Solar-Terrestrial Physics Solar-Terrestrial Physics Solar-Terrestrial Physics 2500-0535 41216 10.12737/stp-72202103 Results of current research Results of current research Results of current research Acceleration of particles in a constant magnetic field and an electric field perpendicular to it, increasing with time Acceleration of particles in a constant magnetic field and an electric field perpendicular to it, increasing with time Кичигин Геннадий Николаевич Kichigin Gennadiy Nikolaevich king@iszf.irk.ru

доктор физико-математических наук;

doctor of physical and mathematical sciences;

 Институт солнечно-земной физики СО РАН Иркутск Россия Institute of Solar Terrestrial Physics SB RAS Irkutsk Russian Federation 7 2 22 27 14 12 2020 25 02 2021 https://naukaru.ru/en/nauka/article/41216/view

The paper addresses the problem of acceleration of particles in a constant, uniform magnetic field of magnitude B and a uniform electric field perpendicular to it, which slowly increases with time. Assuming that the electric field grows linearly up to the maximum value Em=B, approximate analytical relations have been found which determine the particle velocity dependence on the acceleration time. The particles are shown to accelerate for the entire time of the increase in the electric field to a certain final energy, whose value depends on the acceleration rate. It has been established that the lower the acceleration rate, the greater the limiting energy. In the case when the ratio Em/B <0.9, using the solution method proposed by Alfvén in the drift approximation, an analytical solution of the relativistic equation of particle motion has been obtained. The results can be used to find the energy of particles in various pulsed processes in space plasma.

The paper addresses the problem of acceleration of particles in a constant, uniform magnetic field of magnitude B and a uniform electric field perpendicular to it, which slowly increases with time. Assuming that the electric field grows linearly up to the maximum value Em=B, approximate analytical relations have been found which determine the particle velocity dependence on the acceleration time. The particles are shown to accelerate for the entire time of the increase in the electric field to a certain final energy, whose value depends on the acceleration rate. It has been established that the lower the acceleration rate, the greater the limiting energy. In the case when the ratio Em/B <0.9, using the solution method proposed by Alfvén in the drift approximation, an analytical solution of the relativistic equation of particle motion has been obtained. The results can be used to find the energy of particles in various pulsed processes in space plasma.

 particle acceleration crossed electric and magnetic fields constant magnetic field time-varying electric field space plasma particle acceleration crossed electric and magnetic fields constant magnetic field time-varying electric field space plasma The work was performed under Project II.16.1.3 of SB RAS Basic Research Program II.16.1 (research priority II.16) The work was performed under Project II.16.1.3 of SB RAS Basic Research Program II.16.1 (research priority II.16)

Alfvén H. Kosmicheskaya plazma. Moscow, Mir Publ., 1983, 216 p. (In Russian). English Edition: Alfvén H. Cosmic Plasma. Dordrecht, Reidel Publishing Company, 1981, 213 p. Alfvén H. Kosmicheskaya plazma. Moscow, Mir Publ., 1983, 216 p. (In Russian). English Edition: Alfvén H. Cosmic Plasma. Dordrecht, Reidel Publishing Company, 1981, 213 p. Alfvén H., Falthammar K.G. Kosmicheskaya elektrodinamika. Moscow, Mir Publ., 1967. 206 p. English Edition: Alfvén H., Falthammar K.G. Cosmical Electrodynamics. Intern. Ser. of Monographs on Physics. Oxford, Clarendon Press, 1963, 260 p. Alfvén H., Falthammar K.G. Kosmicheskaya elektrodinamika. Moscow, Mir Publ., 1967. 206 p. English Edition: Alfvén H., Falthammar K.G. Cosmical Electrodynamics. Intern. Ser. of Monographs on Physics. Oxford, Clarendon Press, 1963, 260 p. Dorman L.I., Smirnov V.S., Tyasto M.I. Kosmicheskie luchi v magnitnom pole Zemli [Cosmic Rays in the Earth’s Magnetic Field]. Moscow, Nauka Publ., 1971, 399 p. (In Russian). Dorman L.I., Smirnov V.S., Tyasto M.I. Kosmicheskie luchi v magnitnom pole Zemli [Cosmic Rays in the Earth’s Magnetic Field]. Moscow, Nauka Publ., 1971, 399 p. (In Russian). Dvornikov V.M., Sdobnov V.E. Variations in the rigidity spectrum and anisotropy of cosmic rays at the period of Forbush effect on 12-15 July 1982. International J. Geomagnetism and Aeronomy. 2002, vol. 3, no. 3, pp. 217-228. Dvornikov V.M., Sdobnov V.E. Variations in the rigidity spectrum and anisotropy of cosmic rays at the period of Forbush effect on 12-15 July 1982. International J. Geomagnetism and Aeronomy. 2002, vol. 3, no. 3, pp. 217-228. Dvornikov V.M., Kravtsova M.V., Sdobnov V.E. Diagnostics of the electromagnetic characteristics of the interplanetary medium based on cosmic ray effects. Geomagnetism and Aeronomy. 2013, vol. 53, iss. 4, pp. 430-440. DOI: 10.1134/S0016793213040075. Dvornikov V.M., Kravtsova M.V., Sdobnov V.E. Diagnostics of the electromagnetic characteristics of the interplanetary medium based on cosmic ray effects. Geomagnetism and Aeronomy. 2013, vol. 53, iss. 4, pp. 430-440. DOI: 10.1134/S0016793213040075. Landau L.D., Livshits E.M. Teoriya polya [Field Theory]. Moscow, Nauka Publ., 1967, 460 p. (In Russian). Landau L.D., Livshits E.M. Teoriya polya [Field Theory]. Moscow, Nauka Publ., 1967, 460 p. (In Russian). Lindberg L. Plasma flow in a curved magnetic field. Astrophys. Space Sci. 1978, vol. 55, p. 203-225. DOI: 10.1007/BF00642589. Lindberg L. Plasma flow in a curved magnetic field. Astrophys. Space Sci. 1978, vol. 55, p. 203-225. DOI: 10.1007/BF00642589. Lindberg L., Kristoferson L. Reverse deflection and contraction of a plasma beam entering a curved magnetic field. Cosmic Electrodynamics. 1971, vol. 2, pp. 305-380. Lindberg L., Kristoferson L. Reverse deflection and contraction of a plasma beam entering a curved magnetic field. Cosmic Electrodynamics. 1971, vol. 2, pp. 305-380. Morozov A.I., Solov’ev. L.S. Motion of charged particles in electromagnetic fields. Voprosy teorii plazmy [Reviews of Plasma Physics]. Moscow, Gosatomizdat Publ., 1963. Iss. 2. P. 177-255. (In Russian). English Edition: Morozov A.I., Solov’ev L.S. Reviews of Plasma Physics, Vol. 2. Authorized translation from the Russian by Herbert Lashinsky, University of Maryland, USA. Published by Consultants Bureau, New York, 1966, 201 p. Morozov A.I., Solov’ev. L.S. Motion of charged particles in electromagnetic fields. Voprosy teorii plazmy [Reviews of Plasma Physics]. Moscow, Gosatomizdat Publ., 1963. Iss. 2. P. 177-255. (In Russian). English Edition: Morozov A.I., Solov’ev L.S. Reviews of Plasma Physics, Vol. 2. Authorized translation from the Russian by Herbert Lashinsky, University of Maryland, USA. Published by Consultants Bureau, New York, 1966, 201 p. Parker E.N. Interplanetary dynamical processes. New York, London, Interscience Publ., 1963, 284 p. Parker E.N. Interplanetary dynamical processes. New York, London, Interscience Publ., 1963, 284 p.