Abstract
We derive general nonlinear equations relevant to describe the propagation of powerful pump electromagnetic fields launched within a plasma (underdense or overdense). The powerful pump (such as obtained with short laser pulses) creates nonlinear-induced collective electromagnetic perturbations with matter lying in the relativistic regime. One main result is the self-consistent treatment of the coupled equations between the pump and the perturbations. In particular, the self-generated magnetic field could modify the pump propagation. We point out a mechanism due to the relativistic ponderomotive force (whose derivation is provided) to produce a magnetic field that may be stronger than those fields derived with a non-self-consistent approach. As an application we investigate the possibility of relativistic magnetic guiding of light under the combined action of the self-induced density and magnetic field.
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