Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)3220310.22363/2658-4670-2022-30-3-217-230Research ArticleNumerical simulation of cold emission in coaxial diode with magnetic isolationBelovAlexandr A.<p>Candidate of Physical and Mathematical Sciences, Researcher of Faculty of Physics, M. V. Lomonosov Moscow State University; Assistant professor of Department of Applied Probability and Informatics of Peoples’ Friendship University of Russia</p>aa.belov@physics.msu.ruhttps://orcid.org/0000-0002-0918-9263LozaOleg T.<p>Doctor of Physical and Mathematical Sciences, Professor of Institute of Physical Research and Technology</p>loza-ot@rudn.ruhttps://orcid.org/0000-0003-4676-6303LovetskiyKonstantin P.<p>Candidate of Physical and Mathematical Sciences, Associate professor of Department of Applied Probability and Informatics</p>lovetskiy-kp@rudn.ruhttps://orcid.org/0000-0002-3645-1060KarnilovichSergey P.<p>Candidate of Physical and Mathematical Sciences, Assistant professor of Institute of Physical Research and Technology</p>karnilovich-sp@rudn.ruhttps://orcid.org/0000-0001-5696-1546SevastianovLeonid A.<p>Doctor of Physical and Mathematical Sciences, Professor of Department of Applied Probability and Informatics</p>sevastianov-la@rudn.ruhttps://orcid.org/0000-0002-1856-4643Lomonosov Moscow State UniversityPeoples’ Friendship University of Russia (RUDN University)0510202230321723005102022Copyright © 2022, Belov A.A., Loza O.T., Lovetskiy K.P., Karnilovich S.P., Sevastianov L.A.2022<p style="text-align: justify;">Due to the emergence and active development of new areas of application of powerful and super-powerful microwave vacuum devices, interest in studying the behavior of ensembles of charged particles moving in the interaction space has increased. An example is an electron beam formed in a coaxial diode with magnetic isolation. Numerical simulation of emission in such a diode is traditionally carried out using particle-in-cell methods. They are based on the simultaneous calculation of the equations of motion of particles and the Maxwell’s equations for the electromagnetic field. In the present work, a new computational approach called the point macroparticle method is proposed. In it, the motion of particles is described by the equations of relativistic mechanics, and explicit expressions are written out for fields in a quasi-static approximation. Calculations of the formation of a relativistic electron beam in a coaxial diode with magnetic isolation are performed and a comparison is made with the known theoretical relations for the electron velocity in the beam and for the beam current. Excellent agreement of calculation results with theoretical formulas is obtained.</p>coaxial diode with magnetic isolationcold emissionpoint macroparticlesкоаксиальный диод с магнитной изоляциейхолодная эмиссияточечные макрочастицы[M. V. Kuzelev et al., “Plasma relativistic microwave electronics,” Plasma Physics Reports, vol. 27, no. 8, pp. 669-691, 2001. DOI: 10.1134/1.1390539.][S. P. Bugaev, E. A. Litvinov, G. A. Mesyats, and D. I. Proskurovskii, “Explosive emission of electrons,” Physics Uspekhi, vol. 18, no. 1, pp. 51-61, 1975. DOI: 10.3367/UFNr.0115.197501d.0101.][O. T. Loza and I. E. Ivanov, “Measurements of the transverse electron velocities in high-current microsecond relativistic electron beams in a strong magnetic field,” Technical Physics, vol. 48, no. 9, pp. 1180-1185, 2003. DOI: 10.1134/1.1611905.][D. K. Ul’yanov et al., “Controlling the radiation frequency of a plasma relativistic microwave oscillator during a nanosecond pulse,” Technical Physics, vol. 58, no. 10, pp. 1503-1506, 2013. DOI: 10.1134/S1063784213100265.][S. Y. Belomyttsev, A. A. Grishkov, S. D. Korovin, and V. V. Ryzhov, “The current of an annular electron beam with virtual cathode in a drift tube,” Technical Physics Letters, vol. 29, no. 7, pp. 666-668, 2003. DOI: 10.1134/1.1606783.][S. V. Polyakov, “Mathematical modeling using multiprocessor computing systems of electronic transport processes in vacuum and solid-state micro- and nanostructures [Matematicheskoye modelirovaniye s pomoshchʹyu nogoprotsessornykh vychislitelʹnykh sistem protsessov elektronnogo transporta v vakuumnykh i tverdotelʹnykh mikro- i nanostrukturakh],” in Russian, Diss.. Doctor of Physical and Mathematical Sciences, M. V. Keldysh IAM, RAS, 2010.][A. A. Vlasov, “The vibrational properties of an electron gas,” Physics Uspekhi, vol. 10, no. 6, pp. 721-733, 1968. DOI: 10.3367/UFNr.0093.196711f.0444.][I. A. Kvasnikov, Thermodynamics and statistical physics. Vol. 3. Theory of nonequilibrium systems [Termodinamika i statisticheskaya fizika, Tom 3, Teoriya ravnovesnykh sistem, Teoriya neravnovesnykh sistem]. Moscow: URSS, 2003, in Russian.][R. W. Hockney and J. W. Eastwood, Computer simulation using particles. McGraw-Hill Inc., 1981.][V. P. Tarakanov, User’s Manual for Code KARAT. Va, USA: BRA Inc., 1992.][L. V. Borodachev, “Discrete modeling of low-frequency processes in plasma [Diskretnoye modelirovaniye nizkochastotnykh protsessov v plazme],” in Russian, Diss.. Doctor of Physical and Mathematical Sciences, M. V. Lomonosov MSU, 2012.][V. V. Andreev et al., Physical electronics and its modern applications [Fizicheskaya elektronika i yeye sovremennyye prilozheniya]. Moscow: RUDN University, 2008, in Russian.][S. E. Ernyleva, V. O. Litvin, O. T. Loza, and I. L. Bogdankevich, “Promising source of high-power broadband microwave pulses with radiation frequency variable up to two octaves,” Technical Physics, vol. 59, no. 8, pp. 1228-1232, 2014. DOI: 10.1134/S1063784214080106.][F. Hecht, “New development in FreeFem++,” Journal of numerical mathematics, vol. 20, no. 3-4, pp. 251-266, 2012. DOI: 10.1515/jnum2012-0013.][V. I. Denisov, Introduction to electrodynamics of material media [Vvedeniye v elektrodinamiku materialʹnykh sred]. Moscow: M. V. Lomonosov MSU, 1989, in Russian.]