Stationary Relativistic Electron Vortices in Cold Plasmas with Immobile Ions
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Radiophysics and Quantum Electronics, Vol. 62, No. 11, April, 2020 (Russian Original Vol. 62, No. 11, November, 2019)
STATIONARY RELATIVISTIC ELECTRON VORTICES IN COLD PLASMAS WITH IMMOBILE IONS A. V. Korzhimanov1,2 ∗ and M. A. Lazareva1,2
UDC 533.9.01
Based on a joint solution of the system of Maxwell equations and relativistic hydrodynamics equations for an electron liquid we study stationary two-dimensional electron vortices in a cold plasma with immobile ions. In particular, we consider the case of a two-parameter family of exponentially decaying electron density profiles. The main properties of a vortex as functions of its radius and thickness are explored. A parameter range in which relativistic effects are significant has been identified. In that range, dependences of the energy density in a vortex on its parameters are found, and it is shown that in experimentally attainable conditions the ratio of the vortex radius to the thickness of the plasma skin layer is approximately equal to the ratio of the total energy in a plasma per electron to the electron rest energy.
1.
INTRODUCTION
The interaction of intense laser radiation with matter leads to the formation of a dense, fully ionized plasma and is often accompanied by the emergence of coherent, relatively long-lived structures, in particular electromagnetic solitons and electron vortices. When the radiation intensity is above 1018 W/cm2 the energy of electrons becomes equal to their rest energy, and it becomes necessary to take into account relativistic effects [1]. The electromagnetic field localized in coherent structures can be measured by electron or proton radiography methods, which makes them important information sources in the experiments on laser-plasma particle acceleration [2], inertial thermonuclear fusion [3], or laboratory astrophysics [4]. One of the characteristic scenarios for the formation of coherent structures in a laser plasma is the development of modulation and filamentation instabilities during propagation of short (femtosecond and picosecond) laser pulses in an underdense plasma, which lead to an efficient absorption of laser energy and its transformation into the energy of Langmuir oscillations with the subsequent plasma turbulization. In the course of numerical simulation of such a turbulent plasma, the formation of electromagnetic solitons and electron vortices in it was predicted [5–7], which was also confirmed by experimental data [8]. The formation of coherent structures was also predicted for the late stages of development of the Weibel instability in the interpenetrating flows of both the electron–ion [9] and electron–positron plasmas [10]. In two-dimensional geometry, electron vortices are localized structures, in which the total magnetic flux is non-zero. This makes them different from electromagnetic solitons, which are electromagnetic waves localized in electron cavities. In three-dimensional geometry, however, these vortices and solitons turn out to be intertwined with each other, forming more complex structures [11]. Neverthel
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