, 0, :]), label="Superfish") ax.plot(z2, np.real(FM2.Ez[0, 0, :]), label="ANSYS") ax.set_xlabel(r"$z$ (m)") ax.set_ylabel(r"$E_z$ (V/m)") plt.legend()

Out[7]:

<matplotlib.legend.Legend at 0x7f2186ca0c20>

In [8]:

fig, ax = plt.subplots()
ax.plot(z1, np.imag(FM1.Btheta[4, 0, :]), label="superfish")
ax.plot(z2, np.imag(FM2.Btheta[1, 0, :]), label="ansys")

ax.set_title(rf"$r$ = {FM2.dr*1000} mm")
ax.set_xlabel(r"$z$ (m)")
ax.set_ylabel(r"$B_\theta$ (T)")
plt.legend()

fig, ax = plt.subplots() ax.plot(z1, np.imag(FM1.Btheta[4, 0, :]), label="superfish") ax.plot(z2, np.imag(FM2.Btheta[1, 0, :]), label="ansys") ax.set_title(rf"$r$ = {FM2.dr*1000} mm") ax.set_xlabel(r"$z$ (m)") ax.set_ylabel(r"$B_\theta$ (T)") plt.legend()

Out[8]:

<matplotlib.legend.Legend at 0x7f2186b0fcb0>

The magnetic field is out of phase, so use the im_ syntax:

In [9]:

FM2.plot("im_Btheta", aspect="equal", figsize=(12, 4))

FM2.plot("im_Btheta", aspect="equal", figsize=(12, 4))

Max on-axis field:

In [10]:

np.abs(FM2.Ez[0, 0, :]).max()

np.abs(FM2.Ez[0, 0, :]).max()

Out[10]:

np.float64(1.0153992993439902)

Verify the oscillation¶

Complex fields oscillate as $e^{-i\omega t}$. For TM fields, the spatial components $E_z$ and $B_\theta$ near the axis

$\Re E_{z} = -\frac{r}{2}\frac{\omega}{c^2} \Im B_\theta$

In [11]:

def check_oscillation(FM, label=""):
    c_light = 299792458.0

    dr = FM.dr
    omega = FM.frequency * 2 * np.pi

    # Check the first off-axis grid points
    z0 = FM.z
    Ez0 = np.real(FM.Ez[0, 0, :])
    B1 = -np.imag(FM.Btheta[1, 0, :])

    plt.plot(z0, Ez0, label=r"$\Re \left( E_z\right)$")
    plt.plot(
        z0,
        B1 * 2 / dr * c_light**2 / omega,
        "--",
        label=r"$-\frac{r}{2}\frac{\omega}{c^2} \Im\left(B_\theta\right)$",
    )
    plt.ylabel("field (V/m)")
    plt.xlabel("z (m)")
    plt.legend()
    plt.title(rf"Complex field oscillation{label}")

def check_oscillation(FM, label=""): c_light = 299792458.0 dr = FM.dr omega = FM.frequency * 2 * np.pi # Check the first off-axis grid points z0 = FM.z Ez0 = np.real(FM.Ez[0, 0, :]) B1 = -np.imag(FM.Btheta[1, 0, :]) plt.plot(z0, Ez0, label=r"$\Re \left( E_z\right)$") plt.plot( z0, B1 * 2 / dr * c_light**2 / omega, "--", label=r"$-\frac{r}{2}\frac{\omega}{c^2} \Im\left(B_\theta\right)$", ) plt.ylabel("field (V/m)") plt.xlabel("z (m)") plt.legend() plt.title(rf"Complex field oscillation{label}")

In [12]:

check_oscillation(FM1, ", Superfish")

check_oscillation(FM1, ", Superfish")

In [13]:

check_oscillation(FM2, ", ANSYS")

check_oscillation(FM2, ", ANSYS")