FieldMesh Conversion¶

In [1]:

from pmd_beamphysics import FieldMesh

import numpy as np
import matplotlib.pyplot as plt

from pmd_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 0x7f92acfd02d0>

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 0x7f92ad486ad0>

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 0x7f92acf56cf0>

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 0x7f92a4d52350>

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")