Nonlinear relativistic plasma resonance: Renormalization group approach
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Nonlinear Relativistic Plasma Resonance: Renormalization Group Approach I. I. Metelskiia, b*, V. F. Kovalevb, c**, and V. Yu. Bychenkova, b*** a
Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia b Dukhov All-Russian Research Institute of Automatics, Moscow, 127055 Russia c Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia e-mail: *[email protected],** [email protected], ***[email protected] Received April 20, 2016; in final form, June 21, 2016
Abstract—An analytical solution to the nonlinear set of equations describing the electron dynamics and electric field structure in the vicinity of the critical density in a nonuniform plasma is constructed using the renormalization group approach with allowance for relativistic effects of electron motion. It is demonstrated that the obtained solution describes two regimes of plasma oscillations in the vicinity of the plasma resonance— stationary and nonstationary. For the stationary regime, the spatiotemporal and spectral characteristics of the resonantly enhanced electric field are investigated in detail and the effect of the relativistic nonlinearity on the spatial localization of the energy of the plasma relativistic field is considered. The applicability limits of the obtained solution, which are determined by the conditions of plasma wave breaking in the vicinity of the resonance, are established and analyzed in detail for typical laser and plasma parameters. The applicability limits of the earlier developed nonrelativistic theories are refined. DOI: 10.1134/S1063780X1702009X
1. INTRODUCTION The effect of linear transformation of a p -polarized electromagnetic wave into a plasma wave in the vicinity of the plasma resonance, where the laser frequency ω0 is equal to the plasma frequency ω L , is well known in the theory of interaction of laser radiation with a nonuniform plasma. The resonance between laser field oscillations and plasma electron oscillations leads to the enhancement of the electrostatic oscillations, i.e., to the resonance growth of the potential electric field in the vicinity of the critical plasma density [1, 2]. In the linear approximation, the field amplitude is limited by either collisional dissipation of plasma oscillations in the case of cold plasma or escape of plasma waves from the resonance region in the case of hot plasma. The stationary structure of the electric field under linear transformation of the electromagnetic wave was studied in the pioneer works [1–4]. Fundamental and applied interest in studying the effect of the plasma resonance in a nonuniform plasma is motivated by the important role played by this effect in many processes occurring in laser plasma, such as resonance absorption [5, 6], generation of higher harmonics [7–10], and fast particle acceleration [11–13]. High laser intensity requires taking into consideration both nonrelativistic [14] and relativistic [15, 16] nonlinear effects in the plasma resonance.
Strongly nonlinear plasma oscillat
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