We analyze the extended model of the dynamics of a thin plasma layer under the influence of a short laser pulse with a constant magnetic field. The model predictions show good correspondence to the single and multi-particle particle-in-cell simulations. It is also demonstrated that polarization of the attosecond XUV radiation generated by a short intense laser pulse interacting with a thin foil could be tuned using an external magnetic field via the Faraday effect. 

We consider the dynamics of a thin foil irradiated by a relativistic-intensity few-cycle laser pulse under an applied magnetic field parallel to the direction of laser propagation. To this end, we extend the self-consistent theoretical model developed by Bulanov et al. in 2013 [1], by adding an external static magnetic field of arbitrary amplitude. 

Numerical simulations using PIC codes indicate that the presence of a longitudinal magnetic field affects the polarization of the irradiated field. Namely, if the incident pulse is linearly polarized, then during reflection the ellipticity of the upshifted pulse changes. The formulas derived from the Bulanov model can qualitatively explain the effect of longitudinal magnetic field: electrons gain additional push or pull in the traverse directions during the interaction with the laser. Because of this the oscillations on the plasma surface stop following linearly polarized forces in the traverse axes of the electric field. This leads to the occurrence of rotation of the polarization plane (Faraday effect). During the rotation the electrons at first gain some spin angular momentum. Coupled with the frequency upshifting due to the Doppler effect when electrons are separated from the plasma and travel back, they can form an elliptically polarized XUV pulse. 

To model this behavior, first, we need to neglect the movement of the electrons along the longitudinal axis. It is possible because the back-and-forth movement of the electrons acts symmetrically on both the traverse axes. Hence, removing it should keep the relative dynamics of the electrons in traversal directions intact but help get rid of the Doppler effect and thus simplify the solution of the equations. Second, we use the continuous laser pulse (i.e. the pulse has no finite duration). This also does not affect the traversal dynamics of the experiment, but it allows us to simplify the governing equations to the extent that we can write the analytical solution of the linear ODE system in a fairly comprehensible form.