Electron distribution function in gas plasma per Maxwell

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.

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 \(2.07 \, \text{eV}\).

Symbol:

E_0

Latex:

\(E_0\)

Dimension:

energy

law

f = E_0 * sqrt(e * V) / E^(3/2) * exp(-1.55 * e * V / E)

Latex:

\[f = \frac{E_0 \sqrt{e V}}{E^{\frac{3}{2}}} \exp{\left(- \frac{1.55 e V}{E} \right)}\]