Engineering:Ball-pen probe

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Ball-pen probe used on tokamak CASTOR in 2004. A stainless steel collector moves inside a ceramic (boron nitride) shielding tube.
Schematic picture of a single ball-pen probe. Ions (in red) have a large gyromagnetic radius and can reach the collector more easily than electrons (in blue).

A ball-pen probe[1] is a modified Langmuir probe used to measure the plasma potential[2] in magnetized plasmas. The ball-pen probe balances the electron and ion saturation currents, so that its floating potential is equal to the plasma potential. Because electrons have a much smaller gyroradius than ions, a moving ceramic shield can be used to screen off an adjustable part of the electron current from the probe collector.

Ball-pen probes are used in plasma physics, notably in tokamaks such as CASTOR, (Czech Academy of Sciences Torus)[1][2][3] ASDEX Upgrade,[4][5][6][7][8][9][10] COMPASS,[6][7][11][12][13][14][10][15][16][17][1] ISTTOK,[10][18] MAST,[19][20] TJ-K,[21][22] RFX,[23] H-1 Heliac,[24][25] IR-T1,[26][27][28] GOLEM[29] as well as low temperature devices as DC cylindrical magnetron in Prague[21][30][31][32][33] and linear magnetized plasma devices in Nancy[34][35] and Ljubljana.[21][30][36]

Principle

If a Langmuir probe (electrode) is inserted into a plasma, its potential is not equal to the plasma potential [math]\displaystyle{ \Phi }[/math] because a Debye sheath forms, but instead to a floating potential [math]\displaystyle{ V_{fl} }[/math]. The difference with the plasma potential is given by the electron temperature [math]\displaystyle{ T_e }[/math]:

[math]\displaystyle{ \Phi - V_{fl} = \alpha*T_e }[/math]

where the coefficient [math]\displaystyle{ \alpha }[/math] is given by the ratio of the electron and ion saturation current density ([math]\displaystyle{ j^{sat}_e }[/math] and [math]\displaystyle{ j^{sat}_i }[/math]) and collecting areas for electrons and ions ([math]\displaystyle{ A_e }[/math] and [math]\displaystyle{ A_i }[/math]):

[math]\displaystyle{ \alpha = ln\left(\frac{A_e j^{sat}_e}{A_i j^{sat}_i}\right) = ln(R) }[/math]

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

[math]\displaystyle{ V_{fl} = \Phi }[/math]

Design and calibration

Potential and ln(R) of the ball-pen probe for different positions of the collector.

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 [math]\displaystyle{ R }[/math] 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] 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 [math]\displaystyle{ R }[/math] is close to unity, though not exactly.[1][5][37] 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. [clarification needed]

Electron temperature measurements

Using two measurements of the plasma potential with probes whose coefficient [math]\displaystyle{ \alpha }[/math] 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 [math]\displaystyle{ R }[/math] is close to zero) the electron temperature is given by:

[math]\displaystyle{ T_e = \frac{\Phi-V_{fl}}{\alpha} }[/math]

where [math]\displaystyle{ \Phi }[/math] is measured by the ball-pen probe, [math]\displaystyle{ V_{fl} }[/math] by the standard Langmuir probe, and [math]\displaystyle{ \alpha }[/math] 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.[38][39]

In practice, the ratio [math]\displaystyle{ R }[/math] for the ball-pen probe is not exactly equal to one,[5] so that the coefficient [math]\displaystyle{ \alpha }[/math] must be corrected by an empirical value for [math]\displaystyle{ R }[/math]:

[math]\displaystyle{ T_e = \frac{\Phi_{BPP}-V_{fl}}{\bar{\alpha}}, }[/math]

where [math]\displaystyle{ \bar{\alpha}=\alpha - ln(R). }[/math]

References

  1. ↑ 1.0 1.1 1.2 1.3 Adámek, J.; J. Stöckel; M. Hron; J. Ryszawy; M. Tichý; R. Schrittwieser; C. Ionită; P. Balan et al. (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. Bibcode: 2004CzJPS..54C..95A. 
  2. ↑ 2.0 2.1 Adámek, J.; J. Stöckel; I. Ďuran; M. Hron; R. Pánek; M. Tichý; R. Schrittwieser; C. Ionit et al. (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. Bibcode: 2005CzJPh..55..235A. 
  3. ↑ 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) [1]
  4. ↑ Adamek, J.; V. Rohde; H.W. Müller; A. Herrmann; C. Ionita; R. Schrittwieser; F. Mehlmann; J. Stöckel et al. (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. Bibcode: 2009JNuM..390.1114A. http://edoc.mpg.de/431639. 
  5. ↑ 5.0 5.1 5.2 Adamek, J.; J. Horacek; H.W. Müller; V. Rohde; C. Ionita; R. Schrittwieser; F. Mehlmann; B. Kurzan et al. (2010). "Ball-Pen Probe Measurements in L-Mode and H-Mode on ASDEX Upgrade". Contributions to Plasma Physics 50 (9): 854–859. doi:10.1002/ctpp.201010145. Bibcode: 2010CoPP...50..854A. 
  6. ↑ 6.0 6.1 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". Contributions to Plasma Physics 54 (4): 279–284. doi:10.1002/ctpp.201410072. Bibcode: 2014CoPP...54..279A. 
  7. ↑ 7.0 7.1 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 [2]
  8. ↑ Horacek, J.; J. Adamek; H.W. Müller; J. Seidl; C. Ionita; F. Mehlmann; A.H. Nielsen; V. Rohde et al. (2010). "Interpretation of fast measurements of plasma potential, temperature and density in SOL of ASDEX Upgrade". Nuclear Fusion 50 (10): 105001. doi:10.1088/0029-5515/50/10/105001. Bibcode: 2010NucFu..50j5001H. http://edoc.mpg.de/463860. 
  9. ↑ Müller, H.W.Expression error: Unrecognized word "et". (2011). "Latest investigations on fluctuations, ELM filaments and turbulent transport in the SOL of ASDEX Upgrade". Nuclear Fusion 51 (7): 073023. doi:10.1088/0029-5515/51/7/073023. Bibcode: 2011NucFu..51g3023M. http://edoc.mpg.de/570069. 
  10. ↑ 10.0 10.1 10.2 Adamek, J.; H.W. Müller; C. Silva; R. Schrittwieser; C. Ionita; F. Mehlmann; S. Costea; J. Horacek et al. (2016). "Profile measurements of the electron temperature on the ASDEX Upgrade, COMPASS, and ISTTOK tokamak using Thomson scattering, triple, and ball-pen probes". Review of Scientific Instruments 87 (4): 043510. doi:10.1063/1.4945797. PMID 27131677. Bibcode: 2016RScI...87d3510A. 
  11. ↑ 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 [3]
  12. ↑ 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. [4]
  13. ↑ 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 [5]
  14. ↑ Panek, R.; J. Adamek; M. Aftanas; P. Bilkova; P. Böhm; F. Brochard; P. Cahyna; J. Cavalier et al. (2016). "Status of the COMPASS tokamak and characterization of the first H-mode". Plasma Phys. Control. Fusion 58 (1): 014015. doi:10.1088/0741-3335/58/1/014015. Bibcode: 2016PPCF...58a4015P. 
  15. ↑ Grover, O.; J. Adamek; J. Seidl; A. Devitre; M. Sos; P. Vondracek; P. Bilkova; M. Hron (2017). "First simultaneous measurements of Reynolds stress with ball-pen and Langmuir probes". Review of Scientific Instruments 88 (6): 063501. doi:10.1063/1.4984240. PMID 28668002. Bibcode: 2017RScI...88f3501G. 
  16. ↑ Adamek, J.; J. Seidl; M. Komm; V. Weinzettl; R. Panek; J. Stöckel; M. Hron; P. Hacek et al. (2017). "Fast measurements of the electron temperature and parallel heat flux in ELMy H-mode on the COMPASS tokamak". Nuclear Fusion 57 (2): 022010. doi:10.1088/0029-5515/57/2/022010. Bibcode: 2017NucFu..57b2010A. https://zenodo.org/record/3453490. 
  17. ↑ Adamek, J.; J. Seidl; J. Horacek; M. Komm; T. Eich; R. Panek; J. Cavalier; A. Devitre et al. (2017). "Electron temperature and heat load measurements in the COMPASS divertor using the new system of probes". Nuclear Fusion 57 (11): 116017. doi:10.1088/1741-4326/aa7e09. Bibcode: 2017NucFu..57k6017A. https://zenodo.org/record/3495879. 
  18. ↑ 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. Bibcode: 2015PPCF...57b5003S. 
  19. ↑ Walkden, N R; J. Adamek; S. Allan; B. D. Dudson; S. Elmore; G. Fishpool; J. Harrison; A. Kirk et al. (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. PMID 25725845. Bibcode: 2015RScI...86b3510W. 
  20. ↑ N. R. Walkden, "Properties of Intermittent Transport in the Mega Ampere Spherical Tokamak", PhD Thesis, [6]
  21. ↑ 21.0 21.1 21.2 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". Contributions to Plasma Physics 53 (1): 39–44. doi:10.1002/ctpp.201310007. Bibcode: 2013CoPP...53...39A. 
  22. ↑ "Plasma Dynamics and Diagnostics | Institute of Interfacial Process Engineering and Plasma Technology | University of Stuttgart". 13 September 2023. http://www.igvp.uni-stuttgart.de/forschung/projekte-pd/tjk.en.html. 
  23. ↑ "Welcome to Consorzio RFX site". http://www.igi.cnr.it/. 
  24. ↑ Michael, C.A.; F. Zhao; B. Blackwell; M. F. J. Vos; J. Brotankova; S. R. Haskey; B. Seiwald; J. Howard (2017). "Influence of magnetic configuration on edge turbulence and transport in the H-1 Heliac". Plasma Physics and Controlled Fusion 59 (2): 024001. doi:10.1088/1361-6587/59/2/024001. Bibcode: 2017PPCF...59b4001M. https://openresearch-repository.anu.edu.au/bitstream/1885/112461/2/01_Michael_Influence_of_Magnetic_2016.pdf. 
  25. ↑ Hole, M.J.; B.D. Blackwell; G. Bowden; M. Cole; A. Koenies; C.A. Michael; F. Zhao; S.R. Haskey (2017). "Global Alfven eigenmodes in the H-1 heliac". Plasma Physics and Controlled Fusion 59 (12): 125007. doi:10.1088/1361-6587/aa8bdf. Bibcode: 2017PPCF...59l5007H. 
  26. ↑ 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. [7]
  27. ↑ S. Meshkani, M. Ghoranneviss, M. Lafouti, "Effect of Biasing on Electron Temperature in IR-T1 Tokamak", Proceedings of the 5th International Conference on Development, Energy, Environment, Economics (DEEE '14), Florence, Italy November 22–24, 2014 [8]
  28. ↑ Ghoranneviss, M.; S. Meshkani (2016). "Techniques for improving plasma confinement in IR-T1 Tokamak". International Journal of Hydrogen Energy 41 (29): 12555–12562. doi:10.1016/j.ijhydene.2016.03.075. [9]
  29. ↑ 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, [10]
  30. ↑ 30.0 30.1 Adamek, Jiri; J. Adamek; M. Peterka; P. Kudrna; M. Tichy T.; Gyergyek (2012). "CDiagnostics of magnetized low temperature plasma by ball-pen probe". Nukleonika 57 (2): 297–300. [11]
  31. ↑ 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 (3): 033516. doi:10.1063/1.4916572. Bibcode: 2015PhPl...22c3516Z. 
  32. ↑ 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) [12]
  33. ↑ 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) [13]
  34. ↑ 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) [14]
  35. ↑ 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): 013505–013505–8. doi:10.1063/1.4775491. ISSN 0034-6748. PMID 23387648. Bibcode: 2013RScI...84a3505B. 
  36. ↑ L. Šalamon, G. Ikovic, T. Gyergyek, J. Kovačič and B. Fonda, "Ball-pen probe diagnostics of a weakly magnetized discharge plasma column", 1st EPS conference on Plasma Diagnostics, 14–17 April 2015, Frascati, Italy, [15]
  37. ↑ 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. Bibcode: 2015PPCF...57b5003S. 
  38. ↑ Stangeby P.C.: The Plasma Boundary of Magnetic Fusion Devices, Institute of Physics Publishing. Bristol and Philadelphia (2000).
  39. ↑ Hutchinson I.H.: Principles of Plasma Diagnostics, Cambridge University Press (1992).

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