Langmuir Probe I-V Sweep

2D twin of the 3D Langmuir probe laboratory: electrons and ions near a biased tip, the I-V curve, and a fit that recovers the plasma parameters.

Presets

Playback

Plasma and probe

A negative probe repels electrons and collects ions; a positive one collects electron current.

Measurement

Model checks

The science

What is modelled

An idealised collisionless, unmagnetised Maxwellian plasma and a small planar probe. Below the plasma potential Vp the electron current falls exponentially; above it, it saturates. Ions give a small, nearly constant current set by the Bohm criterion.

Equations

  • Electron current Ie = Ies exp((V - Vp)/Te) for V < Vp, with Ies = e n A sqrt(kTe / 2πme).
  • Ion saturation Iis = 0.61 e n A sqrt(kTe/mi) (Bohm).
  • Floating potential Vf = Vp + Te ln(Iis/Ies); Debye length λD = sqrt(ε0 kTe / n e2).

Honest limits

Teaching-grade model: no magnetic field, collisions, sheath expansion or RF; the fit is not uncertainty-calibrated. The sheath circle is a schematic, not to scale.

What to try
  • Pick Helium, hot electrons: the semilog slope flattens as Te rises and the Debye length grows.
  • Raise the noise to 5 percent and see how the fitted Te and density degrade.
  • Move the bias below the floating potential and watch the net current turn negative (ions dominate).
Probe I-V curve (blue: noisy sweep, orange: ideal)
Semilog electron current with the Te fit
Debye length against electron temperature
Ion and electron components
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