TECHNICAL MECHANICS
ISSN (Print): 1561-9184, ISSN (Online): 2616-6380

English
Russian
Ukrainian
Home > Journal Issues > No 3 (2022) Technical mechanics > 9
___________________________________________________

UDC 533.9

Technical mechanics, 2022, 3, 91 - 98

Calculation of the ion current to a conducting cylinder in a supersonic flow of a collisionless plasma

DOI: https://doi.org/10.15407/itm2022.03.091

D. N. Lazuchenkov, N. M. Lazuchenkov

      ABOUT THE AUTHORS

D. N. Lazuchenkov
Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine

N. M. Lazuchenkov
Institute of Technical Mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine

      ABSTRACT

      The diagnostics of low-temperature plasma flows using cylindrical probes is based on the classical Langmuir relation for the ion current to a thin, in comparison with the Debye length, cylinder. The aim of this work is to study the applicability of the Langmuir relation for a cylinder whose radius exceeds the Debye length.
      The interaction of a conducting cylinder with a rarefied plasma flow was simulated numerically. The cylinder had a negative potential with respect to the plasma. Free molecular flow around the cylinder was simulated on the basis of a two-dimensional system of the Vlasov–Poisson equations. The electron-repulsing local equilibrium self-consistent electric field was calculated using the Poisson–Boltzmann model in the approximation of local equilibrium electrons and taking into account an electron sink on the cylinder surface in the central field approximation. The Vlasov equations for ions and the Poisson–Boltzmann equations for the self-consistent electric field were solved on nested grids by a finite-difference relaxation method with splitting by physical processes and using the method of characteristics. The reliability of the calculated results was confirmed by the solution of known model problems and a comparison with the results of other authors and the results of solving identical physical problems with the use of different mathematical models and methods.
      The ion current to a cylinder placed transversely to a plasma flow was calculated as a function of the cylinder potential, the ion velocity ratio, and the ratio of the characteristic dimension of the cylinder to the Debye length. From the calculated results, numerical estimates were obtained for the range of applicability of the classical Langmuir relation for the ion current to a cylinder whose radius exceeds the Debye length. The results obtained may be used in the diagnostics of supersonic flows of a low-temperature rarefied plasma.
      Pdf (English)







      KEYWORDS

rarefied nonisothermal plasma flow, transverse free molecular flow around a long circular cylinder, numerical simulation, system of Vlasov–Poisson equations, calculation of the ion current to a cylinder

      FULL TEXT:

Pdf (English)









      REFERENCES

1. Boyd R. Langmuir probes on spacecraft. In: Plasma Diagnostics. W. Lochte-Holtgreven (Ed.). New York: AIP Press, 1995. Pp. 732-776.

2. Mott-Smith H., Langmuir I. The theory of collectors in gaseous discharges. Phys. Rev. 1926. V. 28. No. 5. Pp. 727-763. https://doi.org/10.1103/PhysRev.28.727

3. Hoegy W. R., Wharton L. E. Current to a moving cylindrical electrostatic probe. Journal of Applied Physics. 1973. V. 44. No. 12. Pp. 5365-5371. https://doi.org/10.1063/1.1662157

4. Lazuchenkov D. N., Lazuchenkov N. M. Mathematical modeling of probe measurements in a supersonic flow of a four-component collisionless plasma. Teh. Meh. 2020. No. 4. Pp. 97-108. https://doi.org/10.15407/itm2020.04.097

5. Lazuchenkov D. N., Lazuchenkov N. M. Estimation of probe measurements reliability in a supersonic flow of a four-component collisionless plasma. Teh. Meh. 2021. No. 3. Pp. 57-69. https://doi.org/10.15407/itm2021.03.057

6. Godard R., Laframboise J. Total current to cylindrical collectors in collisionless plasma flow. Planetary Space Science. 1983. V. 31. No. 3. Ðp. 275-283. https://doi.org/10.1016/0032-0633(83)90077-6

7. Xu G. Z. The interaction of a moving spacecraft with the ionosphere: Current collection and wake structure : Ph.D. dissertation. York University, 1992. 258 pp.

8. Choiniere E. Theory and experimental evaluation of a consistent steady-state kinetic model for two-dimensional conductive structures in ionospheric plasmas with application to bare electrodynamic tethers in space : Ph.D. dissertation. University of Michigan, 2004. 288 pp.

9. Lazuchenkov D. N., Lazuchenkov N. M. Mathematical simulation of a supersonic collisionless plasma flow around a conducting cylinder. Teh. Meh. 2019. No. 1. Pp. 63-74. (in Russian). https://doi.org/10.15407/itm2019.01.063

10. Al'pert Ya. L., Gurevich A. V., Pitaevskij L. P. Artificial satellites in low-density plasma. Moscow: Nauka, 1964. 382 pp. (in Russian).

11. Lazuchenkov D. N. Calculation of the electron-retarding self-consistent electric field near a cylinder in a rarefied plasma flow. Teh. Meh. 2012. No. 4. Pp. 27-35. (in Russian).





Copyright (©) 2022 D. N. Lazuchenkov, N. M. Lazuchenkov

Copyright © 2014-2022 Technical mechanics


____________________________________________________________________________________________________________________________
GUIDE
FOR AUTHORS
Guide for Authors ==================== Open Access Policy
Open Access Policy ==================== REGULATIONS
on the ethics of publications
REGULATIONS on the ethics of publications ====================