wellbalanced

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Global (0D) and 1D fluid models of low-temperature plasmas.

A global model balances, averaged over a chamber, the density of every species and the electron energy (and optionally the gas temperature): the reactions, the losses to the walls, the feed and pumping of the gases and external sources such as a fast beam. Reactions take their rates from plasmacoll’s cross sections, the same data its Monte Carlo collisions use, so a fluid and a kinetic model of the same plasma differ in their physics, not their data.

:class:Fluid1D resolves the same plasma along one dimension: drift-diffusion of every species, the electron energy and Poisson’s equation, implicit, with boundaries that can be changed between steps.

:class:GasDynamics is the neutral gas of a sputtering magnetron, argon and the sputtered metal as one compressible gas in one or two dimensions (its boundaries and sources are in :mod:wellbalanced.gasdynamics).

:class:RFDriver is a 0D RF driver: a global model of its plasma and a transformer model of the coil’s coupling, giving the coil current and the RF power transfer efficiency (:mod:wellbalanced.driver). The spatially resolved models are in :mod:wellbalanced.spatial: :class:InductiveField2D, the inductive RF field of coil windings, conductors and a prescribed plasma in a 2D cut or in r–z, with cold or viscous electrons, and :class:DriverCoupling, that field with a power-dependent plasma.

The solves, time steps and runs carry scope-profiler regions tagged "wellbalanced", an opt-in tag: they record nothing unless an application enables it, e.g. with scope_profiler.setup(enable_tags=["wellbalanced"]).

Attributes

Name	Description
`ELECTRON`	No description.
`MATERIALS`	No description.

Classes

Name	Description
`Boundary`	The condition of one species at one end.
`CellGrid`	Cells of a tensor-product grid with any edges, in a cut or in r–z.
`Chamber`	The volume and walls of the plasma.
`Coil`	The RF coil: turns windings of radius (m) over length (m).
`Conductor`	A perfect conductor (E = 0 inside): one or several connected shapes.
`Cusp`	Multicusp magnetic confinement: cusp lines with a field at the wall.
`DriftFluid2D`	The magnetron plane of the module docstring.
`DriftFluid2DState`	The fields on the (nx, ny) cells.
`DriverCoupling`	A field model and a power-dependent plasma model, solved together.
`DriverState`	A driver at one absorbed power: its plasma and the coil's view of it.
`Fluid1D`	A plasma between x = 0 and length on cells cells; see the module docstring.
`FluidSpecies`	A species carried by the fluid model.
`FluidState`	The fields on the cells and the fluxes on the faces.
`GasDynamics`	Two-species compressible gas in 1D or 2D; see the module docstring.
`GasState`	The gas on the grid: the primitive variables at one time.
`GasTemperature`	The gas temperature as a balance: heating by the reactions against conduction.
`GlobalModel`	The balances of a plasma in a chamber; see the module docstring.
`GlobalState`	A solution of the global model, with every term of its balances.
`InductiveField2D`	The magnetoquasistatic field of coil windings, conductors and a plasma.
`InductiveSolution`	The time-harmonic field of :meth:InductiveField2D.solve, as complex amplitudes.
`Magnetron`	The ionization region of a magnetron: geometry, gas and target; see the module docstring.
`PlasmaRegion`	The cells of a plasma: the union of shapes minus the union of excluded.
`PotentialBoundary`	The potential at one end: a value (V) or the field E (V/m) there.
`RFDriver`	A cylindrical RF driver: its plasma's global model and its coil.
`Reaction`	One reaction of the model.
`Species`	A species of the plasma or the gas.
`SpokeReport`	What a run says about its azimuthal structure, in the terms of the experiments.
`TargetMaterial`	The sputtered metal and the response of the target to the ions.
`VolumeSource`	An external volume source, e.g. ionization or stripping by a fast beam.
`WallReaction`	A neutral species lost at the walls, with a probability per impact.
`Winding`	One coil winding: a region carrying sign times the coil current.

Functions

Name	Description
`spoke_report`	The :class:SpokeReport of a run over a time window (the last half by default).
`stack`	The datasets of a scan joined along the scanned parameter.

Modules

datasetsThe results as xarray datasets, labelled for plotting.
driftfluid2dA 2D axial-azimuthal drift-fluid model of a magnetron: gradient-drift instability and spokes.
driverA 0D model of an inductive RF driver: a global model and a transformer model.
fluid1dA 1D fluid model of a low-temperature plasma: drift-diffusion, electron energy, Poisson.
gasdynamicsA compressible neutral-gas model for the gas in front of a sputtering target.
global_modelA global (volume-averaged, 0D) model of a low-temperature plasma.
magnetronA global model of the ionization region of a (HiPIMS) magnetron discharge.
neutralizerA beam-driven plasma neutralizer: the beam's charge states and the plasma it makes.
reactionsReactions: reactants, products, a rate coefficient and the energy they exchange.
spatialSpatially resolved (2D) models: the inductive RF field of a driver, in a cut or in r–z.
speciesSpecies of a plasma: name, mass and charge.

`ELECTRON`attributemodule attribute#

Re-exported from wellbalanced.speciesView source

ELECTRON = Species('e', ELECTRON_MASS, -1)

`MATERIALS`attributemodule attribute#

Re-exported from wellbalanced.magnetronView source

MATERIALS: dict[str, TargetMaterial] = {
  m.name: m for m in (
    _material('Al', 26.982, 5.986, 3, 0.65, 0.55),
    _material('Cr', 51.996, 6.767, 1, 0.9, 0.8),
    _material('Cu', 63.546, 7.726, 1, 1.0, 1.0),
    _material('Ti', 47.867, 6.828, 2, 0.4, 0.3),
    _material('Au', 196.967, 9.226, 1, 2.4, 2.5),
    _material('Mo', 95.95, 7.092, 1, 0.7, 0.8),
    _material('Nb', 92.906, 6.759, 1, 0.5, 0.6)
  )
}

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`Boundary`classdataclass#

Re-exported from wellbalanced.fluid1dView source

class Boundary(kind: str, value: float = 0.0, temperature: float | None = None, reflection: float = 0.0)

The condition of one species at one end.

Use the constructors: :meth:wall, :meth:density, :meth:flux, :meth:symmetry. value is the density (m^-3) or the flux into the domain (m^-2 s^-1); temperature (eV) the electron temperature of a prescribed electron density; reflection the wall’s reflection coefficient.

Name	Type	Default	Description
`x_edges`	`Sequence[float] \| np.ndarray`	required	Cell edges of the first axis (`x`, or `r` from `>= 0`) [m].
`y_edges`	`Sequence[float] \| np.ndarray`	required	Cell edges of the second axis (`y`, or `z`) [m].
`geometry`	`Geometry`	`'cartesian'`	`"cartesian"` or `"cylindrical"`.
`boundaries`	`tuple[AxisBoundary, AxisBoundary]`	`('dirichlet', 'dirichlet')`	The boundary of each axis: `"dirichlet"` (the field is 0 at the edge), `"neumann"` (no flux) or `"periodic"`. In r–z the radial axis cannot be periodic, and its lower boundary is the axis when the first edge is 0, whatever is given.

Name	Type	Description
`volume`	`float`	The volume in m^3.
`wall_area`	`float`	The total wall area in m^2, seen by the neutrals.
`ion_loss_area`	`float \| None`	The area in m^2 through which ions leave unconfined; the whole wall if `None`.
`h_factor`	`float`	The edge-to-centre density ratio at that area.
`cusp`	`Cusp \| None`	Magnetic cusps through which ions leave as well.

Name	Type	Description
`shapes`	`Sequence[Any]`	The shapes it is made of (anything with `contains_points`).
`floating`	`bool`	`False` (grounded, the default): `a = 0` inside, the value of the far boundary, any net current. `True` (in a cut only): one uniform unknown `A_z` and zero net current, a closed loop of plates.
`name`	`str`	A label for :attr:`InductiveSolution.conductor_currents`.

Name	Type	Description
`length_x`	`float`	The cathode-anode gap (m).
`length_y`	`float`	The azimuthal period (m).
`nx`	`int`	Cells along `x`.
`ny`	`int`	Cells along `y` (at least 4).
`voltage`	`float`	The discharge voltage (V): the cathode is at `-voltage`, the anode at 0.
`magnetic_field`	`Callable[[Any], Any] \| float`	`B_z(x)` in T: a callable of the cell positions, or a number.
`gas_density`	`float`	The neutral density at rest `N_0` (m^-3).
`electron_temperature`	`float \| None`	`T_e` held fixed (eV), or `None` for the energy equation.
`momentum_rate`	`float \| Callable[[Any], Any]`	Electron-neutral momentum-transfer rate coefficient `k_en` (m^3/s), `nu_en = k_en N`: a number, or a function of `T_e` (eV; the default is the PLACEHOLDER :func:`argon_momentum_rate`).
`ion_friction_rate`	`float`	Ion-neutral momentum-transfer rate coefficient (m^3/s). PLACEHOLDER.
`ion_mass_u`	`float`	The ion mass in atomic mass units (argon).
`ion_temperature`	`float`	`T_i` in eV (also the gas temperature).
`ionization_rate`	`Callable[[Any], Any]`	Rate coefficient (m^3/s) as a function of `T_e` (eV).
`excitation_rate`	`Callable[[Any], Any] \| None`	Excitation rate coefficient (m^3/s) as a function of `T_e`, or `None` for none; `excitation_energy_ev` is the energy it costs (eV), and `ionization_energy_ev` the energy an ionization costs. Both are channels of the electron energy loss, with the elastic loss `3 (m / M) nu_en (T_e - T_i)`.
`secondary_emission`	`float`	Electrons emitted per ion hitting the cathode. PLACEHOLDER.
`cathode_current_density`	`float \| None`	If given (A/m^2), the cathode emits this net electron current density, whatever the ion flux, instead of `secondary_emission` per ion. This is the condition of Boeuf’s PIC (`j_e0 = 0.03 A/m^2`, the electrons returning to the cathode re-emitted): a fixed `gamma` makes the discharge an avalanche whenever `gamma M >= 1` (`M` the multiplication), a fixed emitted current gives a stable steady state with `gamma_net = j_e0 / j_ion`.
`secondary_energy_ev`	`float`	Temperature of the emitted electrons (eV).
`refill_rate`	`float`	Relaxation rate (1/s) of the gas towards `N_0` (the gas flow and the sputter wind): the explicit parameter, with `depletion`, of the neutral dynamics.
`depletion`	`float`	Fraction of the ionization events that remove a neutral (1: full depletion, 0: a frozen gas).
`field_bc`	`float \| None`	`None` for the electrodes at `-voltage` and 0 V. A number `E_0` (V/m) replaces them by a fixed axial field `E_x = E_0` at both ends (a pinned potential), so that a perturbation can be uniform along `x`: the setting for comparing with the local dispersion relation.
`heating_scale`	`float`	Factor on the Joule heating of the electron energy (a diagnostic switch).
`floor_added`	`dict`	Running total of the density (summed over cells, m^-3) that the floor `N_FLOOR` on `ne`, `ni` and `N` created in the Euler stages, a diagnostic of how much charge the limiter invents; reset it to zero to start counting.
`anode_thermal_flux`	`bool`	Adds the thermal flux of an absorbing wall, `n v_bar / 2` with `v_bar = sqrt(8 e T_e / (pi m))` (Hagelaar et al. 2000, reflection 0), to the drift flux of the electrons at the anode, which otherwise only leave at the drift rate; the outflow is then the larger of the two, and the density next to the anode falls to what carries the current. Tested for Boeuf’s case without success: the 1D discharge then decays and runs away (no sheath barrier for the wall flux), so it is off.
`diamagnetic`	`float`	Factor on the electron pressure-gradient (diamagnetic) force in the fluxes and the Poisson solve (a diagnostic switch for the linear analysis; 1 is the model).
`periodic_x`	`bool`	Periodic along `x` as well, for a uniform plasma in a uniform field `field_bc` (required) and a uniform `B`: pure Fourier modes `(k_x, k_y)` exist, which is what the local dispersion relation describes.
`bohm`	`float`	`alpha` of the anomalous frequency `alpha omega_ce / 16` (0 off).
`external_sources`	`dict[str, np.ndarray]`	Volume sources added to the time derivative of an unknown (`"ne"`, `"ni"`, `"N"`, `"vx"`, `"vy"`, `"w"`), numbers or arrays on the cells, per unit time. :meth:`stationary_sources` returns the ones that make a given state stationary.

Name	Type	Default	Description
`state`	`DriftFluid2DState`	required	The initial state.
`t_end`	`float`	required	The duration (s).
`dt`	`float \| None`	`None`	A fixed step (s); by default the step is re-chosen from `cfl` every 20 steps.
`cfl`	`float`	`0.4`	The Courant number of the chosen step.
`record_every`	`float \| None`	`None`	The recording interval (s); `t_end / 200` by default.
`probe_x`	`float \| None`	`None`	Where along `x` to record (m); mid-gap by default.
`callback`	`Callable[[DriftFluid2DState], None] \| None`	`None`	Called with the state at every recording.

Name	Type	Description
`x`	`np.ndarray`	Cell centres along `x` (m).
`y`	`np.ndarray`	Cell centres along `y` (m).
`electron_density`	`np.ndarray`	`n_e` (m^-3).
`ion_density`	`np.ndarray`	`n_i` (m^-3).
`ion_velocity`	`np.ndarray`	`(v_x, v_y)` of the ions, shape `(2, nx, ny)` (m/s).
`gas_density`	`np.ndarray`	The neutral density `N` (m^-3).
`electron_temperature`	`np.ndarray`	`T_e` (eV).
`potential`	`np.ndarray`	`phi` (V).
`time`	`float`	Time (s).

Name	Type	Description
`field`	`Callable[[PlasmaProfile], InductiveField2D]`	`profile -> InductiveField2D`.
`plasma`	`Callable[[float], tuple[PlasmaProfile, Any]]`	`absorbed power [W] -> (PlasmaProfile, anything)`.
`network_resistance`	`float`	`R_net` [Ohm].
`depth`	`float \| None`	The effective depth of a cut [m]; `None` in r–z.

Name	Type	Description
`plasma`	`GlobalState`	The steady state of the driver’s global model.
`power`	`float`	The power the plasma absorbs in W.
`frequency`	`float`	The RF frequency in Hz.
`collision_frequency`	`float`	The electrons’ momentum-transfer frequency `nu_m` (1/s).
`coil_impedance`	`complex`	`Z_s` in Ohm; its real part is `R_s`.
`network_resistance`	`float`	`R_net` in Ohm.
`skin_depth`	`float`	`1 / Re k` in m.

Name	Type	Description
`species`	`Sequence[FluidSpecies]`	The fluid species, the electrons (`"e"`) included.
`reactions`	`Sequence[Reaction]`	The volume reactions; reactants that are not fluid species must be in `fixed`.
`length`	`float`	The domain length (m).
`cells`	`int`	The number of cells.
`fixed`	`Mapping[str, float \| np.ndarray]`	Densities of species not carried by the model, e.g. the gas (m^-3, a number or an array on the cells).
`gas_temperature`	`float`	`T_g` in eV.
`electron_temperature`	`float \| None`	`None` solves the electron energy equation; a number holds `T_e` fixed (isothermal electrons).
`boundaries`	`dict[str, dict[str, Boundary]]`	`{"left": {species: Boundary}, "right": {...}}`; a species missing at an end has a wall there.
`potential`	`dict[str, PotentialBoundary]`	`{"left": PotentialBoundary, "right": ...}`; grounded if missing.
`heating`	`float \| np.ndarray`	Power to the electrons (W/m^3), a number or an array on the cells.
`sources`	`Mapping[str, float \| np.ndarray]`	External volume sources `{species: rate}` (m^-3 s^-1), numbers or arrays on the cells.
`volume_sources`	`Sequence[VolumeSource]`	External sources as for the global model, e.g. a beam’s (:meth:`wellbalanced.neutralizer.Neutralizer.beam_sources`): rates per unit density of fluid or fixed species, numbers or arrays on the cells, with the energy they give the electrons.

Name	Type	Description
`species`	`Species`	Name, mass and charge.
`mobility`	`float`	`mu` in m^2/(V s) (charged species).
`diffusion`	`float \| None`	`D` in m^2/s; for a charged species `None` takes the Einstein relation `D = mu T` (`T_e` for electrons, `T_g` for ions).
`momentum`	`bool`	Solve the momentum equation of this ion species (with the friction `e / (M mu)` of its mobility) instead of drift-diffusion.

Name	Type	Description
`reactants`	`Sequence[str]`	Species names, repeated for a species that appears twice.
`products`	`Sequence[str]`	Species names, repeated likewise.
`rate`	`float \| RateTable \| RateFunction`	`K` in m^3/s (for two reactants): a number, a :class:`plasmacoll.RateTable`, or a function of the temperature in eV.
`temperature`	`str`	`"electron"` or `"gas"`, the temperature `K` depends on.
`electron_energy_loss`	`float`	Energy in eV the electrons lose per reaction (negative for a gain, e.g. superelastic or detachment energy).
`gas_heating`	`float`	Energy in eV the gas gains per reaction (Franck-Condon fragments, charge exchange).
`elastic_mass`	`float \| None`	For an elastic electron collision, the target mass in kg: the electrons then lose `3 (m_e / M) (T_e - T_g)` per collision.
`name`	`str`	A name for diagnostics; built from the equation if empty.

Name	Type	Description
`mode`	`int`	The dominant azimuthal mode number `m >= 1` (largest time-averaged amplitude).
`wavelength`	`float`	`length_y / m` (m).
`growth_rate`	`float`	Growth rate (1/s) of that mode over the window.
`phase_velocity`	`float`	Phase velocity (m/s) along `+y`.
`exb_velocity`	`float`	The azimuthal E x B velocity (m/s) at the probe, averaged over the window and `y`.
`relative_direction`	`int`	`+1` if the mode moves along E x B, `-1` against it.
`speed_ratio`	`float`	`\|phase_velocity\| / \|exb_velocity\|`.
`cathode_modulation`	`float`	Peak-to-peak density modulation next to the cathode, `(max - min) / (2 mean)` along `y`, averaged over the window.
`potential_hump`	`float`	`max_y(phi) - mean_y(phi)` at the probe (V), window average.
`azimuthal_field`	`float`	`max_y \|E_y\|` at the probe (V/m), window average.
`window`	`tuple[float, float]`	The `(t0, t1)` (s) of the analysis.

Name	Type	Description
`x`	`np.ndarray`	Cell centres (m).
`faces`	`np.ndarray`	Face positions (m).
`densities`	`dict[str, np.ndarray]`	Density of every fluid species on the cells (m^-3).
`electron_temperature`	`np.ndarray`	`T_e` on the cells (eV).
`potential`	`np.ndarray`	`phi` on the cells (V).
`fluxes`	`dict[str, np.ndarray]`	Flux of every fluid species on the faces (m^-2 s^-1), positive along `x`; `"energy"` is the electron energy flux (eV m^-2 s^-1).
`reaction_rates`	`dict[str, np.ndarray]`	Volume rate of every reaction on the cells (m^-3 s^-1).
`time`	`float`	Time (s) of the state; `inf` for a steady state.
`converged`	`bool`	Whether the last solve converged.

Name	Type	Description
`time`	`float`	The time in s.
`x`	`np.ndarray`	Cell centres along the axis, m.
`y`	`np.ndarray`	Cell centres across, m.
`gas_density`	`np.ndarray`	Argon mass density, kg/m^3, shape `(nx, ny)`.
`metal_density`	`np.ndarray`	Metal mass density, kg/m^3.
`u`	`np.ndarray`	Axial velocity, m/s.
`v`	`np.ndarray`	Azimuthal velocity, m/s.
`pressure`	`np.ndarray`	Pressure, Pa.
`temperature`	`np.ndarray`	Temperature, K.
`gas_number`	`np.ndarray`	Argon number density, m^-3.
`metal_number`	`np.ndarray`	Metal number density, m^-3.

Name	Type	Description
`species`	`Sequence[Species]`	Every species, the electrons (named `"e"`) included.
`reactions`	`Sequence[Reaction]`	The volume reactions.
`chamber`	`Chamber`	Volume, walls and confinement.
`power`	`float \| Callable[[float], float]`	Power absorbed by the electrons in W, or a function of the time in s, `power(t)`, for :meth:`GlobalModel.evolve` (a steady state is then taken at `t = 0`).
`fixed`	`Mapping[str, float]`	Densities held fixed (m^-3), e.g. a gas at a given pressure.
`feed`	`Mapping[str, float]`	Particles per second fed into the chamber, by species.
`pumping_speed`	`float`	Volume per second (m^3/s) pumped out, of every neutral species that is not held fixed.
`sources`	`Sequence[VolumeSource]`	External volume sources.
`wall_reactions`	`Sequence[WallReaction]`	Losses of neutral species at the walls.
`ion_wall_products`	`Mapping[str, Mapping[str, float]]`	What an ion returns to the volume after reaching the wall, `{ion: {product: number}}`, e.g. `{"H2+": {"H2": 1}}`.
`gas_temperature`	`float \| GasTemperature`	A fixed gas temperature in eV, or its balance.
`thermalize_electrons`	`bool`	Keep `T_e >= T_g`. Without sources of energy the wall losses cool the electrons of a decaying plasma below the gas, which no elastic collision allows; set it for afterglows.

Name	Type	Description
`densities`	`dict[str, float]`	Every species’ density in m^-3, the electrons included.
`electron_temperature`	`float`	`T_e` in eV.
`gas_temperature`	`float`	`T_g` in eV.
`reaction_rates`	`dict[str, float]`	Volume rate of every reaction (m^-3 s^-1), by name.
`wall_losses`	`dict[str, float]`	Volume rate at which every species reaches the walls (m^-3 s^-1), the electrons included.
`power`	`dict[str, float]`	Electron power terms in W (positive: gained), by channel; at steady state they sum to zero.
`particle_balance`	`dict[str, float]`	`dn/dt` of every species (m^-3 s^-1); zero at steady state, except for a species held fixed, where it is the rate the reactions consume it at (and its feed would have to make up).
`converged`	`bool`	Whether the steady state was reached.

Name	Type	Default	Description
`x_edges`	`Sequence[float] \| np.ndarray \| None`	`None`	Cell edges of the first axis (`x`, or `r` from `>= 0`) [m]: a tensor grid; or give `grid`.
`y_edges`	`Sequence[float] \| np.ndarray \| None`	`None`	Cell edges of the second axis (`y`, or `z`) [m].
`frequency`	`float`	required	The driving frequency [Hz].
`windings`	`Sequence[Winding]`	`()`	The coil windings; each carries `sign` times the coil current.
`conductors`	`Sequence[Conductor]`	`()`	The perfect conductors.
`electron_density`	`CellField`	`0.0`	`n_e` [m^-3] on the cells (set to zero in the windings, the conductors and outside `plasma_region`).
`collision_frequency`	`CellField`	`0.0`	The electron momentum-transfer frequency `nu` [1/s].
`electron_temperature`	`CellField \| None`	`None`	`T_e` [eV]: with it, the electrons carry the collisional viscosity `(2/3) n_e e T_e / nu` (`nu > 0` in the plasma).
`electron_viscosity`	`CellField \| None`	`None`	`mu_e` [Pa s] directly, instead of from `T_e`; zero gives the momentum balance without viscosity (the cold plasma, solved with `u`).
`plasma_region`	`PlasmaRegion \| None`	`None`	Where the plasma is; everywhere if `None`.
`boundaries`	`tuple[AxisBoundary, AxisBoundary] \| None`	`None`	The boundary of each axis (see :class:`CellGrid`); default `("dirichlet", "dirichlet")`, or the grid’s.
`geometry`	`Geometry \| None`	`None`	`"cartesian"` (a cut, `A_z`) or `"cylindrical"` (r–z, `A_phi`); default `"cartesian"`, or the grid’s.
`electron_drift`	`Any`	`None`	The in-plane electron velocity for the RF Lorentz force; not implemented until `Fluid2D` provides it.
`grid`	`CellGrid \| PatchGrid \| None`	`None`	A grid instead of the edges, e.g. a :class:`~wellbalanced.spatial.patches.PatchGrid` (its geometry and boundaries are the model’s).

Name	Type	Description
`material`	`TargetMaterial`	The target material.
`target_area`	`float`	The area of the racetrack the ions hit, in m^2.
`region_height`	`float`	The height of the ionization region above it in m; the volume is `target_area * region_height`.
`side_area`	`float`	The other boundaries ions leave the region through, in m^2.
`h_factor`	`float`	The edge-to-centre density ratio at the boundaries.
`pressure`	`float`	The argon filling pressure in Pa, at `gas_temperature`.
`gas_temperature`	`float`	The gas temperature in K.
`refill_time`	`float`	The time in s in which the argon of the region is replaced.
`wind_efficiency`	`float`	Ar atoms pushed out per sputtered atom (0: no sputter wind).
`heating_fraction`	`float`	The share of the secondary electron energy the plasma electrons keep: at most 1 if the secondary electron yield is right; a larger value, as :meth:`calibrate_heating` may find, means the yield of the placeholder material is too low (only the product matters).
`seed`	`float`	A pair source in m^-3 s^-1 that stands for the residual plasma and preionization at the start of a pulse; it keeps the density from decaying to zero in the afterglow.

Name	Type	Description
`shapes`	`Sequence[Any]`	Shapes whose union is the region (e.g. the driver and the expansion region as two rectangles, a T in r–z).
`excluded`	`Sequence[Any]`	Shapes cut out of it (e.g. an internal structure).

Name	Type	Description
`species`	`Sequence[Species]`	Every species, the electrons (`"e"`) included.
`reactions`	`Sequence[Reaction]`	The volume reactions.
`fixed`	`Mapping[str, float]`	Densities held fixed (m^-3), the gases.
`radius`	`float`	The plasma radius `R` in m.
`length`	`float`	The driver’s length in m.
`coil_turns`	`float`	The coil’s turns `N`.
`coil_radius`	`float`	The coil’s radius `b` in m.
`coil_length`	`float \| None`	The coil’s length `l` in m; the driver’s if `None`.
`frequency`	`float`	The RF frequency in Hz.
`network_resistance`	`float`	`R_net` in Ohm.
`momentum_transfer`	`Sequence[str]`	Names of the reactions whose rates per electron make up `nu_m` (the elastic electron collisions).
`ion_mean_free_path`	`float`	`lambda_i` in m.
`skin_density_factor`	`float`	The electron density of the skin layer over the volume average.
`field_factor`	`float \| None`	The coil’s inductance over the long-solenoid one; Nagaoka’s coefficient if `None`.
`coupling`	`Literal['transformer', 'solenoid']`	`"transformer"` (:func:`transformer_impedance`) or `"solenoid"`, the exact uniform column (:func:`solenoid_impedance`).
`model_options`	`Mapping[str, Any]`	Further fields of the :class:`GlobalModel` (gas temperature, wall reactions, ion wall products, …).

Name	Type	Description
`name`	`str`	A unique name, used by the reactions (`"e"` for electrons).
`mass`	`float`	The mass in kg.
`charge`	`int`	The charge in elementary charges.

Name	Type	Description
`name`	`str`	The element, e.g. `"Ti"`; the species are `name` and `name+`.
`mass_u`	`float`	The atomic mass in u.
`ionization_energy`	`float`	The first ionization energy in eV.
`outer_electrons`	`int`	The electrons of the outer shell in the Lotz formula.
`argon_yield`	`float`	Atoms sputtered per `Ar+` at the cathode-fall energy.
`self_yield`	`float`	Atoms sputtered per metal ion (self-sputtering).
`argon_secondary`	`float`	Secondary electrons emitted per `Ar+`.
`self_secondary`	`float`	Secondary electrons emitted per metal ion.
`charge_exchange`	`float`	Rate of `Ar+ + M -> Ar + M+` in m^3/s.
`verified`	`bool`	`False` while the yields and rates are placeholders.

wellbalanced

ELECTRONattributemodule attribute#

MATERIALSattributemodule attribute#

Boundaryclassdataclass#

kindattributeinstance attribute#

reflectionattributeclass attributeinstance attribute#

temperatureattributeclass attributeinstance attribute#

valueattributeclass attributeinstance attribute#

densitymethodclassmethod#

fluxmethodclassmethod#

symmetrymethodclassmethod#

wallmethodclassmethod#

CellGridclass#

boundariesattributeinstance attribute#

cell_areasattributeinstance attribute#

cell_volumesattributeinstance attribute#

circumferenceattributeinstance attribute#

geometryattributeinstance attribute#

shapeattributeinstance attribute#

sizeattributeinstance attribute#

xattributeinstance attribute#

x_edgesattributeinstance attribute#

yattributeinstance attribute#

y_edgesattributeinstance attribute#

coordinate_namesproperty#

cylindricalproperty#

dimsproperty#

on_axisproperty#

cell_fieldmethod#

coordinatesmethod#

curlmethod#

curl_curlmethod#

locatemethod#

maskmethod#

net_currentmethod#

union_maskmethod#

wall_cellsmethod#

Chamberclassdataclass#

cuspattributeclass attributeinstance attribute#

h_factorattributeclass attributeinstance attribute#

ion_loss_areaattributeclass attributeinstance attribute#

volumeattributeinstance attribute#

wall_areaattributeinstance attribute#

ion_areamethod#

Coilclassdataclass#

field_factorattributeclass attributeinstance attribute#

lengthattributeinstance attribute#

radiusattributeinstance attribute#

turnsattributeinstance attribute#

factorproperty#

inductanceproperty#

Conductorclassdataclass#

floatingattributeclass attributeinstance attribute#

nameattributeclass attributeinstance attribute#

shapesattributeinstance attribute#

Cuspclassdataclass#

fieldattributeinstance attribute#

line_lengthattributeinstance attribute#

areamethod#

leak_widthmethod#

DriftFluid2Dclassdataclass#

anode_thermal_fluxattributeclass attributeinstance attribute#

bohmattributeclass attributeinstance attribute#

cathode_current_densityattributeclass attributeinstance attribute#

depletionattributeclass attributeinstance attribute#

diamagneticattributeclass attributeinstance attribute#

electron_temperatureattributeclass attributeinstance attribute#

excitation_energy_evattributeclass attributeinstance attribute#

excitation_rateattributeclass attributeinstance attribute#

external_sourcesattributeclass attributeinstance attribute#

field_bcattributeclass attributeinstance attribute#

floor_addedattributeclass attributeinstance attribute#

gas_densityattributeclass attributeinstance attribute#

heating_scaleattributeclass attributeinstance attribute#

ion_friction_rateattributeclass attributeinstance attribute#

ion_mass_uattributeclass attributeinstance attribute#

ion_temperatureattributeclass attributeinstance attribute#

ionization_energy_evattributeclass attributeinstance attribute#

ionization_rateattributeclass attributeinstance attribute#

length_xattributeinstance attribute#

`ELECTRON`attributemodule attribute#

`MATERIALS`attributemodule attribute#

`Boundary`classdataclass#

`kind`attributeinstance attribute#

`reflection`attributeclass attributeinstance attribute#

`temperature`attributeclass attributeinstance attribute#

`value`attributeclass attributeinstance attribute#

`density`methodclassmethod#

`flux`methodclassmethod#

`symmetry`methodclassmethod#

`wall`methodclassmethod#

`CellGrid`class#

`boundaries`attributeinstance attribute#

`cell_areas`attributeinstance attribute#

`cell_volumes`attributeinstance attribute#

`circumference`attributeinstance attribute#

`geometry`attributeinstance attribute#

`shape`attributeinstance attribute#

`size`attributeinstance attribute#

`x`attributeinstance attribute#

`x_edges`attributeinstance attribute#

`y`attributeinstance attribute#

`y_edges`attributeinstance attribute#

`coordinate_names`property#

`cylindrical`property#

`dims`property#

`on_axis`property#

`cell_field`method#

`coordinates`method#

`curl`method#

`curl_curl`method#

`locate`method#

`mask`method#

`net_current`method#

`union_mask`method#

`wall_cells`method#

`Chamber`classdataclass#

`cusp`attributeclass attributeinstance attribute#

`h_factor`attributeclass attributeinstance attribute#

`ion_loss_area`attributeclass attributeinstance attribute#

`volume`attributeinstance attribute#

`wall_area`attributeinstance attribute#

`ion_area`method#

`Coil`classdataclass#

`field_factor`attributeclass attributeinstance attribute#

`length`attributeinstance attribute#

`radius`attributeinstance attribute#

`turns`attributeinstance attribute#

`factor`property#

`inductance`property#

`Conductor`classdataclass#

`floating`attributeclass attributeinstance attribute#

`name`attributeclass attributeinstance attribute#

`shapes`attributeinstance attribute#

`Cusp`classdataclass#

`field`attributeinstance attribute#

`line_length`attributeinstance attribute#

`area`method#

`leak_width`method#

`DriftFluid2D`classdataclass#

`anode_thermal_flux`attributeclass attributeinstance attribute#

`bohm`attributeclass attributeinstance attribute#

`cathode_current_density`attributeclass attributeinstance attribute#

`depletion`attributeclass attributeinstance attribute#

`diamagnetic`attributeclass attributeinstance attribute#

`electron_temperature`attributeclass attributeinstance attribute#

`excitation_energy_ev`attributeclass attributeinstance attribute#

`excitation_rate`attributeclass attributeinstance attribute#

`external_sources`attributeclass attributeinstance attribute#

`field_bc`attributeclass attributeinstance attribute#

`floor_added`attributeclass attributeinstance attribute#

`gas_density`attributeclass attributeinstance attribute#

`heating_scale`attributeclass attributeinstance attribute#

`ion_friction_rate`attributeclass attributeinstance attribute#

`ion_mass_u`attributeclass attributeinstance attribute#

`ion_temperature`attributeclass attributeinstance attribute#

`ionization_energy_ev`attributeclass attributeinstance attribute#

`ionization_rate`attributeclass attributeinstance attribute#

`length_x`attributeinstance attribute#

`length_y`attributeinstance attribute#

Name	Type	Description
`shape`	`Any`	A 2D shape with `contains_points` (e.g. a :class:`simgeometry.Circle` of the tube’s radius).
`sign`	`float`	The direction of the current: `+1` or `-1` (the two sides of a driver in a cut carry opposite signs), or a turn count.
`name`	`str`	A label for the diagnostics.

Name	Type	Default	Description
`results`	`Sequence[_HasDataset]`	required	The results, e.g. of :meth:`GlobalModel.scan`.
`dim`	`str`	required	The name of the new dimension, e.g. `"power"`.
`values`	`Sequence[Any] \| np.ndarray`	required	The parameter’s value of every result.
`long_name`	`str \| None`	`None`	Its label; `dim` if `None`.
`units`	`str`	`''`	Its units.
`attrs`	`Mapping[str, Any] \| None`	`None`	Further attributes of the dataset.