Electron distribution function in gas plasma per Druyvestein

In a gas discharge, electrons have a wide range of energies, which is described by the electron energy distribution function. Electrons in a gas-discharge plasma acquire their energy under the action of an electric field. Energy consumption occurs due to elastic and, especially, inelastic collisions with atoms. In addition, energy exchange between electrons is also possible in plasma. Depending on the relationship between all these factors, different electron energy distributions are established. Under equilibrium conditions, the Maxwell distribution is most common. But in the case of intense ionization, the number of fast electrons decreases in the distribution function, and it passes into the Druyvestein distribution function.

Notation:

1. \(e\) (e) is elementary_charge.

Links:

1. Comsol, possible similar formula here.

distribution_function

Electron distribution function.

Symbol:

f

Latex:

\(f\)

Dimension:

dimensionless

voltage

voltage between electrodes.

Symbol:

V

Latex:

\(V\)

Dimension:

voltage

electron_energy

Electron energy.

Symbol:

E

Latex:

\(E\)

Dimension:

energy

energy_constant

Constant equal to \(1.04 \, \text{eV}\).

Symbol:

E_0

Latex:

\(E_0\)

Dimension:

energy

law

f = E_0 * sqrt(e * V) / E^(3/2) * exp(-0.55 * (e * V)^2 / E^2)

Latex:

\[f = \frac{E_0 \sqrt{e V}}{E^{\frac{3}{2}}} \exp{\left(- \frac{0.55 \left(e V\right)^{2}}{E^{2}} \right)}\]