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Simulation of Emission Processes in Strong Electromagnetic Fields

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Abstract

The problem of calculating the processes of electron emission from metal surfaces in strong electromagnetic fields is considered with allowance for relativistic effects. One of the methods of simulation in these processes is the particle method combined with grid calculation of fields on the basis of Maxwell’s equations. Similar techniques have been developed since the 1960s to the present. However, existing approaches have certain limitations. In this work, for an axisymmetric geometry of the generating system, a new numerical technique simulating the processes of electron emission from metal cathode surfaces is presented. The technique uses the representation of large smoothed Gaussian particles and implements the calculation of electromagnetic fields on Cartesian spatial grids. The software implementation is oriented to parallel computing. The aim of numerical experiments was to determine the parameters of electron emission. Diode and triode cylindrical systems were chosen as test problems. In numerical calculations, the spatiotemporal characteristics of relativistic electron beams generated by emission processes are obtained, including the reproduction of the Child–Langmuir current. The numerical technique developed has confirmed its correctness and efficiency.

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REFERENCES

  1. V. V. Vasiliev, Mechanics of Composite Structures (Taylor & Francis, New York, 1993).

    Google Scholar 

  2. M. L. Kerber, Polymer Composite Materials: Structure, Properties, Technologies (Professiya, St. Petersburg, 2008) [in Russian].

    Google Scholar 

  3. A. A. Rukhadze, L. S. Bogdankevich, S. E. Rosinskii, and V. G. Rukhlin, Physics of Strongly Relativistic Electron Beams (Atomizdat, Moscow, 1980) [in Russian].

    Google Scholar 

  4. R. B. Miller, Introduction to the Physics of Intense Charged Particle Beams (Plenum, New York, 1982).

    Book  Google Scholar 

  5. V. I. Boiko and V. V. Evstigneev, Introduction to the Physics of the Interaction of Intense Charged Particle Beams with Matter (Energoatomizdat, Moscow, 1988) [in Russian].

    Google Scholar 

  6. G. A. Mesyats, Ectons (Nauka, Yekaterinburg, 1993) [in Russian].

    Google Scholar 

  7. A. N. Didenko and Yu. G. Yushkov, Intense Nanosecond Microwave Pulses (Energoatomizdat, Moscow, 1984) [in Russian].

    Google Scholar 

  8. S. N. Voronkov, O. T. Loza, and P. S. Strelkov, “Limits on the length of radiation pulses generated by microwave oscillators using microsecond relativistic electron beams,” Plasma Phys. Rep. 17 (6), 439–442 (1991).

    Google Scholar 

  9. S. P. Bugaev, E. A. Litvinov, G. A. Mesyats, and D. I. Proskurovskii, “Explosive emission of electrons,” Sov. Phys. Usp. 18 (1), 51–61 (1975).

    Article  Google Scholar 

  10. G. A. Mesyats, Explosive Electron Emission (Fizmatlit, Moscow, 2011) [in Russian].

    Google Scholar 

  11. C. Herring and M. H. Nichols, “Thermionic emission,” Rev. Mod. Phys. 21, 185–270 (1949).

    Article  Google Scholar 

  12. E. P. Sheshin, Surface Structure and Field Emission Properties of Carbon Materials (Mosk. Fiz.-Tekh. Inst., Moscow, 2001) [in Russian].

    Google Scholar 

  13. O. A. Ivanov, M. A. Lobaev, V. V. Chernov, et al., “Experimental study of high-current cathodes based on diamond films as elements of high-power compressors of microwave pulses,” Radiophys. Quantum Electron. 57, 711–719 (2015).

    Article  Google Scholar 

  14. Computer Techniques for Electromagnetics, Ed. by R. Mittra (Pergamon, New York, 1973).

    Google Scholar 

  15. C. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).

    Google Scholar 

  16. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech, Boston, 2005).

    MATH  Google Scholar 

  17. U. S. Inan and R. A. Marshall, Numerical Electromagnetics: The FDTD Method (Cambridge Univ. Press, Cambridge, UK, 2011).

    Book  Google Scholar 

  18. A. D. Grigoriev, Methods of Computational Electrodynamics (Fizmatlit, Moscow, 2012) [in Russian].

    Google Scholar 

  19. COMSOL Multiphysics. https://www.comsol.ru/comsol-multiphysics

  20. ANSYS. http://www.ansys.com/

  21. V. P. Tarakanov, User’s Manual for Code KARAT (Berkeley Res., Springfield, VA, 1992).

    Google Scholar 

  22. MEEP. https://meep.readthedocs.io/en/latest/Materials

  23. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14 (3), 302–307 (1966).

    Article  MATH  Google Scholar 

  24. J. Benford, J. Swegle, and E. Schamiloglu, High Power Microwaves, 2nd ed. (Taylor & Francis, New York, 2007), pp. 1–12.

    Book  Google Scholar 

  25. F. H. Harlow, “The particle-in-cell computing method for fluid dynamics,” in Methods in Computational Physics, Vol. 3: Fundamental Methods in Hydrodynamics, Ed. by B. Alder, S. Fernbach, and M. Rotenberg (Academic, New York, 1964), pp. 319–343.

  26. V. F. D’yachenko, “On calculations in the problems of a collision-free plasma,” USSR Comput. Math. Math. Phys. 25 (2), 193–196 (1985).

    Article  Google Scholar 

  27. Yu. N. Grigoriev, V. A. Vshivkov, and M. P. Fedoruk, Numerical 'Particle-in-Cell’ Methods: Theory and Applications (VSP, Utrecht, Boston, 2002).

    Book  Google Scholar 

  28. O. M. Belotserkovskii and Yu. M. Davydov, Large-Particle Method in Gas Dynamics (Nauka, Moscow, 1982) [in Russian].

    Google Scholar 

  29. D. V. Sadin, “Efficient implementation of the hybrid large particle method,” Math. Models Comput. Simul. 14, 946–954 (2022).

    Article  MathSciNet  MATH  Google Scholar 

  30. C. K. Birsdall and D. Fuss, “Clouds-in-clouds, clouds-in-cells physics for many-body plasma simulation,” J. Comput. Phys. 3 (4), 494–511 (1969).

    Article  Google Scholar 

  31. Jianguo Wang, Dianhui Zhang, Chunliang Liu, Yongdong Li, Yue Wang, Hongguang Wang, Hailiang Qiao, and Xiaoze Li, “UNIPIC code for simulations of high power microwave devices,” Phys. Plasmas 16, 033108 (2009).

  32. Monaghan J.J. An introduction to SPH. // Comp. Phys. Comm. 1988. V. 48. P. 88–96.

    Article  MATH  Google Scholar 

  33. L. N. Dobretsov, Electron and Ion Emission (Gostekhteorizdat, Moscow, 1952) [in Russian].

    Google Scholar 

  34. Yu. P. Raizer, Gas Discharge Physics (Springer-Verlag, Berlin, 1991).

    Book  Google Scholar 

  35. V. Lisovskiy and V. Yegorenkov, “Validating the collision-dominated Child–Langmuir law for a dc discharge cathode sheath in an undergraduate laboratory,” Eur. J. Phys. 30 (6), 1345–1351 (2009).

    Article  Google Scholar 

  36. A. A. Samarskii and A. V. Gulin, Numerical Methods (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  37. Official documentation and manuals on MPI. http://mpiforum.org/

  38. Official documentation and manuals on OpenMP. http://www.openmp.org, http://www.llnl.gov/computing/tutorials/openMP

  39. B. F. Smith, “Domain decomposition methods for partial differential equations,” in Parallel Numerical Algorithms, Ed. by D. E. Keyes, A. Sameh, and V. Venkatakrishnan (Springer, Dordrecht, 1997), pp. 225–243.

    Google Scholar 

  40. V. Dolean, P. Jolivet, and F. Nataf, An Introduction to Domain Decomposition Methods: Algorithms, Theory and Parallel Implementation (SIAM, Philadelphia, 2015). https://hal.science/cel-01100932v6

  41. A. A. Alakeel, “Guide to dynamic load balancing in distributed computer systems,” Int. J. Comput. Sci. Network Secur. 10 (6), 153–160 (2009).

    Google Scholar 

  42. P. Sanders, K. Mehlhorn, M. Dietzfelbinger, and R. Dementiev, Sequential and Parallel Algorithms and Data Structures: The Basic Toolbox (Springer Nature, Cham, Switzerland, 2019).

    Book  MATH  Google Scholar 

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Correspondence to T. A. Kudryashova, S. V. Polyakov or N. I. Tarasov.

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Translated by E. Chernokozhin

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Kudryashova, T.A., Polyakov, S.V. & Tarasov, N.I. Simulation of Emission Processes in Strong Electromagnetic Fields. Comput. Math. and Math. Phys. 63, 1486–1498 (2023). https://doi.org/10.1134/S0965542523080109

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