# Ball-pen probe

A ball-pen probe is novel technique used to measure directly the plasma potential[1][2] in magnetized plasmas. The probe was invented by Jiří Adámek in the Institute of Plasma Physics [3] AS CR in 2004. The ball-pen probe balances the electron saturation current to the same magnitude as that of the ion saturation current. In this case, its floating potential becomes identical to the plasma potential. This goal is attained by a ceramic shield, which screens off an adjustable part of the electron current from the probe collector due to the much smaller gyro–radius of the electrons. First systematic measurements have been performed in the CASTOR tokamak in 2004. The probe has been already used at different fusion devices as ASDEX Upgrade,[3][4][5] COMPASS[4][5][4], ISTTOK,[6] TJ-K[7][5], RFX [6], MAST, H-1NF,IR-T1 as well as non-fusion devices as DC cylindrical magnetron[7] in Prague and linear magnetized plasma devices [8] in Nancy and Ljubljana.[7]

Ball-pen probe used on tokamak CASTOR in 2004. It consists of stainless steel collector, which is movable inside the ceramic (boron nitride) shielding tube.

## How the ball-pen probe measures the plasma potential

Schematic picture of a single ball-pen probe.

If Langmuir probe (electrode) is inserted into a plasma, its potential generally lies considerably below the plasma potential $\Phi$ due to what is termed a Debye sheath. Thus, the potential of Langmuir probe is named as floating potential $V_{fl}$. 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]

$V_{fl} = \Phi - \alpha*T_e$

and the coefficient $\alpha$. The coefficient is given by the ratio of the electron and ion saturation current density ($j^{sat}_e$ and $j^{sat}_i$) and collecting areas for electrons and ions ($A_e$ and $A_i$)

$\alpha = ln(\frac{A_e j^{sat}_e}{A_i j^{sat}_i}) = ln(R)$

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 $\alpha$ is equal to zero and floating potential of ball-pen probe is equal to the plasma potential independently on electron temperature

$V_{fl} = \Phi$

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 potential and ln(R) of the Ball-pen probe for different position of collector on tokamak CASTOR.

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 ball-pen probe collector in order to reach $R = 1$, which strongly depends on value of the magnetic field. The physics of ball-pen probe is not yet fully understood, but the collector retraction should be roughly below the ion 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 both electron and ion saturation currents. 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 to one, but not equal.[1][3][6] The I-V characteristics remain symmetric as well as for deeper position of ball-pen probe collector.

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 ball-pen probe remains almost constant as well as for deeper position.

## 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

$T_e = ln(\frac{\Phi-V_{fl}}{\alpha})$

The value of coefficient $\alpha$ 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 $\alpha$ can be calculated theoretically,[9][10] 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 mentioned above.[3] Therefore, the difference between ball-pen probe and Langmuir probe potential is given by the electron temperature, coefficient $\alpha$ and empirically found the ratio $R$.[3] Therefore, the electron temperature can be simply measured by using formula

The ball-pen probe (2mm collector) and Langmuir probe ring used on tokamak CASTOR for direct electron temperature measurements.

$T_e = ln(\frac{\Phi_{BPP}-V_{fl}}{\bar{\alpha}})$

with new coefficient $\bar{\alpha}$ for different plasma condition

Device Magnetic field gas $\bar{\alpha}$
COMPASS 1.15T Deuterium 2.2
CASTOR 1T Hydrogen 2.8
ISTTOK 0.6T Hydrogen 2.3
TJ-K 0.07T Hydrogen 3.0
DC cylindrical magnetron 0.04T Argon 5.2
Linear device Mirabelle 0.08T Argon 4.1
Linear device Mirabelle 0.08T Helium 2.9

## References

1. ^ a b Adámek, J.; J. Stöckel; M. Hron; J. Ryszawy; M. Tichý; R. Schrittwieser; C. Ionită; P. Balan; E. Martines; G. Van Oost (2004). "A novel approach to direct measurement of the plasma potential". Czechoslovak Journal of Physics 54 (3): 95–99. doi:10.1007/BF03166386. ISSN 1572-9486.
2. ^ Adámek, J.; J. Stöckel, I. Ďuran, M. Hron, R. Pánek, M. Tichý, R. Schrittwieser, C. Ionit, P. Balan, E. Martines, G. Oost (2005). "Comparative measurements of the plasma potential with the ball-pen and emissive probes on the CASTOR tokamak". Czechoslovak Journal of Physics 55 (3): 235–242. doi:10.1007/s10582-005-0036-8. ISSN 0011-4626.
3. ^ a b c d Adamek, J.; J. Horacek, H.W. Müller, V. Rohde, C. Ionita, R. Schrittwieser, F. Mehlmann, B. Kurzan, J. Stöckel, R. Dejarnac, V. Weinzettl, J. Seidl, M. Peterka, (2010). "Ball-Pen Probe Measurements in L-Mode and H-Mode on ASDEX Upgrade". Contrib. Plasma Phys. 50 (9): 854–859. doi:10.1002/ctpp.201010145.
4. ^ a b Adamek, J.; J. Horacek, J. Seidl, H.W. Müller, R. Schrittwieser, F. Mehlmann, P. Vondracek, S. Ptak, (2014). "Direct Plasma Potential Measurements by Ball-Pen Probe and Self-Emitting Langmuir Probe on COMPASS and ASDEX Upgrade". Contrib. Plasma Phys. 54 (4): 279–284. doi:10.1002/ctpp.201410072.
5. ^ a b J. Adamek, H.W. Müller, J. Horacek, R. Schrittwieser, P. Vondracek, B. Kurzan, P. Bilkova, P. Böhm, M. Aftanas, R. Panek. "Radial profiles of the electron temperature on COMPASS and ASDEX Upgrade from ball-pen probe and Thomson scattering diagnostic",41st EPS Conference on Plasma Physics, P2.011, [1]
6. ^ a b C. Silva, J. Adamek, H. Fernandes, P. Duarte(2013). "Comparison of fluctuations properties measured by Langmuir and by ball-pen probes in the ISTTOK boundary plasma",41st EPS Conference on Plasma Physics, P5.103, [2]
7. ^ a b c Adamek, Jiri; Matej Peterka, Tomaz Gyergyek, Pavel Kudrna, Mirko Ramisch, Ulrich Stroth, Jordan Cavalier, and Milan Tichy, (2013). "Application of the ball-pen probe in two low-temperature magnetised plasma devices and in torsatron TJ-K". Contrib. Plasma Phys. 53 (1): 39–44. doi:10.1002/ctpp.201310007.
8. ^ Bousselin, G.; J. Cavalier; J. F. Pautex; S. Heuraux; N. Lemoine; G. Bonhomme (2013). "Design and validation of the ball-pen probe for measurements in a low-temperature magnetized plasma". Review of Scientific Instruments 84 (1): 013505. doi:10.1063/1.4775491. ISSN 0034-6748.
9. ^ Stangeby P.C.: The Plasma Boundary of Magnetic Fusion Devices, Institute of Physics Publishing. Bristol and Philadelphia (2000).
10. ^ Hutchinson I.H.: Principles of Plasma Diagnostics, Cambridge University Press (1992).