A 1D argon discharge between two grounded walls: profiles from the fluid model.

Electrons and ions drift and diffuse in their own field (Poisson’s equation), the electrons are heated uniformly and lose energy in ionization, which sustains the plasma against the losses to the walls. The plasma sits a few electron temperatures above the walls, with a sheath at each. The transport coefficients and the step cross section are illustrative, not argon data. The steady state is an xarray dataset (state.to_dataset()), plotted with plasma-plots.

Python source

"""A 1D argon discharge between two grounded walls: profiles from the fluid model.

Electrons and ions drift and diffuse in their own field (Poisson's equation),
the electrons are heated uniformly and lose energy in ionization, which sustains
the plasma against the losses to the walls. The plasma sits a few electron
temperatures above the walls, with a sheath at each. The transport coefficients
and the step cross section are illustrative, not argon data. The steady state is
an xarray dataset (``state.to_dataset()``), plotted with plasma-plots.
"""

import numpy as np
import plasma_plots
from plasmacoll import CrossSection
from plasmacoll.constants import ELECTRON_MASS

from wellbalanced import ELECTRON, Fluid1D, FluidSpecies, Reaction, Species

argon_ion = Species.atomic("Ar+", 39.948, 1)
ionization = Reaction.from_cross_section(
    ("e", "Ar"),
    ("e", "e", "Ar+"),
    CrossSection.constant(2.0e-20, threshold=15.76),
    ELECTRON_MASS,
    electron_energy_loss=15.76,
    name="ionization",
)
length = 0.05
model = Fluid1D(
    species=[
        FluidSpecies(ELECTRON, mobility=1.0e3),
        FluidSpecies(argon_ion, mobility=10.0),
    ],
    reactions=[ionization],
    length=length,
    cells=200,
    fixed={"Ar": 1.0e21},
    heating=2.0e4,  # W/m^3
)
guess = 1.0e15 * np.sin(np.pi * model.x / length) + 1.0e12
state = model.steady_state(model.pack({"e": guess, "Ar+": guess}, 3.0, 0.0))
print(f"converged: {state.converged}")
print(
    "energy balance (eV m^-2 s^-1):",
    {k: f"{v:.3e}" for k, v in model.energy_balance(state).items()},
)

profiles = state.to_dataset()
profiles = profiles.assign_coords(x=profiles.x * 1e3)
profiles.x.attrs.update(long_name="x", units="mm")
with plasma_plots.figure(1, 3, figsize=(12, 3.6)) as fig:
    profiles.density.plasma.plot.profiles(x="x", over="species", ax=fig[0])
    profiles.electron_temperature.plasma.plot.lineout(ax=fig[1])
    profiles.potential.plasma.plot.lineout(ax=fig[2])

Plots