Relativistic Effects in Faraday Rotation Probing of Laser Wakefield Acceleration

In laser wakefield acceleration (LWFA), an intense femtosecond laser pulse drives a plasma wave capable of trapping and accelerating electrons to GeV energies. Future applications of LWFA as the first stage in a next-generation accelerator or a bright ultrashort X-ray source require high peak electron energy and high charge yield. Visualizing the wakefield evolution is important for optimizing the conditions for LWFA. Faraday rotation diagnostics imprint the magnetic field, plasma density and electron flow velocity of the wakefield onto the polarization of a probe pulse. I will present theory, predictions and experimental data on the importance of relativistic effects in Faraday rotation probe streaks of wakefields. I will also discuss the general case of Faraday rotation in a magnetized relativistic plasma and the possibility of extracting plasma velocities from the polarization dependence of nonlinear Faraday rotation.