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

4. Effect of RF on the I-V curve

5. An RF compensated probe

6. Slope of semi-log plot of Ie  1/Te

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

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

9. However, there can be an absorption radius

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

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

12. The problem is charge-exchange collisions

13. 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

14. The resonant impedance of the chokes is used

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

16. We used this part of the characteristic

17. In every case the I2 – V curve was closely linear

18. The electron plot is extended by subtracting Isat and iterating

19. The ABR and BRL theories do not fit the data

20. 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

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

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

23. 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!

24. Experimental difficulties 1

25. Experimental difficulties 2
Electron current can heat the probe

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

27. However the beam depends on the ion extrapolation

28. Experimental difficulties 4: potential pulling

29. 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