What it does
A Langmuir probe is a small bare wire put into a plasma. Sweeping its voltage and measuring the current gives an I-V curve that holds the plasma’s electron temperature, density and potential. This page does the classic analysis in your browser:
- Fits a straight line to the ion saturation part (large negative voltage) and subtracts it, leaving the electron current.
- Finds the floating potential Vf, where the net current is zero.
- Fits a straight line to ln(electron current) in the transition region: the slope is 1/Tₑ, so the electron temperature comes straight out in electronvolts.
- Finds the plasma potential Vp at the knee, where the exponential line meets the electron-saturation line.
- Works out the density twice: from the electron saturation current (¼ n e A v̄) and from the ion saturation current (Bohm, 0.61 n e A √(kTₑ/mᵢ)).
How to use it
- Paste two columns, voltage and current, or use Open a file for CSV, TSV, text or Excel. A header row is fine.
- Choose the current unit and the sign convention. Many systems plot electron current as positive; if yours is negative, switch it.
- Give the probe’s collecting area in mm² and the gas, which sets the ion mass.
- The fit ranges are automatic. If the ln Iₑ plot shows the straight part somewhere else, type the Te fit from/to voltages, or the voltage below which the ion line is fitted.
Worked example
The made-up example is an argon plasma measured with a 2 mm² probe from −40 V to +30 V. The page finds Tₑ = 2.97 eV, Vf = −3.38 V and Vp = 12 V. The ion saturation current is 5.22 µA and the electron saturation current 932 µA. The density is 1.01 × 10¹⁶ m⁻³ from the electrons and 9.97 × 10¹⁵ m⁻³ from the ions, a ratio of 1.01, so the trace is consistent. The trace was generated with Tₑ = 3 eV and n = 10¹⁶ m⁻³, so the analysis recovers them within 1 %.
Tips
- Use the log plot: the straight part should be long and clean. Curvature there means two electron populations or RF pick-up.
- If the two densities disagree by more than a factor of 2, check the area (sheath expansion makes the effective area bigger on small probes) and the gas.
- In a magnetised plasma, trust the ion density and Tₑ more than the electron saturation current.
FAQ
Why is the ion current taken at Vf? The ion line slopes because the sheath grows with voltage. The value at the floating potential is the usual compromise.
What does Vp − Vf tell me? For Maxwellian electrons it is Tₑ × ln(√(mᵢ/2πmₑ)/0.61), about 5.2 Tₑ for argon. A very different value suggests a non-Maxwellian plasma or a bad fit.
Is my data uploaded? No. Everything runs in your browser.
Can I rely on it? It is the standard first analysis, for study and planning; it is not a substitute for professional judgement or more complete probe theories (orbital motion limited, Laframboise).
Where the numbers come from
- Single-probe theory: Langmuir and Mott-Smith (1926); standard treatments in Hutchinson, I. H., Principles of Plasma Diagnostics, and Chen, F. F. (2003), Langmuir probe diagnostics (IEEE ICOPS mini-course). Bohm ion flux factor 0.61 = exp(−1/2).
- Checked against an independent NumPy re-implementation of the same fitting steps on the example trace, and against the made-up plasma (Tₑ = 3 eV, n = 10¹⁶ m⁻³, Vp = 12 V) used to generate it.
- The example trace is made up: computed from the probe equations with a little added noise.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.