Langmuir Probe Diagnostics

A Langmuir probe is a small electrode inserted into a plasma to measure its local properties — electron temperature, electron density, and plasma potential. It is one of the most widely used plasma diagnostic tools.

I-V Characteristic

When a bias voltage (V) is applied to the probe, the current has contributions from ions and electrons:

$I(V) = I_{\text{sat,i}} + I_{e,\text{sat}} \exp\!\left(\frac{e(V - V_p)}{k_B T_e}\right)$

Below the plasma potential (V_p), ions flow freely and electrons are repelled, giving a characteristic exponential shape.

Bohm Velocity and Ion Saturation Current

Ions enter the probe's sheath at the Bohm velocity:

$v_{\text{Bohm}} = \sqrt{\frac{k_B T_e}{m_i}}$

The ion saturation current is:

$I_{\text{sat}} = 0.5 \cdot n \cdot e \cdot A \cdot v_{\text{Bohm}}$

where (A) is the probe area and (e = 1.602 \times 10^{-19}) C.

Electron Temperature from Two Points

On the electron-retardation part of the I-V curve, the current grows exponentially with voltage. Measuring two points ((V_1, I_1)) and ((V_2, I_2)) gives:

$T_e = \frac{V_1 - V_2}{\ln(I_1 / I_2)} \quad \text{[eV]}$

This is the standard method for extracting electron temperature from a Langmuir probe trace.