A ball-pen probe is novel technique used to measure directly the plasma potential in strongly as well as weakly magnetized plasmas. The probe was invented by Jiří Adámek in the Institute of Plasma Physics  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 on the CASTOR tokamak. The probe has been already used at different fusion devices as ASDEX Upgrade, COMPASS, ISTTOK, TJ-K, RFX , MAST, H-1NF, IR-T1  as well as low temperature devices as DC cylindrical magnetron in Prague and linear magnetized plasma devices in Nancy and Ljubljana.
How the ball-pen probe measures the plasma potential
If Langmuir probe (electrode) is inserted into a plasma, its potential generally lies considerably below the plasma potential due to what is termed a Debye sheath. Thus, the potential of Langmuir probe is named as floating potential . 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 [eV]:
and the coefficient . The coefficient is given by the ratio of the electron and ion saturation current density ( and ) and collecting areas for electrons and ions ( and )
The ball-pen probe, in magnetized plasma, modifies the collecting areas for electrons and ions and makes the ratio equal to one. Thus, the coefficient is equal to zero and floating potential of ball-pen probe is equal to the plasma potential independently on electron temperature
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 ball-pen probe collector in order to reach , 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 is close to one. However, the experimental observation at different fusion devices confirmed that the ratio is close to one, but not equal. 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
The value of coefficient 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 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 of ball-pen probe is close to one, but not equal to one as mentioned above. Therefore, the difference between ball-pen probe and Langmuir probe potential is given by the electron temperature, coefficient of Langmuir probe and empirical value of the ratio  of ball-pen probe (or you can use approximation ). Therefore, the electron temperature can be simply measured by using formula
with new coefficient for different plasma condition
|COMPASS (divertor region)||1.15T||Deuterium||2.2|
|ASDEX Upgrade||1.9T (on LFS)||Deuterium||2.2|
|DC cylindrical magnetron||0.04T||Argon||5.2|
|Linear device Mirabelle||0.08T||Argon||4.1|
|Linear device Mirabelle||0.08T||Helium||2.9|
- 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.
- 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.
- J. Adámek, C. Ionita, R. Schrittwieser, J. Stöckel, M. Tichy, G. Van Oost. "Direct Measurements of the Electron Temperature by a Ball-pen/Langmuir probe", 32nd EPS Conference on Plasma Phys. Tarragona, 27 June - 1 July 2005 ECA Vol.29C, P-5.081 (2005) 
- Adamek, J.; V. Rohde; H.W. Müller; A. Herrmann; C. Ionita; R. Schrittwieser; F. Mehlmann; J. Stöckel; J. Horacek; J. Brotankova (2009). "Direct measurements of the plasma potential in ELMy H-mode plasma with ball-pen probes on ASDEX Upgrade tokamak". Journal of Nuclear Materials. 390–391: 1114–1117. doi:10.1016/j.jnucmat.2009.01.286.
- 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.
- 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.
- 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, Berlin, P2.011 
- J. Seidl, B. Vanovac, J. Adamek, J. Horacek, R. Dejarnac, P. Vondracek, M. Hron "Probe measurement of radial and parallel propagation of ELM filaments in the SOL of the COMPASS tokamak", 41st EPS Conference on Plasma Physics, Berlin, P5.059 
- Loureiro, J.; C. Silva; J. Horacek; J. Adamek; J. Stockel (2014). "Scrape-off layer width of parallel heat flux on tokamak COMPASS". Plasma Physics&Technology 1 (3): 121–123. ISSN 2336-2634.
- J. Adamek, J. Seidl, R. Panek, M. Komm, P. Vondracek, J. Stöckel. "Fast measurements of the electron temperature in divertor region of the COMPASS tokamak using ball-pen probe", 42nd EPS Conference on Plasma Physics, lisbon, P4.101 
- Silva, C.; J. Adamek, H. Fernandes, H. Figueiredo , (2015). "Comparison of fluctuations properties measured by Langmuir and ball-pen probes in the ISTTOK boundary plasma". Plasma Physics and Controlled Fusion 57 (2): 025003. doi:10.1088/0741-3335/57/2/025003.
- Adamek, Jiri; Matej Peterka; Tomaz Gyergyek; Pavel Kudrna; Mirko Ramisch; Ulrich Stroth; Jordan Cavalier; Milan Tichy (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.
- Walkden, N R; J. Adamek; S. Allan; B. D. Dudson; S. Elmore; G. Fishpool; J. Harrison; A. Kirk; M. Komm (2015). "Profile measurements in the plasma edge of MAST using a ball pen probe". Review of Scientific Instruments 86 (2): 023510. doi:10.1063/1.4908572.
- N. R. Walkden, "Properties of Intermittent Transport in the Mega Ampere Spherical Tokamak", PhD Thesis, 
- C.A. Michael, M. Vos, B. Blackwell, J. Brotankova, J. Howard, H. Chen, S. Haskey. "Turbulence and transport measurements in the H-1 Heliac" 
- Meshkani, S.; M. Ghoranneviss, A. Salar Elahi, M. Lafouti , (2015). "Design and Fabrication of Comparative Langmuir Ball-Pen Probe (LBP) for the Tokamak". Journal of Fusion 34 (2): 394–397. doi:10.1007/s10894-014-9811-5. ISSN 1572-9591. 
- S. Meshkani,M. Ghoranneviss, M. Lafouti, "Effect of Biasing on Electron Temperature in IR-T1 Tokamak", roceedings of the 5th International Conference on Development, Energy, Environment, Economics (DEEE '14),Florence, Italy November 22–24, 2014 
- Adamek, Jiri; Matěj Peterka; Tomaž Gyergyek; Pavel Kudrna; Milan Tichý (2012). "Diagnostics of magnetized low temperature plasma by ball-pen probe". NUKLEONIKA 57 (2): 297–300.
- Zanaska, Michal; J. Adamek; M. Peterka; P. Kudrna; M. Tichy (2015). "Comparative measurements of plasma potential with ball-pen and Langmuir probe in low-temperature magnetized plasma". Physics of Plasmas 22: 033516. doi:10.1063/1.4916572.
- Peterka M., "Experimental and theoretical study of utilization of probe methods for plasma diagnostics", Diploma Thesis, Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, 2014 (only Czech language) 
- Zanaska M., "Measurement of the plasma potential by means of the ball-pen and Langmuir probe", Bachelor thesis, Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University in Prague, 2013 (only Czech language) 
- 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.
- Silva, C.; J. Adamek, H. Fernandes, H. Figueiredo , (2014). "Comparison of fluctuations properties measured by Langmuir and ball-pen probes in the ISTTOK boundary plasma". Plasma Physics and Controlled Fusion 57 (2): 025003. doi:10.1088/0741-3335/57/2/025003.
- Stangeby P.C.: The Plasma Boundary of Magnetic Fusion Devices, Institute of Physics Publishing. Bristol and Philadelphia (2000).
- Hutchinson I.H.: Principles of Plasma Diagnostics, Cambridge University Press (1992).
- PhD thesis, Jiri Adamek (Czech and English language) 
- Overview: Ball-pen probe design, theory and first results at different fusion devices .
- 40th EPS Conference on Plasma, ISTTOK measurements .
- Examination of plasma current spikes and general analysis of H-mode shots in the tokamak COMPASS 
- Electrical Probe Measurements on the COMPASS Tokamak 
- Probe Measurements on the COMPASS Tokamak 
- Scanning ion sensitive probe for plasma profile measurements in the boundary of the Alcator C-Mod tokamak 
- Development of Probes for Assessment of Ion Heat Transport and Sheath Heat Flux in the Boundary of the Alcator C-Mod Tokamak 
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