Discrete and Continuous Models and Applied Computational ScienceDiscrete 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)4999410.22363/2658-4670-2026-34-1-125-138UOSEFXPhysics and AstronomyФизикаResearch ArticleMathematical models of low-pressure discharge in a magnetic field supported by UHF electromagnetic fieldМатематические модели разряда низкого давления в магнитном поле, поддерживаемого быстропеременным электромагнитным полемhttps://orcid.org/0000-0002-0163-92826602388907J-6595-2012DvininSergey A.ДвининС. А.

Doctor of Physical and Mathematical Sciences, Professor of Lomonosov Moscow State University, leading researcher of Institute of Physical Research and Technology of Peoples’ Friendship University of Russia (RUDN University)

dvininsa@phys.msu.ruhttps://orcid.org/0000-0002-6768-61966508067157O-3193-2013ChuprovDenis V.ЧупровД. В.

Senior Lecturer, Research Associate of Institute of Physical Research and Technology of Peoples’ Friendship University of Russia (RUDN University)

chuprov-dv@rudn.ruhttps://orcid.org/0000-0002-7574-566X57213826116KornevKonstantin N.КорневК. Н.

Lead engineer, of Lomonosov Moscow State university, research intern of Institute of Physical Research and Technology of Peoples’ Friendship University of Russia (RUDN University)

singuliarnost@yandex.ruhttps://orcid.org/0009-0004-2276-378657220783014NMK-4101-2025QodirzodaZafari A.КодирзодаЗ. А.

Candidate of Science, Associate Professor 

zafar.kodirzoda@yandex.ruhttps://orcid.org/0009-0006-8624-327457215526726SolikhzodaDavlat K.СолихзодаД. К.

Doctor of Science, Professor 

davlat56@mail.ruRUDN UniversityРоссийский университет дружбы народовLomonosov Moscow State UniversityМосковский Государственный университет имени М. В. ЛомоносоваTajik National UniversityТаджикский национальный университет30042026341Vol 34, No 1 (2026)ТОМ 34, № 1 (2026)12513829042026Copyright ©; 2026, Dvinin S.A., Chuprov D.V., Kornev K.N., Qodirzoda Z.A., Solikhzoda D.K.Copyright ©; 2026, Двинин С.А., Чупров Д.В., Корнев К.Н., Кодирзода З.А., Солихзода Д.К.2026Dvinin S.A., Chuprov D.V., Kornev K.N., Qodirzoda Z.A., Solikhzoda D.K.Двинин С.А., Чупров Д.В., Корнев К.Н., Кодирзода З.А., Солихзода Д.К.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/miph/article/view/49994

Electron cyclotron resonance (ECR) discharges are an effective way to generate plasma at low working gas pressure. The aim of this work is to develop a mathematical model of the ECR discharge implemented at the RAPIRA facility (RUDN University), which is used for a wide range of scientific research. The evolution of plasma particles is described within the framework of the hydrodynamic approximation (a two-dimensional model with cylindrical symmetry). A three-dimensional model of cold plasma is used to calculate the spatial distribution of the electromagnetic field. Calculations have shown that in the operating mode of the facility (gas pressures from $4\cdot 10^{-4}$ to $10^{-2}$ Torr, magnetic field up to 2500 G), the electron temperature is equalized along the magnetic field lines, and at the same time, the magnetic field ensures a decrease in energy losses to the side walls of the facility. The spatial distributions of the electron density and temperature and the electromagnetic field in the plasma are calculated. The implemented model can serve as a basis for developing a more advanced set of software codes that take into account the non-Maxwellian nature of the electron velocity distribution function, caused by the non-adiabatic nature of their heating in a non-uniform magnetic field.

Разряды использующие электронный циклотронный резонанс (ЭЦР) для нагрева электронов, представляют собой эффективный способ создания плазмы при низком давлении рабочего газа. Цель данной работы --- разработка математической модели ЭЦР разряда, реализованного на установке RAPIRA (РУДН), применяемой для реализации целого ряда научных исследований. Эволюция частиц плазма описывается в рамках гидродинамического приближения/ (двумерная модель с цилиндрической симметрией), При расчете пространственного распределения электромагнитного поля используется трехмерная модель холодной плазмы. Расчеты показали, что в рабочем режиме установки (давления газа от $4\cdot 10^{-4}$ до $10^{-2}$ Торр, магнитное поле до 2500 Гс) происходит выравнивание температуры электронов вдоль силовых магнитного поля, и в то же время магнитное поле обеспечивает уменьшение потерь энергии на боковые стенки установки. Рассчитаны пространственные распределения плотности и температуры электронов и электромагнитного поля в плазме. Реализованная модель может служить основой для разработки более совершенного набора программных кодов, учитывающих немаксвелловскую природу функции распределения скоростей электронов, обусловленную неадиабатическим характером их нагрева в неоднородном магнитном поле.

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