Ball-pen probe

A ball-pen probe is a modified Langmuir probe used to measure the plasma potential in magnetized plasmas. The ball-pen probe balances the electron and ion saturation currents, so that its floating potential is equal to the plasma potential. Because electrons have a much smaller gyroradius than ions, a moving ceramic shield can be used to screen off an adjustable part of the electron current from the probe collector.
Ball-pen probes are used in plasma physics, notably in tokamaks such as CASTOR, (Czech Academy of Sciences Torus) ASDEX Upgrade, COMPASS, ISTTOK, MAST, TJ-K, RFX, H-1 Heliac, IR-T1, GOLEM as well as low temperature devices as DC cylindrical magnetron in Prague and linear magnetized plasma devices in Nancy and Ljubljana.
Principle.
If a Langmuir probe (electrode) is inserted into a plasma, its potential is not equal to the plasma potential formula_1 because a Debye sheath forms, but instead to a floating potential formula_2. The difference with the plasma potential is given by the electron temperature formula_3:
formula_4
where the coefficient formula_5 is given by the ratio of the electron and ion saturation current density (formula_6 and formula_7) and collecting areas for electrons and ions (formula_8 and formula_9):
formula_10
The ball-pen probe modifies the collecting areas for electrons and ions in such a way that the ratio formula_11 is equal to one. Consequently, formula_12 and the floating potential of the ball-pen probe becomes equal to the plasma potential regardless of the electron temperature:
formula_13
Design and calibration.
A ball-pen probe consists of a conically shaped collector (non-magnetic stainless steel, tungsten, copper, molybdenum), which is shielded by an insulating tube (boron nitride, Alumina). The collector is fully shielded and the whole probe head is placed perpendicular to magnetic field lines.
When the collector slides within the shield, the ratio formula_14 varies, and can be set to 1. The adequate retraction length strongly depends on the magnetic field's value. The collector retraction should be roughly below the ion's Larmor radius. Calibrating the proper position of the collector can be done in two different ways:
Electron temperature measurements.
Using two measurements of the plasma potential with probes whose coefficient formula_16 differ, it is possible to retrieve the electron temperature passively (without any input voltage or current). Using a Langmuir probe (with a non-negligible) and a ball-point probe (whose associated formula_17 is close to zero) the electron temperature is given by:
formula_18
where formula_1 is measured by the ball-pen probe, formula_2 by the standard Langmuir probe, and formula_5 is given by the Langmuir probe geometry, plasma gas composition, the magnetic field, and other minor factors (secondary electron emission, sheath expansion, etc.) It can be calculated theoretically, its value being about 3 for a non-magnetized hydrogen plasma.
In practice, the ratio formula_14 for the ball-pen probe is not exactly equal to one, so that the coefficient formula_5 must be corrected by an empirical value for formula_11:
formula_25
where
formula_26