Ball pen probe

How the ball-pen probe measures the plasma potential

If a Langmuir probe (electrode) is inserted into a plasma, its potential generally lies considerably below the plasma potential Φ due to what is termed a Debye sheath. Thus, the potential of Langmuir probe is named as floating potential V f l . Therefore, it is impossible to measure directly the plasma potential by simple Langmuir probe. The difference between plasma and floating potential is given by the electron temperature T e [eV]:

V f l = Φ − α ∗ T e

and the coefficient α . The coefficient is given by the ratio of the electron and ion saturation current density ( j e s a t and j i s a t ) and collecting areas for electrons and ions ( A e and A i )

α = l n ( A e j e s a t A i j i s a t ) = l n ( R )

The ball-pen probe, in magnetized plasma, modifies the collecting areas for electrons and ions and makes the ratio R equal to one. Thus, the coefficient α is equal to zero and floating potential of ball-pen probe is equal to the plasma potential independently on electron temperature

V f l = Φ

The ball-pen probe inserted into the magnetized plasma is directly on the plasma potential without additional power supplies or electronics.

The ball-pen probe design

The design of the ball-pen probe is shown in the schematic picture. The 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 must be oriented perpendicularly to the magnetic field lines. It is necessary to find the sufficient retraction of the ball-pen probe collector in order to reach R = 1 , which strongly depends on the magnetic field's value. The physics of the ball-pen probe are not yet fully understood, but the collector retraction should be roughly below the ion's Larmor radius. This "calibration" can be done in two different ways:

1) the ball-pen probe collector is biased by swept voltage (low frequency) to provide the I-V characteristics and see the saturation current of electrons as well as ions. The ball-pen probe collector is systematically retracted until the I-V characteristics become symmetric. In this case, the ratio R is close to one. However, the experimental observation at different fusion devices confirmed that the ratio R is close, but not equal, to one. The I-V characteristics remain symmetric for deeper positions of the ball-pen probe collector too.

2) the ball-pen probe collector is fully floating. The ball-pen probe collector is systematically retracted until its potential saturates at some value, which is above Langmuir probe potential. The floating potential of the ball-pen probe remains almost constant for deeper positions too.

The electron temperature measurements without power supply

The electron temperature can be measured by using ball-pen probe and common Langmuir probe with high temporal resolution in magnetized plasma without any external power supply. The electron temperature can be obtain from previous equation, assuming Maxwellian plasma

T e = Φ − V f l α

The value of coefficient α is given by the Langmuir probe geometry, plasma gas (Hydrogen, Deuterium, Helium, Argon, Neon,...) and magnetic field. It can be partially effected by other features like secondary electron emission, sheath expansion etc. The coefficient α can be calculated theoretically, and its value is around 3 for non-magnetized hydrogen plasma. This value is obtained under assumption that the ion and electron temperatures are equal and there are no other above mentioned effects (sheath expansion, ...). It should be also taken into account that ratio R of ball-pen probe is close to one, but not equal to one as it is assumed in previous chapter. Therefore, the difference between ball-pen probe and Langmuir probe potential is given by the electron temperature, coefficient α of Langmuir probe and empirical value of the ratio R of ball-pen probe (if there is no empirical value of R it can be used an approximation R = 1 ). Therefore, the electron temperature can be simply measured by using formula

T e = Φ B P P − V f l α ¯ ,

where

α ¯ = α − l n ( R ) .

The coefficient α ¯ for different plasma condition: