Ball-pen probe

If a Langmuir probe (electrode) is inserted into a plasma, its potential is not equal to the plasma potential $\backslash Phi$ because a Debye sheath forms, but instead to a floating potential $V\_\{fl\}$. The difference with the plasma potential is given by the electron temperature $T\_e$:

$$

\Phi - V_{fl} = \alpha T_e

where the coefficient $\backslash alpha$ 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\left(\frac{A_e j^{sat}_e}{A_i j^{sat}_i}\right) = \ln(R)

The ball-pen probe modifies the collecting areas for electrons and ions in such a way that the ratio $R$ is equal to one. Consequently, $\backslash alpha\; =\; 0$ and the floating potential of the ball-pen probe becomes equal to the plasma potential regardless of the electron temperature:

$$

V_{fl} = \Phi

File:Vfl lnIsat Ball-pen probe 80mm.png

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 $R$ 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.{{citation needed|reason=Please cite a peer-reviewed article that explicitly says this.|date=September 2017}} Calibrating the proper position of the collector can be done in two different ways:

1. 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 $R$ is close to unity, though not exactly.{{cite journal|last=Silva|first=C. |author2=J. Adamek |author3=H. Fernandes |author4=H. Figueiredo |year=2014|title=Comparison of fluctuations properties measured by Langmuir and ball-pen probes in the ISTTOK boundary plasma|journal=Plasma Physics and Controlled Fusion|volume=57|issue=2|pages=025003|doi=10.1088/0741-3335/57/2/025003|bibcode=2015PPCF...57b5003S|citeseerx=10.1.1.691.3443 |s2cid=59151012 }} If the probe is retracted deeper, the I-V characteristics remain symmetric.
2. 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.{{clarify |date=September 2017 |reason= How does this amount to a "calibration" of the correct length, exactly?}}

Using two measurements of the plasma potential with probes whose coefficient $\backslash alpha$ 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 $R$ is close to zero) the electron temperature is given by:

$$

T_e = \frac{\Phi-V_{fl}}{\alpha}

where $\backslash Phi$ is measured by the ball-pen probe, $V\_\{fl\}$ by the standard Langmuir probe, and $\backslash alpha$ 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 $R$ for the ball-pen probe is not exactly equal to one, so that the coefficient $\backslash alpha$ must be corrected by an empirical value for $R$:

$$

T_e = \frac{\Phi_{BPP}-V_{fl}}{\bar{\alpha}},

where

$$

\bar{\alpha}=\alpha - ln(R).

{{Reflist|refs=

{{cite journal|last=Adámek|first=J.|author2=J. Stöckel |author3=M. Hron |author4=J. Ryszawy |author5=M. Tichý |author6=R. Schrittwieser |author7=C. Ionită |author8=P. Balan |author9=E. Martines |author10=G. Van Oost |year=2004|title=A novel approach to direct measurement of the plasma potential|journal=Czechoslovak Journal of Physics|volume=54|issue=3|pages=95–99|issn=1572-9486|doi=10.1007/BF03166386 |bibcode=2004CzJPS..54C..95A|s2cid=54869196}}

{{cite journal|last=Adámek|first=J. |author2=J. Stöckel |author3=I. Ďuran |author4=M. Hron |author5=R. Pánek |author6=M. Tichý |author7=R. Schrittwieser |author8=C. Ionit |author9=P. Balan |author10=E. Martines |author11=G. Oost|year=2005|title=Comparative measurements of the plasma potential with the ball-pen and emissive probes on the CASTOR tokamak|journal=Czechoslovak Journal of Physics|volume=55|issue=3|pages=235–242|issn=0011-4626|doi=10.1007/s10582-005-0036-8 |bibcode=2005CzJPh..55..235A|s2cid=54002051 }}

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) [http://epsppd.epfl.ch/Tarragona/pdf/P5_081.pdf]

{{cite journal|last=Bousselin|first=G.|author2=J. Cavalier |author3=J. F. Pautex |author4=S. Heuraux |author5=N. Lemoine |author6=G. Bonhomme |year=2013|title=Design and validation of the ball-pen probe for measurements in a low-temperature magnetized plasma|journal=Review of Scientific Instruments|volume=84|issue=1|pages=013505–013505–8|issn=0034-6748|doi=10.1063/1.4775491|pmid=23387648|bibcode=2013RScI...84a3505B|doi-access=free}}

G. Bousselin, J. Cavalier, J. Adamek, G. Bonhomme. "Ball-pen probe measurements in a low-temperature magnetized plasma", 39th EPS Conference & 16th Int. Congress on Plasma Physics, Stockholm, Sweden, P4.042 (2012) [http://ocs.ciemat.es/epsicpp2012pap/pdf/P4.042.pdf]

{{cite journal|last=Adamek|first=J. |author2=V. Rohde |author3=H.W. Müller |author4=A. Herrmann |author5=C. Ionita |author6=R. Schrittwieser |author7=F. Mehlmann |author8=J. Stöckel |author9=J. Horacek |author10=J. Brotankova|year=2009|title=Direct measurements of the plasma potential in ELMy H-mode plasma with ball-pen probes on ASDEX Upgrade tokamak|journal=Journal of Nuclear Materials|volume=390–391 |pages=1114–1117|doi=10.1016/j.jnucmat.2009.01.286|bibcode=2009JNuM..390.1114A|url=http://edoc.mpg.de/431639 |hdl=11858/00-001M-0000-0026-F6E0-E |hdl-access=free }}

{{cite journal|last=Adamek|first=J. |author2=J. Horacek |author3=H.W. Müller |author4=V. Rohde |author5=C. Ionita |author6=R. Schrittwieser |author7=F. Mehlmann |author8=B. Kurzan |author9=J. Stöckel |author10=R. Dejarnac |author11=V. Weinzettl |author12=J. Seidl |author13=M. Peterka |year=2010|title=Ball-Pen Probe Measurements in L-Mode and H-Mode on ASDEX Upgrade|journal=Contributions to Plasma Physics|volume=50 |issue=9|pages=854–859|doi=10.1002/ctpp.201010145|bibcode=2010CoPP...50..854A|s2cid=122712744 |doi-access=free }}

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 [http://ocs.ciemat.es/EPS2014PAP/pdf/P2.011.pdf]

{{cite journal|last=Horacek|first=J. |author2=J. Adamek |author3=H.W. Müller |author4=J. Seidl |author5=C. Ionita |author6=F. Mehlmann |author7=A.H. Nielsen |author8=V. Rohde |author9=E. Havlickova|year=2010|title=Interpretation of fast measurements of plasma potential, temperature and density in SOL of ASDEX Upgrade|journal=Nuclear Fusion|volume=50 |issue=10 |pages=105001|doi=10.1088/0029-5515/50/10/105001|bibcode=2010NucFu..50j5001H|url=http://edoc.mpg.de/463860 |hdl=11858/00-001M-0000-0026-EFA1-2 |s2cid=123227789 |hdl-access=free }}

{{cite journal|last=Müller|first=H.W. |author2=J. Adamek |author3=R. Cavazzana |author4=G.D. Conway|author5=C. Fuchs |author6=J.P. Gunn |author7=A. Herrmann |author8=J. Horacek |display-authors=et al|year=2011|title=Latest investigations on fluctuations, ELM filaments and turbulent transport in the SOL of ASDEX Upgrade|journal=Nuclear Fusion|volume=51 |issue=7 |pages=073023|doi=10.1088/0029-5515/51/7/073023|bibcode=2011NucFu..51g3023M|hdl=11858/00-001M-0000-0026-EBAB-0 |s2cid=121614262 |url=http://edoc.mpg.de/570069 |hdl-access=free }}

{{cite journal|last=Adamek|first=J. |author2=H.W. Müller |author3=C. Silva |author4=R. Schrittwieser |author5=C. Ionita |author6=F. Mehlmann |author7=S. Costea |author8=J. Horacek |author9=B. Kurzan |author10=P. Bilkova |author11=P. Böhm |author12=M. Aftanas |author13=P. Vondracek |author14=J. Stöckel |author15=R. Panek |author16=H. Fernandes |author17=H. Figueiredo |year=2016|title=Profile measurements of the electron temperature on the ASDEX Upgrade, COMPASS, and ISTTOK tokamak using Thomson scattering, triple, and ball-pen probes|journal=Review of Scientific Instruments|volume=87 |issue=4 |pages=043510|doi=10.1063/1.4945797|pmid=27131677 |bibcode=2016RScI...87d3510A }}

{{cite journal|last=Grover|first=O. |author2=J. Adamek |author3=J. Seidl |author4=A. Devitre |author5=M. Sos |author6=P. Vondracek |author7=P. Bilkova |author8=M. Hron |year=2017|title=First simultaneous measurements of Reynolds stress with ball-pen and Langmuir probes |journal=Review of Scientific Instruments|volume=88 |issue=6 |pages=063501|doi=10.1063/1.4984240|pmid=28668002 |bibcode=2017RScI...88f3501G}}

{{cite journal|last=Adamek|first=J. |author2=J. Seidl |author3=M. Komm |author4=V. Weinzettl |author5=R. Panek |author6=J. Stöckel |author7=M. Hron |author8=P. Hacek |author9=M. Imrisek |author10=P. Vondracek |author11=J. Horacek |author12=A. Devitre |year=2017|title=Fast measurements of the electron temperature and parallel heat flux in ELMy H-mode on the COMPASS tokamak|journal=Nuclear Fusion|volume=57 |issue=2 |pages=022010|doi=10.1088/0029-5515/57/2/022010|bibcode=2017NucFu..57b2010A|s2cid=125525532 |url=https://zenodo.org/record/3453490 }}

{{cite journal|last=Adamek|first=J. |author2=J. Seidl |author3=J. Horacek |author4=M. Komm |author5=T. Eich |author6=R. Panek |author7=J. Cavalier |author8=A. Devitre |author9=M. Peterka |author10=P. Vondracek |author11=J. Stöckel| author12=D. Sestak |author13=O. Grover |author14=P. Bilkova |author15=P. Böhm |author16=J. Varju | author17=A. Havranek | author18=V. Weinzettl | author19=J. Lovell | author20=M. Dimitrova | author21=K. Mitosinkova | author22=R. Dejarnac |author23=M. Hron |year=2017|title=Electron temperature and heat load measurements in the COMPASS divertor using the new system of probes|journal=Nuclear Fusion|volume=57|number=11|pages=116017|doi=10.1088/1741-4326/aa7e09|bibcode=2017NucFu..57k6017A|hdl=11858/00-001M-0000-002D-BA59-3 |s2cid=125143428 |url=https://zenodo.org/record/3495879 |hdl-access=free }}

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 [http://ocs.ciemat.es/EPS2014PAP/pdf/P5.059.pdf]

{{cite journal|last=Loureiro|first=J.|author2=C. Silva |author3=J. Horacek |author4=J. Adamek |author5=J. Stockel |year=2014|title=Scrape-off layer width of parallel heat flux on tokamak COMPASS|journal=Plasma Physics & Technology|volume=1|issue=3|pages=121–123|issn=2336-2634}}[https://ppt.fel.cvut.cz/articles/2014/loureiro.pdf]

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 [http://ocs.ciemat.es/EPS2015PAP/pdf/P4.101.pdf]

{{cite journal|last=Panek|first=R. |author2=J. Adamek|author3=M. Aftanas|author4=P. Bilkova|author5=P. Böhm |author6=F. Brochard|author7=P. Cahyna |author8=J. Cavalier|author9=R.Dejarnac |author10=M. Dimitrova |author11=O. Grover |author12=J. Harrison|author13= P. Hacek|author14=J. Havlicek|author15=A. Havranek|author16=J. Horacek|author17= M. Hron|author18=M. Imrisek|author19= F. Janky|author20= A. Kirk|author21= M. Komm|author22= K. Kovarik|author23= J. Krbec|author24= L. Kripner|author25= T. Markovic|author26= K. Mitosinkova|author27= J. Mlynar|author28= D. Naydenkova|author29= M. Peterka|author30= J. Seidl|author31= J. Stöckel |author32= E. Stefanikova|author33= M. Tomes|author34= J. Urban|author35= P. Vondracek|author36= M. Varavin|author37= J. Varju|author38= V. Weinzettl|author39= J. Zajac|title=Status of the COMPASS tokamak and characterization of the first H-mode|journal=Plasma Phys. Control. Fusion |volume=58|issue=1 |pages=014015|year=2016|doi=10.1088/0741-3335/58/1/014015|bibcode=2016PPCF...58a4015P|doi-access=free}}

{{cite journal|last=Silva|first=C. |author2=J. Adamek |author3=H. Fernandes |author4=H. Figueiredo |year=2015|title=Comparison of fluctuations properties measured by Langmuir and ball-pen probes in the ISTTOK boundary plasma|journal=Plasma Physics and Controlled Fusion|volume=57|issue=2|pages=025003|doi=10.1088/0741-3335/57/2/025003|bibcode=2015PPCF...57b5003S|citeseerx=10.1.1.691.3443 |s2cid=59151012 }}

{{cite journal|last=Ghoranneviss|first=M. |author2=S. Meshkani|year=2016|title=Techniques for improving plasma confinement in IR-T1 Tokamak|journal=International Journal of Hydrogen Energy|doi=10.1016/j.ijhydene.2016.03.075|volume=41|issue=29 |pages=12555–12562|bibcode=2016IJHE...4112555G }}[http://www.sciencedirect.com/science/article/pii/S0360319915316657]

{{cite book |doi=10.22323/1.240.0052|doi-access=free |chapter=Ball-Pen Probe Diagnostics of a Weakly Magnetized Discharge Plasma Column |title=Proceedings of 1st EPS conference on Plasma Diagnostics — PoS(ECPD2015) |date=2016 |last1=Kovacic |first1=Jernej |last2=Salamon |first2=Lino |last3=Ikovic |first3=Gabrijela |last4=Gyergyek |first4=Tomaz |last5=Fonda |first5=Boris |page=052 }}

J. Cerovsky, M. Farnik, M. Sos, J. Svoboda, O. Ficker, M. Hetflejs, P. Svihra, M. Shkut, O. Grover, J. Veverka, V. Svoboda, J. Stockel, J. Adamek, M. Dimitrova, "Tokamak GOLEM for fusion education", 44th EPS Conference on Plasma Physic, 26–30 June 2017, Belfast, Northern Ireland (UK), P1.107, [http://ocs.ciemat.es/EPS2017PAP/pdf/P1.107.pdf]

{{cite journal|last=Adamek|first=Jiri |author2=Matej Peterka |author3=Tomaz Gyergyek |author4=Pavel Kudrna |author5=Mirko Ramisch |author6=Ulrich Stroth |author7=Jordan Cavalier |author8=Milan Tichy|year=2013|title=Application of the ball-pen probe in two low-temperature magnetised plasma devices and in torsatron TJ-K|journal=Contributions to Plasma Physics|volume=53 |issue=1|pages=39–44|doi=10.1002/ctpp.201310007|bibcode=2013CoPP...53...39A|s2cid=120969312 }}

{{cite journal|last=Adamek|first=Jiri|author2=J. Adamek |author3=M. Peterka |author4=P. Kudrna |author5=M. Tichy T. |author6=Gyergyek |year=2012|title=Diagnostics of magnetized low temperature plasma by ball-pen probe |journal=Nukleonika|volume=57|number=2|pages=297–300 |url=http://www.nukleonika.pl/www/back/full/vol57_2012/v57n2p297f.pdf}}

{{cite journal|last=Zanaska|first=Michal|author2=J. Adamek |author3=M. Peterka |author4=P. Kudrna |author5=M. Tichy |year=2015|title=Comparative measurements of plasma potential with ball-pen and Langmuir probe in low-temperature magnetized plasma|journal=Physics of Plasmas|volume=22|issue=3|pages=033516|doi=10.1063/1.4916572|bibcode=2015PhPl...22c3516Z}}

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) [https://is.cuni.cz/webapps/zzp/detail/114152/?lang=en]

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) [https://is.cuni.cz/webapps/zzp/detail/122235/?lang=en]

{{cite journal|last=Walkden|first=N R |author2=J. Adamek |author3=S. Allan |author4=B. D. Dudson |author5=S. Elmore |author6=G. Fishpool |author7=J. Harrison |author8=A. Kirk |author9=M. Komm|year=2015|title=Profile measurements in the plasma edge of MAST using a ball pen probe |journal=Review of Scientific Instruments|volume=86|issue=2|pages=023510|doi=10.1063/1.4908572|pmid=25725845 |arxiv=1411.7298|bibcode=2015RScI...86b3510W|s2cid=21518172 }}

N. R. Walkden, "Properties of Intermittent Transport in the Mega Ampere Spherical Tokamak", PhD Thesis, [http://etheses.whiterose.ac.uk/8674/1/main.pdf]

{{cite journal|last=Michael|first=C.A. |author2=F. Zhao |author3=B. Blackwell |author4=M. F. J. Vos |author5=J. Brotankova |author6=S. R. Haskey |author7=B. Seiwald |author8=J. Howard|year=2017|title=Influence of magnetic configuration on edge turbulence and transport in the H-1 Heliac |journal=Plasma Physics and Controlled Fusion|volume=59 |issue=2|pages=024001|doi=10.1088/1361-6587/59/2/024001|bibcode=2017PPCF...59b4001M|url=https://openresearch-repository.anu.edu.au/bitstream/1885/112461/2/01_Michael_Influence_of_Magnetic_2016.pdf |hdl=1885/112461 |s2cid=73588015 |hdl-access=free }}

{{cite journal|last=Hole|first=M.J. |author2=B.D. Blackwell |author3=G. Bowden |author4=M. Cole |author5=A. Koenies |author6=C.A. Michael |author7=F. Zhao| author8=S.R. Haskey |year=2017|title=Global Alfven eigenmodes in the H-1 heliac |journal=Plasma Physics and Controlled Fusion|volume= 59|issue=12|page=125007|doi=10.1088/1361-6587/aa8bdf|arxiv=1704.02089|bibcode=2017PPCF...59l5007H|s2cid=119096017 }}

{{cite journal|last=Adamek|first=J. |author2=J. Horacek |author3=J. Seidl |author4=H.W. Müller |author5=R. Schrittwieser |author6=F. Mehlmann |author7=P. Vondracek |author8=S. Ptak|year=2014|title=Direct Plasma Potential Measurements by Ball-Pen Probe and Self-Emitting Langmuir Probe on COMPASS and ASDEX Upgrade |journal=Contributions to Plasma Physics|volume=54 |issue=4|pages=279–284|doi=10.1002/ctpp.201410072|bibcode=2014CoPP...54..279A|s2cid=117937384 }}

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).

}}

• [http://is.muni.cz/th/9761/prif_d/disert_final.pdf PhD thesis, Jiri Adamek] (Czech and English language)
• [https://indico.ipp.cas.cz/event/30/attachments/154/341/BPP_overview_ECPD_2025_GDPR_16_9_public.pdf Overview: Advances in Plasma Diagnostics: 20 Years of the Ball-Pen Probe in Fusion and Non-Fusion Research].
• [http://www.scriptiebank.be/sites/default/files/webform/scriptie/Main_0.pdf Examination of plasma current spikes and general analysis of H-mode shots in the tokamak COMPASS]
• [http://lib.ugent.be/fulltxt/RUG01/001/787/469/RUG01-001787469_2012_0001_AC.pdf Electrical Probe Measurements on the COMPASS Tokamak]
• [http://doks.xios.be/doks/do/files/FiSe8ae680b43c26317b013c953679dd020b/200800040_12.pdf?recordId=Sxhl8ae680b43c26317b013c953679dd020a Probe Measurements on the COMPASS Tokamak]
• [https://web.archive.org/web/20150402195109/http://www.psfc.mit.edu/library1/catalog/reports/2010/13ja/13ja020/13ja020_full.pdf Scanning ion sensitive probe for plasma profile measurements in the boundary of the Alcator C-Mod tokamak]
• [http://www.psfc.mit.edu/library1/catalog/reports/2010/13rr/13rr006/13rr006_full.pdf Development of Probes for Assessment of Ion Heat Transport and Sheath Heat Flux in the Boundary of the Alcator C-Mod Tokamak]{{Dead link|date=November 2018 |bot=InternetArchiveBot |fix-attempted=yes }}
• [https://www.youtube.com/watch?v=LXH4v0XY0EA Video: Temporal evolution of Type-I ELM in the divertor region on the COMPASS tokamak.]
• [http://www.ipp.cas.cz/sd/novinky/hlavni-stranka/160913_divertor.html The new divertor Ball-pen and Langmuir probes on the COMPASS tokamak.]

Category:Plasma diagnostics