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wellbalanced
Projects

Full examples

Complete Python examples are listed below. Each page shows the script and its plots.

  • 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.
  • A global model of an argon discharge: electron temperature and density against pressure.: The textbook global model (Lieberman and Lichtenberg, ch. 10): one ion species, ionization from a step cross section averaged over a Maxwellian (with plasmacoll), elastic losses, ions leaving at the Bohm speed. The particle balance alone sets the electron temperature, which falls with the pressure; the power balance then sets the density. Magnetic cusps that cover most of the wall lower both the losses and the electron temperature. The cross sections are illustrative step functions, not argon data. Every scan is one xarray dataset (:func:wellbalanced.stack), plotted with plasma-plots.
  • A global model of a HiPIMS magnetron: rarefaction, metal ions and self-sputtering.: The ionization region of a sputtering magnetron in argon, balanced as a global model: Ar and the sputtered metal, ionized by the electrons the secondary electrons heat, lost at the Bohm speed through the target (where the ions sputter it, by Ar+ and, for self-sputtering, by the metal ions) and through the sides, with the argon replaced on a refill time and pushed out by the sputtered atoms (the sputter wind). Driven by the discharge current and voltage of an experiment, it returns what decides the spoke regime: the argon rarefaction, the metal to argon density ratio, the metal share of the ion flux, the self-sputtering share of the sputtered flux and the electron density. First the dc states from 0.1 to 100 A for three targets, then a 100 A, 100 us pulse every millisecond on titanium, brought to its periodic state. The sputter and secondary electron yields, the geometry, the sputter wind and the heating are placeholders (see wellbalanced.magnetron): the trends are the model’s, the numbers are not data.
  • A beam-driven plasma neutralizer: the neutral fraction against the gas flow.: A 1 MeV, 10 A deuterium negative-ion beam crosses a 3 m channel. On the gas, and on the plasma it makes itself, it changes charge state; the plasma is a global model of the channel fed by the beam’s stripped and secondary electrons. Magnetic cusps on the side walls confine the plasma: it is far denser, but its ionization degree stays below a per cent, too little for stripping on the plasma to raise the neutral fraction much over that of the gas alone. The cross sections and rates are illustrative placeholders, not data (see wellbalanced.neutralizer.illustrative_deuterium_neutralizer): the curves show what the model computes, not what a neutralizer achieves. Every scan is one xarray dataset, plotted with plasma-plots.
  • A 0D RF driver: coil current and RF power transfer efficiency in seconds.: :class:wellbalanced.RFDriver couples a global model of the driver’s hydrogen plasma to a transformer model of the coil (Piejak, Godyak and Alexandrovich 1992; Lieberman and Lichtenberg sec. 12.2): the absorbed power fixes the electron density and temperature, those fix the skin layer and the resistance the coil sees, and that the coil current and the efficiency eta = R_s / (R_s + R_net). Compared with Zielke, Briefi and Fantz (NIBS’22, arXiv:2211.10143) and with the 2D field of rf_driver_inductive_field_2d.py (step R1):
  • The RF field of one and two drivers with a prescribed plasma: mutual coupling and shields.: The geometry of Zielke, Briefi and Fantz (NIBS’22, arXiv:2211.10143, Fig. 2): a horizontal 2D cut through a driver (23.7 cm wide, 17.4 cm long) and the expansion region (24.4 cm), six coil windings (6 mm tubes) on each side, 1 MHz; the backplates and the expansion walls are perfect conductors, and so are the electromagnetic shields (EMS) when present. With :class:wellbalanced.spatial.InductiveField2D and a prescribed plasma shaped like their Fig. 3 (up to 1.4e18 m^-3, depleted at the coil), this computes:
  • The BUG driver in r–z: cold and viscous electrons, and the global model’s plasma.: The 2D cylindrically symmetric domain of Zielke, Briefi, Lishev and Fantz (Plasma Sources Sci. Technol. 31, 035019, 2022, Fig. 1(b), dimensions read off the figure): the driver (radius 12 cm, 17 cm long) opening into the expansion region (radius 19 cm, up to the plasma grid at 42 cm), the driver and source backplates and the expansion wall as perfect conductors, the plasma grid as the right edge of the domain, the surroundings up to r = 50 cm; six coil turns (6 mm tubes) around the driver, 1 MHz, R_net = 0.6 Ohm. With :class:wellbalanced.spatial.InductiveField2D in r–z (no 2D-to-3D depth) this computes:
  • Verification of the 2D drift fluid: a uniform state, the E x B drift and a linear instability.: Three checks of :class:wellbalanced.DriftFluid2D against theory, each in seconds:
  • The sputter wind: the argon in front of a sputtering target, as a compressible gas.: The target of a magnetron is a wall in front of a gas at 1 Pa that emits sputtered metal atoms and, at the same time, the ions that hit it return as neutrals. Here only the sputtered titanium is emitted, at the flux the global model (:class:wellbalanced.Magnetron) finds for a discharge current of 1 to 100 A on a target of 10 cm^2, into 2 cm of argon that is refilled from a reservoir at the far end (wellbalanced.gasdynamics, the argon and the titanium as one compressible gas with one velocity and temperature and the diffusion of the titanium through the argon). Two cases of the energy of the sputtered atoms: cold atoms (they leave at the gas temperature, as the global model assumes: only their number and momentum push the gas) and 5 eV atoms (a mean energy of the order of the one of sputtered metals, a placeholder: their heat goes into the gas).