# Nichtlineare elektromagnetische Wellen in relativistischen Plasmen

- Nonlinear electromagnetic waves in relativistic plasma

Pesch, Thomas Christian; Kull, Hans-Jörg (Thesis advisor)

*Aachen : Publikationsserver der RWTH Aachen University (2010, 2011)*

Dissertation / PhD Thesis

Aachen, Techn. Hochsch., Diss., 2010

Abstract

Nowadays, modern laser systems reach intensities of more than 10^18 W/cm^2. In this intensity regime, a relativistic description of laser-plasma interaction is crucial. A fundamental question is how an ultraintensive laser beam can propagate in a stable manner over large distances in a plasma. Excellent candidates for a stable propagation are stationary relativistic electromagnetic and electrostatic waves. In contrast to the nonrelativistic case the electromagnetic and electrostatic modes are strongly coupled by the relativistic gamma factor, the density modulation and the nonlinear v x B-force. In the present work the propagation of electromagnetic and electrostatic stationary waves in plasmas is investigated analytically and numerically at relativistic intensities. The theoretical framework is the Akhiezer-Polovin model. Although the model was already introduced in the late 50s, analytical solutions are known only in some special cases, e.g. for circular polarization or for periodic waves. The goal of this work is an analytical description and classification of the solutions of the Akhiezer-Polovin model. Mainly the physically interesting case of linear polarization is considered. Furthermore, as a generalization of periodic waves, quasiperiodic waves are investigated. In the case of quasiperiodic waves the electromagnetic wave is superimposed by an additional electrostatic oscillation. Such an oscillation is almost inevitably excited by the light pressure of the laser beam. The resulting nonlinear coupling yields a strong modulation of frequency and amplitude. Important results of the present work are the generalization of the periodic waves to quasiperiodic waves, the determination of the corresponding dispersion relations and the classification of the solutions depending on the plasma density. In the case of small plasma densities an analytical solution is derived with an extended two-time-scale method. The solution completely accounts for frequency and amplitude modulation. The periodic solutions, for which the particle trajectories resemble the famous vacuum figure-eight, are included as a special case. A general method for the derivation of the dispersion relation for arbitrary stationary waves is introduced. With this method the relativistic correction factor to the plasma frequency is derived and it is shown that the factor is substantially modified by the presence of an electrostatic wave. For large plasma densities, the waves are generally very complicated and there is a large variety of solutions. In the periodic case, in addition to the eight like trajectories also novel circular particle orbits are investigated. A deviation from the periodic solution yields for circular and eight like trajectories a completely different behaviour. A novel effective mechanism of nonlinear mode conversion is discussed, which is basically different from other schemes of mode conversion. All possible solutions are classified using Poincare sections. In this representation quasiperiodic solutions can be divided into two classes which are separated by a separatrix. Furthermore, also the case of a medium plasma density is considered. There a symmetry breaking occurs and the solutions change. Finally, the results of the Akhiezer-Polovin model are compared with a relativistic PIC(Particle-In-Cell) simulation which also includes kinetic effects. The stability of the stationary waves is investigated. In addition, also non-stationary waves are considered and compared with the stationary waves. It is shown that for a stable propagation the nonlinear mode coupling of the electromagnetic and electrostatic stationary waves is crucial.

### Identifier

- URN: urn:nbn:de:hbz:82-opus-35277
- RWTH PUBLICATIONS: RWTH-CONV-125326