Generation of Plasma Bunches under Conditions of Gyromagnetic Autoresonance in a Long Magnetic Mirror Machine: Computati
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MA DYNAMICS
Generation of Plasma Bunches under Conditions of Gyromagnetic Autoresonance in a Long Magnetic Mirror Machine: Computational Experiment V. V. Andreeva, V. I. Ilgisonisb, A. A. Novitskya, and A. M. Umnova, * a Peoples’ b
Friendship University of Russia (RUDN University), Moscow, 117198 Russia State Atomic Energy Corporation Rosatom, Moscow, 119017 Russia *e-mail: [email protected]
Received February 20, 2020; revised March 25, 2020; accepted March 26, 2020
Abstract—A numerical simulation of the formation of plasma bunches in a long mirror machine under the gyromagnetic autoresonance was carried out in a magnetic field that increased with time. The process of the formation of plasma bunches with an energetic electronic component was studied as well as their time and space dynamics. The evolution of the energy spectra of the electron and ion components of the plasma was also studied. The analysis of the dependence of the efficiency of the trapping of electrons in the gyromagnetic autoresonance regime on experimental parameters was conducted. It was shown that a collective acceleration of the ion component of plasma bunches is possible. The obtained results are important for the understanding of the mechanisms of generation and confinement of plasma bunches with an energetic electron component in a long mirror machine. Keywords: gyromagnetic autoresonance, plasma bunches, long mirror machine, computational experiment DOI: 10.1134/S1063780X20080012
1. INTRODUCTION Gyromagnetic autoresonance (GA) is the name given to the electron cyclotron resonance (ECR) in a magnetic field that slowly increases in space or time. This term was introduced in [1–3] specifically to emphasize the difference between this phenomenon and the classic cyclotron autoresonance, which is the self-sustained cyclotron resonance between the electron and the transverse electromagnetic wave propagating along a uniform magnetic field [4, 5]. Under conditions of GA, the relativistic change of the electron mass is compensated by the change of the magnetic field and as a result, the cyclotron frequency remains almost constant and thus, the resonance condition is maintained: ωce = eB(t )/(m0 γc) ≅ ω, where ω is the angular frequency of the microwave field, ωce is the electron cyclotron frequency, m0 and e is the electron mass and charge, respectively, c is the speed of light in vacuum, and γ is the relativistic factor. The phase of the electron (the angle between the pulse vector of the electron and the vector of the electric component of the microwave field) trapped in GA is in the interval that provides a quasi-continuous acceleration of the particle. If the magnetic field increases linearly with time, B(t ) = B0 (1 + αωt ) , where B0 = m0cω/e , α is a dimensionless magnetic
field increase velocity, and γ(0) ≈ 1, the kinetic energy of the electron is determined by the formula
W = m0c 2αωt. The increase (on average, during one period of phase oscillations) of the electron energy occurs in the phase interval π/2 < ϕ < 3π/2 . Figure 1 shows th
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