Langmuir probe
The ion velocity will satisfy the Bohm sheath criterion, which is, strictly speaking, an inequality, but which is usually marginally fulfilled.
The Bohm criterion in its marginal form says that the ion velocity at the sheath edge is simply the sound speed given by
The theory of double layers[1] typically employs an expression analogous to the Bohm criterion, but with the roles of electrons and ions reversed, namely
It has a spatial scale that depends on the physics of the ion source but which is large compared to the Debye length and often of the order of the plasma dimensions.
When an electrode is biased to any voltage other than the floating potential, the current it draws must pass through the plasma, which has a finite resistivity.
In either case, the effect is to add a voltage drop proportional to the current drawn, which shears the characteristic.
The deviation from an exponential function is usually not possible to observe directly, so that the flattening of the characteristic is usually misinterpreted as a larger plasma temperature.
Without quantitative modeling of the bulk resistivity, Langmuir probes can only give an upper limit on the electron temperature.
If the electrode is not shadowed by a wall or other nearby object, then the area must be doubled to account for current coming along the field from both sides.
The associated increase in the Debye length must be taken into account when considering ion non-saturation due to sheath effects.
In many geometries, this flux tube will end at a surface in a distant part of the device, and this spot should itself exhibit an I-V characteristic.
It is also likely that the magnetic field plays a decisive role in determining the level of electron saturation, but no quantitative theory is as yet available.
Once one has a theory of the I-V characteristic of an electrode, one can proceed to measure it and then fit the data with the theoretical curve to extract the plasma parameters.
The most straightforward way to measure the I-V characteristic of a plasma is with a single probe, consisting of one electrode biased with a voltage ramp relative to the vessel.
One advantage of the double probe is that neither electrode is ever very far above floating, so the theoretical uncertainties at large electron currents are avoided.
If it is desired to sample more of the exponential electron portion of the characteristic, an asymmetric double probe may be used, with one electrode larger than the other.
The bias voltage is chosen to be a few times the electron temperature so that the negative electrode draws the ion saturation current, which, like the floating potential, is directly measured.
The mean free path of the electrons is greater than the ion sheath about the tips and larger than the probe radius, and 3.)
More sophisticated analysis of triple probe data can take into account such factors as incomplete saturation, non-saturation, unequal areas.
A pin-plate probe consists of a small electrode directly in front of a large electrode, the idea being that the voltage sweep of the large probe can perturb the plasma potential at the sheath edge and thereby aggravate the difficulty of interpreting the I-V characteristic.
Various geometries have been proposed for use as ion temperature probes, for example, two cylindrical tips that rotate past each other in a magnetized plasma.
When the electrode is biased more positive than the plasma potential, the emitted electrons are pulled back to the surface so the I-V characteristic is hardly changed.
The ground is typically an electrode with a large surface area and is usually in contact with the same plasma (very often the metallic wall of the chamber).
is the electron distribution function normalized to unity Taking into account uniform conditions along the probe surface (boundaries are excluded),
, one can find the expression describing the second derivative of the probe I-V characteristic (obtained firstly by M. J. Druyvestein [5] defining the electron distribution function over velocity
For fusion plasmas, graphite electrodes with dimensions from 1 to 10 mm are usually used because they can withstand the highest power loads (also sublimating at high temperatures rather than melting), and result in reduced bremsstrahlung radiation (with respect to metals) due to the low atomic number of carbon.
If there can be significant deposition of conducting materials (metals or graphite), then the insulator should be separated from the electrode by a meander[clarify] to prevent short-circuiting.
In a magnetized plasma, it appears to be best to choose a probe size a few times larger than the ion Larmor radius.
Many plasma physicists feel more comfortable with proud probes, which have a longer tradition and possibly are less perturbed by electron saturation effects, although this is disputed.
Pop-up probes are similar, but the electrodes rest behind a shield and are only moved the few millimeters necessary to bring them into the plasma near the wall.
