Nonlinear Relativistic Interactions between Electromagnetic Waves and Quantum Plasmas

We present models for the nonlinear interaction between a relativistically strong electromagnetic wave and a quantum plasma. The electron dynamics is modeled using collective nonlinear Schrodinger, Klein-Gordon, and Dirac models, which are coupled nonlinearly with the Maxwell equations for the electromagnetic field. We consider the nonlinear propagation of electromagnetic waves, leading to self-induced transparency, as well as parametric instabilities involving Raman and modulational instabilities, and the acceleration of electrons by electrostatic fields and wakes behind short laser pulses. Spin effects lead to frequency up- or downshifts depending on the spin polarization of the plasma and the polarization of the electromagnetic wave. The applications include dense astrophysical bodies and free electron lasers in the quantum regime, where relativistic and quantum effects must be taken into account on an equal footing.