Ionization and reflux dependence of magnetic instability generation and probing inside laser-irradiated solid thin foils

When an intense laser accelerated electron beam, with large current density on the order of 10^12 A/cm^2, enters a solid density plasma, it is well-known to be subject to a number of different types of instabilities that cause it to filament. In this work, we investigate the transport instability of a fast electron beam that is imprinted on the self-generated magnetic filaments inside the solid density plasmas using particle-in-cell simulations. By varying collisional ionization models, our simulations show that the atomic ionization process is crucial to determine the structure of the magnetic filaments. We further attribute the generation of bulk magnetic filaments to Weibel-like instability mechanism caused by counter-propagating hot forward-bulk return current streams and counterpropagating hot forward-reflux current streams. It is found that the magnetic fields in the filament channels near the rear surface are around one order of magnitude higher than those near the front surface of the thin solid target. This asymmetry is likely induced by the very different properties of bulk electron stream and hot reflux electron stream in terms of density and velocity distribution. Finally, we propose to probe the magnetic fields inside the solid density plasmas by X-Ray polarimetry via Faraday rotation using X-Ray free electron lasers (XFELs). The synthetic simulations show that XFELs are capable to detect the magnetic fields from relativistic laser-solid interactions.