Electron current in probe circuit in gas plasma¶
A gas-discharge plasma is an ionized gas in which the concentrations of positively and negatively charged particles are approximately equal to each other, and the Debye shielding radius is significantly smaller than the characteristic size of the volume in which the ionized gas is located.
A probe is an auxiliary metal electrode that is inserted into a plasma volume for its examination. Flat, cylindrical and spherical probesare used. A potential is set relative to one of the electrodes on the probe and the dependence of the incoming current on the value of this potential is removed.
Notation:
\(e\) (
e) iselementary_charge.\(m_\text{e}\) (
m_e) iselectron_rest_mass.\(k_\text{B}\) (
k_B) isboltzmann_constant.
- Symbol:
I- Latex:
\(I\)
- Dimension:
current
- Symbol:
A- Latex:
\(A\)
- Dimension:
area
- electron_concentration¶
Electron concentration (
number_density) in plasma.
- Symbol:
n- Latex:
\(n\)
- Dimension:
1/volume
- plasma_temperature¶
Plasma
temperature.
- Symbol:
T- Latex:
\(T\)
- Dimension:
temperature
- floating_plasma_potential¶
Floating plasma
electric_potential.
- Symbol:
U_f- Latex:
\(U_\mathbf{f}\)
- Dimension:
voltage
- probe_potential¶
electric_potentialat the location of the probe.
- Symbol:
U_E- Latex:
\(U_\mathbf{E}\)
- Dimension:
voltage
- law¶
I = 0.25 * A * e * n * sqrt(8 * k_B * T / (pi * m_e)) * exp(-e * (U_f - U_E) / (k_B * T))- Latex:
- \[I = 0.25 A e n \sqrt{\frac{8 k_\text{B} T}{\pi m_\text{e}}} \exp{\left(- \frac{e \left(U_\mathbf{f} - U_\mathbf{E}\right)}{k_\text{B} T} \right)}\]