MATHEMATICAL MODELING OF ELECTRON DENSITY DETERMINATION USING A STATIONARY CYLINDRICAL LANGMUIR PROBE UNDER IONOSPHERIC CONDITIONS

Abstract

The goal of this article is to theoretically substantiate the applicability of the classical formula of the single cylindrical probe theory to determining the electron density based on measurements of the currents of a floating probe system in ionospheric conditions. Probe measurements in the ionosphere are modeled using a cylindrical probe and the body of a very small satellite placed transversely in the incident supersonic flow of a collisionless plasma. The ionospheric plasma is considered to be Maxwellian and consists of electrons and singly charged atomic ions of oxygen and hydrogen. A mathematical model of current collection by the floating probe system “probe – plasma – satellite body” was developed based on classical relationships for the electron and ion currents to a thin cylinder placed transversally in the incident flow. To model the collection of the hydrogen ion current by the satellite body, the results of numerical calculations of the ion current to the cylinder using the two-dimensional Vlasov-Poisson model were approximated. The probe bias potential was determined such that, under ionospheric conditions, the electron region of the floating probe system's current-voltage characteristic is closest to that of a single probe. The determination of the electron density using the classical calculation formula of the single-probe theory was simulated for probe current measurements in the low voltage portion of the electron region of the current-voltage characteristic of the floating probe system. The limiting methodological error in determining the electron density under ionospheric conditions within the framework of the probe system model considered was estimated. The effect of probe current measurement errors on the determination of the electron density using the calculation formula of the single-probe theory was studied. The obtained results may be used in the preparation and interpretation of ionospheric plasma diagnostics experiments using ultra-small satellites.

REFERENCES

1. Lebreton J. P., Stverak S., Travnicek P. et al. The ISL Langmuir probe experiment processing onboard DEMETER: Scientific objectives, description and first results. Planetary and Space Science. 2006. V. 54. No. 5. Pp. 472 - 486. https://doi.org/10.1016/j.pss.2005.10.017

2. Liu D., Zeren Z., Shen X. et al. Typical ionospheric disturbances revealed by the plasma analyzer package onboard the China Seismo-Electromagnetic Satellite. Advances in Space Research. 2021. V. 68. Pp. 3796 - 3805. https://doi.org/10.1016/j.asr.2021.08.009

3. Davis B. Studying the ionosphere with Langmuir probe with an application to seismic monitoring. Final report. ASEN 5168: Remote Sensing, 2012. 11 pp.

4. Oyama K. DC Langmuir probe for measurement of space plasma : A brief review. Journal Astronomy and Space Science. 2015. V. 32. No. 3. Pp. 167-180. https://doi.org/10.5140/JASS.2015.32.3.167

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

6. Chung, P. M., Talbot L., Touryan K. J. Electric Probes in Stationary and Flowing Plasmas. Springer-Verlag, 1975. 150 pp. https://doi.org/10.1007/978-3-642-65886-0

7. 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

8. Lazuchenkov D. N., Lazuchenkov N. M. Mathematical simulation of ionospheric plasma diagnostics by electric current measurements using an insulated probe system. Teh. Meh. 2024. No. 2. Pp. 112 - 123. https://doi.org/10.15407/itm2024.02.112

9. 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

10. Lazuchenkov D. N., Lazuchenkov N. M. Calculation of the ion current to a conducting cylinder in a supersonic flow of a collisionless plasma. Teh. Meh. 2022. No. 3. Pp. 80 - 88.
https://doi.org/10.15407/itm2022.03.091

11. 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

12. Laframboise J. G. Theory of Spherical and Cylindrical Langmuir Probes in a Collisionless Maxwellian Plasma at Rest. Report, No. 100. Univ. of Torto, Institute of Aerospace Studies. 1966. 210 pp. https://doi.org/10.21236/AD0634596

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

14. 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.

15. International Reference Ionosphere-2012 (IRI-2012). https://ccmc.gsfc.nasa.gov/modelweb/models/iri2012_vitmo.php.