If a Langmuir probe is inserted into a plasma, its potential is not equal to the plasma potential because a Debye sheath forms, but instead to a floating potential. The difference with the plasma potential is given by the electron temperature : where the coefficient is given by the ratio of the electron and ion saturation current density and collecting areas for electrons and ions : The ball-pen probe modifies the collecting areas for electrons and ions in such a way that the ratio is equal to one. Consequently, and the floating potential of the ball-pen probe becomes equal to the plasma potential regardless of the electron temperature:
A ball-pen probe consists of a conically shaped collector, which is shielded by an insulating tube. 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 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:
The ball-pen probe collector is biased by a low-frequency voltage that provides the I-V characteristics and obtain the saturation current of electrons and ions. The collector is then retracted until the I-V characteristics becomes symmetric. In this case, the ratio is close to unity, though not exactly. If the probe is retracted deeper, the I-V characteristics remain symmetric.
The ball-pen probe collector potential is left floating, and the collector is retracted until its potential saturates. The resulting potential is above the Langmuir probe potential.
Using two measurements of the plasma potential with probes whose coefficient differ, it is possible to retrieve the electron temperature passively. Using a Langmuir probe and a ball-point probe the electron temperature is given by:
where is measured by the ball-pen probe, by the standard Langmuir probe, and is given by the Langmuir probe geometry, plasma gas composition, the magnetic field, and other minor factors It can be calculated theoretically, its value being about 3 for a non-magnetized hydrogen plasma. In practice, the ratio for the ball-pen probe is not exactly equal to one, so that the coefficient must be corrected by an empirical value for : where