Quantum-mechanical model of ion thruster for small spacecraft

The article presents a quantum mechanical model of an ion thruster. The basic equations describing the shape of the accelerated beam are considered. Detector plates demonstrating the interference pattern in thin films are presented. A mathematical description of the relief of thin films is given using the resulting wave function. The operation of a low-power ion engine is demonstrated. The results of numerical solution of the model with different initial values are shown. Based on the results of calculations, diagrams of the trajectories of charged particles are constructed.

1. Chernyshev T., Son E., Gorshkov O. Kinetic simulation of Hall Effect Thruster, including azimuthal waves and diamagnetic effect // Journal of Physics D: Applied Physics. 2019. Vol. 52, no. 44. P. 444002. DOI: 10.1088/1361-6463/ab35cb. (In Engl.).

2. Kawamura E., Birdsall C. K., Vahedi V. Physical and numerical methods of speeding up particle codes and paralleling as applied to RF discharges // Plasma Sources Science and Technology. 2000. Vol. 9, no. 3. P. 413–428. DOI: 10.1088/0963-0252/9/3/319. (In Engl.).

3. Li H., Yuan X., Yang J. [et al.]. Numerical and theoretical modeling of the sheath upstream of ion optics: sheath structure transition and its effect on the beam divergence // Plasma Sources Science and Technology. 2021. Vol. 30, no. 7. P. 075019. DOI: 10.1088/1361-6595/abfbec. (In Engl.).

4. Nikiforov N. N. Modelirovaniye protsessov uskoreniya protonov pri obluchenii AU-misheni femtosekundnym lazernym impul’som [Simulation of proton acceleration processes under au-target irradiation with a femtosecond laser pulse] //sNK2022. SSC-2022. Moscow, 2022. P. 249–256. EDN: KGMFPA. (In Russ.).

5. Chizhonkov E. V. O pogreshnostyakh v PIC-metode pri modelirovanii lengmyurovskikh kolebaniy [On errors in the PIC-method when modeling Langmuir oscillations] // Vychislitel’nyye metody i programmirovaniye. Numerical Methods and Programming. 2024. Vol. 25, no. 1. P. 47–63. DOI:10.26089/NumMet.v25r105. (In Russ.).

6. Bastykova N. Kh., Kodanova S. K., Ramazanov T. S. [et al.]. Modelirovaniye osnovnykh svoystv kompleksnoy plazmy vysokochastotnogo razryada [Simulation of main properties of complex plasma in RF discharge] // Zhurnal problem evolyutsii otkrytykh sistem. Scientific Journals Al-Farabi Kazakh National University. 2016. Vol. 18, no. 2. P. 14–22. (In Russ.).

7. Ivanov V. A., Sakharov A. S. Mikroplazmennyye razryady na metallakh: eksperiment, teoriya, prilozheniya [Microplasma discharges on metals: experiment, theory, applications] // Fizika nizkotemperaturnoy plazmy. FNTP-2014. The Physics of Low Temperature Plasma. PLTP-2014. In 2 vols. Kazan, 2014. Vol. 2. P. 14–18. ISBN 978-5-7882-1580-8. (In Russ.).

8. Taccogna F. Monte Carlo Collision method for low temperature plasma simulation // Journal of Plasma Physics. 2015. Vol. 81, no. 1. P. 1–14. DOI: 10.1017/S0022377814000567. (In Engl.).

9. Liu W., Cai G., Jinrui Z. [et al.]. Numerical investigation of plasma behavior in a micro DC ion thruster using the particlein-cell/Monte Carlo collision (PIC/MCC) method // Journal of Physics D: Applied Physics. 2021. Vol. 54, no. 44. P. 445202. DOI:10.1088/1361-6463/ac1a0c. (In Engl.).

10. Kusoglu Sarikaya C., Rafatov I., Kudryavtsev A. A. Particle in cell/Monte Carlo collision analysis of the problem of identification of impurities in the gas by the plasma electron spectroscopy method // Physics of Plasmas. 2016. Vol. 23, no. 6. P. 063524. DOI: 10.1063/1.4954917. (In Engl.).

11. Bohm D. A suggested interpretation of the quantum theory in terms of «Hidden» Variables. I // Physical Review. 1952. Vol. 85, no. 2. P. 166–179. DOI: 10.1103/PhysRev.85.166. (In Engl.).

12. Philippidis C., Dewdney C., Hiley B. J. Quantum interference and the quantum potential // II Nuovo Cimento B. 1979. Vol. 52, no. 1. P. 15–28. DOI: 10.1007/BF02743566. (In Engl.).

13. Kiran M., Moncy V. J. Interfering Quantum Trajectories Without Which-Way Information // Foundations of Physics. 2017. Vol. 47. P. 873–886. DOI: 10.1007/s10701-017-0088-1. (In Engl.).

14. Bohm D. A suggested interpretation of the quantum theory in terms of «Hidden» Variables. II // Physical Review. 1952. Vol. 85, no. 2. P. 180–193. DOI: 10.1103/PhysRev.85.180. (In Engl.).

15. Guay E., Marchildon L. Wave functions and Bohmian trajectories in interference phenomena // arXiv. preprint quantph/0407077. 2004. P. 1–23. URL: https://archive.org/details/arxiv-quant-ph0407077/page/n3/mode/2up (accessed: 20.03.2024) (In Engl.).

16. Kats M. A., Blanchard R., Ramanathan S. [et al.]. Thin-film interference in lossy, ultra-thin layers // Optics and Photonics News. 2014. Vol. 25, no. 1. P. 40–47. DOI: 10.1364/OPN.25.1.000040. (In Engl.).

17. Ganzherli N. M. Vliyaniye interferentsii v tonkikh plenkakh na opticheskiye kharakteristiki gologramm, zaregistrirovannykh na sloyakh As-Se [The effect of interference in thin films on the optical characteristics of holograms recorded on As-Se layers] // Optika i spektroskopiya. Optics and Spectroscopy. 2023. Vol. 131, no. 8. P. 1080–1085. DOI: 10.61011/OS.2023.08.56299.4859-23. EDN: VSBOUY. (In Russ.).

18. Mathad G., Pathar D. Thin Film Interference–A Study // International Journal of Research and Analytical Reviews (IJRAR). 2020. Vol. 7, no. 3. P. 586–595. (In Engl.).