Quickstart

First, ensure that wellbalanced is installed.

A global model

Species, reactions with rates from cross sections (averaged over a Maxwellian by plasmacoll), a chamber, and the power the electrons absorb:

from plasmacoll import CrossSection
from plasmacoll.constants import ELECTRON_MASS

from wellbalanced import ELECTRON, Chamber, GlobalModel, Reaction, Species

argon, argon_ion = Species.atomic("Ar", 39.948), 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,
)
model = GlobalModel(
    species=[ELECTRON, argon, argon_ion],
    reactions=[ionization],
    chamber=Chamber(volume=1.0e-3, wall_area=0.06, h_factor=0.5),
    power=100.0,  # W
    fixed={"Ar": 1.0e20},  # m^-3
)
state = model.steady_state()
print(state.electron_temperature, state.electron_density)
print(state.power)  # every term of the electron energy balance, in W

model.scan("power", [50.0, 100.0, 200.0]) returns the steady states for several values, each starting from the last.

Every result is also a labelled xarray dataset, state.to_dataset(), and a scan one dataset along its parameter:

import plasma_plots  # registers the .plasma accessor

from wellbalanced import stack

powers = [50.0, 100.0, 200.0]
scan = stack(model.scan("power", powers), "power", powers, units="W")
scan.density.sel(species="e").plasma.plot.lineout()  # with plasma-plots

A 1D discharge

The same reaction in a slab between two grounded walls, sustained by uniform heating:

import numpy as np

from wellbalanced import Fluid1D, FluidSpecies

model = Fluid1D(
    species=[
        FluidSpecies(ELECTRON, mobility=1.0e3),
        FluidSpecies(argon_ion, mobility=10.0),
    ],
    reactions=[ionization],
    length=0.05,
    cells=200,
    fixed={"Ar": 1.0e21},
    heating=2.0e4,  # W/m^3
)
guess = 1.0e15 * np.sin(np.pi * model.x / 0.05) + 1.0e12
state = model.steady_state(model.pack({"e": guess, "Ar+": guess}, 3.0, 0.0))
print(state.densities["e"].max(), model.energy_balance(state))

FluidSpecies(argon_ion, mobility=10.0, momentum=True) gives the ions their momentum equation instead of drift-diffusion (the friction on the gas from the mobility), so they accelerate through a presheath to the Bohm speed and on through the sheath; with a large mobility the ions are collisionless.

Boundaries are set per species and end, and can be changed between steps: model.set_boundary("left", "e", Boundary.flux(1e16)). Resolve the Debye length with the cells: with an unresolved sheath Newton’s method cannot take long implicit steps.

A neutralizer

A fast beam’s charge states on the gas and on the plasma it makes, with that plasma as a global model of the channel:

from wellbalanced.neutralizer import illustrative_deuterium_neutralizer

model = illustrative_deuterium_neutralizer()  # placeholder numbers: it warns
result = model.solve()
print(result.neutral_fraction, result.plasma.ionization_degree(["D2", "D"]))

Real data go into a Neutralizer with a BeamData (the beam’s cross sections on the gas and the plasma at its energy) or a BeamCrossSections (the same as functions of the beam energy, e.g. plasmacoll CrossSections, and the gas ionization as an energy distribution of its secondary electrons such as plasmacoll.RuddIonization), and the plasma’s species and reactions. model.beam_sources(flux, fractions, energy) gives the beam’s sources where the beam has that flux, those charge-state fractions and that energy: numbers for the global model, or arrays on the cells of a Fluid1D (its volume_sources).

See the API reference for every class and function.