XXXIV International Conference on Plasma Physics and CF, February 12 – 16, 2007, Zvenigorod
RELATIVISTICALLY INTENSE PLANE ELECTROMAGNETIC WAVES IN COLD
UNMAGNETIZED ELECTRON-POSITRON PLASMAS
O.B. Shiryaev
Coherent and Nonlinear Optics Department, General Physics Institute RAS, P.O. Box
119991, 38 Vavilov St., Moscow, Russia
A fully nonlinear self-consistent 1D problem describing the interactions of relativistically intense
plane electromagnetic waves and cold unmagnetized electron-positron plasmas is derived from
Maxwell's equations and the equations of the relativistic electron and positron fluid dynamics [1].
Plasma charge neutrality is not assumed in the derivation. Formally, the problem considered is an
analog of the Akhiezer-Polovin one, which is the classic model of the interaction of plane
electromagnetic waves with plasmas of electrons and inertially frozen ions [2].
Numerical and asymptotic solutions to the equations governing the intense plane electromagnetic
wave propagation in an electron-positron plasma are presented for the substantially underdense
plasma case, where the electromagnetic radiation phase velocity is close to the speed of light. The
electromagnetic field potentials and spectra, the plasma electron and positron momenta, and the
plasma charge concentrations are calculated and analyzed. It is demonstrated that there exist two
distinct regimes of the nonlinear propagation of intense electromagnetic fields in underdense cold
unmagnetized locally non-neutral electron-positron plasmas. One of these regimes is that of the
nonlinear self-modulation – it occurs when the plasma longitudinal field potential magnitude is
below the critical level, which corresponds exactly to the relativistic field strength. The other one is
the regime of harmonics generation and takes place when the plasma field exceeds this critical
level.
The signature of the nonlinear self-modulation regime is a splitting of the propagating field's
spectrum. In this framework, the spacing between the transverse field spectral bands is equal to the
perturbed plasma frequency, which is much lower then that of the transverse field. Generally the
above propagation pattern involving fast and slow oscillation scales is similar to the one of the
electromagnetic modes in plasmas comprising electrons and immobile ions [3] despite the absence
of the stabilizing positive background in the case of an electron-positron plasma.
In the other regime – the harmonics generation one - the propagating electromagnetic field and
the plasma longitudinal field oscillate on the same scale. The former one has a complicated nonuniform structure. An extremely sharp local variation of the electron and positron concentrations is
a typical feature of this regime. In this case the transverse electric field spectrum is a set of
harmonics with the spacing comparable to their frequencies.
References
[1]. O.B. Shiryaev, "Relativistically Intense Plane Electromagnetic Waves in Electron-Positron
Plasmas: Nonlinear Self-Modulation and Harmonics Generation Regimes". Phys. Plasmas 13,
112304 (2006)
[2]. A.I. Akhiezer, R.V. Polovin, Zh. Eksp. Teor. Fiz. 30, 915 (1956) [Sov. Phys. JETP 3(5), 696
(1956)]
[3]. A.V. Borovsky, A.L. Galkin, V.V. Korobkin, O.B. Shiryaev, Phys. Rev. E 59, 2253 (1999)
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