# Nonlinear relativistic plasma resonance: Renormalization group approach

## 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.

- Authors:

- Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)
- Dukhov All-Russian Research Institute of Automatics (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22614044

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Plasma Physics Reports; Journal Volume: 43; Journal Issue: 2; Other Information: Copyright (c) 2017 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANALYTICAL SOLUTION; ELECTRIC FIELDS; EQUATIONS; LASERS; NONLINEAR PROBLEMS; PLASMA DENSITY; PLASMA WAVES; RELATIVISTIC PLASMA; RELATIVISTIC RANGE; RENORMALIZATION; RESONANCE

### Citation Formats

```
Metelskii, I. I., E-mail: metelski@lebedev.ru, Kovalev, V. F., E-mail: vfkvvfkv@gmail.com, and Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru.
```*Nonlinear relativistic plasma resonance: Renormalization group approach*. United States: N. p., 2017.
Web. doi:10.1134/S1063780X1702009X.

```
Metelskii, I. I., E-mail: metelski@lebedev.ru, Kovalev, V. F., E-mail: vfkvvfkv@gmail.com, & Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru.
```*Nonlinear relativistic plasma resonance: Renormalization group approach*. United States. doi:10.1134/S1063780X1702009X.

```
Metelskii, I. I., E-mail: metelski@lebedev.ru, Kovalev, V. F., E-mail: vfkvvfkv@gmail.com, and Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru. Wed .
"Nonlinear relativistic plasma resonance: Renormalization group approach". United States.
doi:10.1134/S1063780X1702009X.
```

```
@article{osti_22614044,
```

title = {Nonlinear relativistic plasma resonance: Renormalization group approach},

author = {Metelskii, I. I., E-mail: metelski@lebedev.ru and Kovalev, V. F., E-mail: vfkvvfkv@gmail.com and Bychenkov, V. Yu., E-mail: bychenk@lebedev.ru},

abstractNote = {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},

journal = {Plasma Physics Reports},

number = 2,

volume = 43,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2017},

month = {Wed Feb 15 00:00:00 EST 2017}

}