An ideal I-V curve Exponential gives Te Isat gives density

Effect of RF on the I-V curve

An RF compensated probe

Slope of semi-log plot of Ie  1/Te

Large probe, dense plasma, thin sheath Small probe, weak plasma, thick sheath Langmuir’s Orbital-Motion-Limited (OML) theory

OML theory for monoenergetic ions But the ion random velocity is small and irrelevant!

However, there can be an absorption radius

Then complicated integrations are necessary Allen-Boyd-Reynolds (ABR) equation: no orbiting Bernstein-Rabinowitz-Laframboise theory: all included

(BRL works in fully ionized plasmas) But they don’t work! (BRL works in fully ionized plasmas)

The problem is charge-exchange collisions

We try to use very thin probes so that the OML theory is valid For Maxwellian ions and no absorption radius, Langmuir gives this very simple formula

The resonant impedance of the chokes is used

We took 100s of I-V curves in this helicon source

We used this part of the characteristic

In every case the I2 – V curve was closely linear

The electron plot is extended by subtracting Isat and iterating

The ABR and BRL theories do not fit the data

How did Langmuir get such a simple formula? This is what he started with for Maxwellian ions: . s is an assumed sheath radius at which ions start with their thermal velocities

Then he made some dubious approximations The ion temperature cancels out!

We tried to vary s and Ti but could not get observed straight I-V curve

Langmuir may have been just lucky! Conclusion: the simple OML formula is independent of Ti, as it should be, since Ti is very small. But the simple formula depends on bad approximations, and the exact formula cannot fit the data. Langmuir may have been just lucky!

Experimental difficulties 1

Experimental difficulties 2 Electron current can heat the probe

Experimental difficulties 3: fake electron beams This models a bi-Maxwellian

However the beam depends on the ion extrapolation

Experimental difficulties 4: potential pulling

Langmuir probes are not as simple as they seem Langmuir probes are not as simple as they seem. It takes a lot of experience to use them properly! The end