Beam density in 2D

Deposit a sheared, tilted Gaussian beam on a 2D grid, then smooth the deposit.

The markers follow a Gaussian whose axes are tilted by 30 degrees. The raw deposit is noisy at this marker count; a few passes of the binomial filter $[1, 2, 1]/4$ along each axis remove the grid-scale noise while keeping the total, as a PIC code does before solving for the field.

Python source

"""Beam density in 2D

Deposit a sheared, tilted Gaussian beam on a 2D grid, then smooth the deposit.

The markers follow a Gaussian whose axes are tilted by 30 degrees. The raw deposit is noisy at
this marker count; a few passes of the binomial filter $[1, 2, 1]/4$ along each axis remove
the grid-scale noise while keeping the total, as a PIC code does before solving for the field.
"""

import matplotlib.pyplot as plt
import numpy as np
import plasma_plots  # noqa: F401

from mpifield import Field

rng = np.random.default_rng(2)
count = 20_000
angle = np.deg2rad(30)
rotation = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])
positions = rotation @ (rng.normal(size=(2, count)) * np.array([[2.0], [0.6]]))

density = Field(
    ndim=2, lower_bound=(-6.0, -4.0), upper_bound=(6.0, 4.0), num_gridpoints=(97, 65)
)
density.scatter(positions, np.ones((1, count)))
smoothed = density.smooth_binomial(passes=4, in_place=False)
print(f"total before {density.sum():.1f}, after smoothing {smoothed.sum():.1f}")

fig, (left, right) = plt.subplots(1, 2, figsize=(11, 4), layout="constrained")
density.plot(ax=left, name="markers per node", title="raw deposit", equal_aspect=True)
smoothed.plot(
    ax=right, name="markers per node", title="4 binomial passes", equal_aspect=True
)
smoothed.plot(y=0.0, name="markers per node")
plt.show()

Plots