Hannover 2010 – wissenschaftliches Programm
P 22.5: Poster
Donnerstag, 11. März 2010, 16:00–18:00, Lichthof
Stability of relativistic superluminal solitons — •Götz Alexander Lehmann and Karl-Heinz Spatschek — Heinrich Heine Universität, Düsseldorf, Germany
The nonlinear interaction of a relativistically intense linearly polarized laser beam with a cold plasma can give rise to superluminal solitons. Within a one-dimensional description the superluminal solitons with phase velocity β > c are solutions to the famous Akhiezer-Polovin equations.
The model starts with the Maxwell-fluid equations describing the interaction of relativistic electromagnetic fields with the cold plasma fluid. Assuming a constant phase velocity, they reduce to coupled nonlinear oscillator equations in the co-moving frame. These equations are of Hamiltonian form. Possible solutions to the oscillators can be discussed with the help of Poincaré plots. Different kinds of solutions can be classified, e.g. periodic, quasiperiodic, chaotic or solitonic structures. The superluminal solitons are represented by the separatrix and consist of relativistic longitudinal and transversal oscillations.
We discuss the linear stability of superluminal solitons with respect to perturbed inital conditions for a broad range of parameters. Since the solitons are not available in analytic form, we use a numerical scheme to perform the stability analysis. It is found that the solutions are always unstable. The possible implications of the linear instability for the nonlinear regime are outlined.