Particle stepper

An example of PlasmaPy’s particle stepper class, currently in need of a rewrite for speed. Currently disabled from running.

import numpy as np
from astropy import units as u
from plasmapy.classes import Plasma, Species

Initialize a plasma. This will be a source of electric and magnetic fields for our particles to move in.

plasma = Plasma(domain_x=np.linspace(-1, 1, 10) * u.m,
                domain_y=np.linspace(-1, 1, 10) * u.m,
                domain_z=np.linspace(-1, 1, 10) * u.m)

Initialize the fields. We’ll take $vec{B}$ in the $hat{x}$ direction and $E$ in the $hat{y}$ direction, which gets us an $E times B$ drift in $hat{z}$.

B0 = 4 * u.T
plasma.magnetic_field[0, :, :, :] = np.ones((10, 10, 10)) * B0

E0 = 2 * u.V / u.m
plasma.electric_field[1, :, :, :] = np.ones((10, 10, 10)) * E0

Initialize the particle. We’ll take one proton p with a timestep of $10^{-10}s$ and run it for 10000 iterations.

species = Species(plasma, 'p', 1, 1, 1e-10 * u.s, 10000)

Initialize the particle’s velocity. We’ll limit ourselves to one in the $hat{x}$ direction, parallel to the magnetic field $vec{B}$ - that way, it won’t turn in the $hat{z}$ direction.

V0 = 1 * (u.m / u.s)
species.v[0][0] = V0

Run the pusher and plot the trajectory versus time.

species.run()
species.plot_time_trajectories()

Plot the shape of the trajectory in 3D.

species.plot_trajectories()

As a test, we calculate the mean velocity in the z direction from the velocity and position

vmean = species.velocity_history[:, :, 2].mean()
print(f"The calculated drift velocity is {vmean:.4f} to compare with the"
      f"theoretical E0/B0 = {E0/B0:.4f}")

and from position:

Vdrift = species.position_history[-1, 0, 2] / (species.NT * species.dt)
normdrift = Vdrift
print(f"The calculated drift velocity from position is {normdrift:.4f}")

Total running time of the script: ( 0 minutes 0.000 seconds)