The Weibel instability, a subject of relevance to many fields of physics ranging from inertial confinement fusion to some astrophysical scenarios, is usually probed with side-on proton radiography. In order to diagnose the strength and wavelength of the spontaneous fields, two concerns that must be settled are how to distinguish the coexisting electric and magnetic fields, and how to overcome the counteracting of deflections in radiographing the filamentary structured fields. In this paper, proton radiography of the Weibel instability in two counterstreaming plasma flows is studied by simulation. It suggests that the electric field dominates the deflection of probe protons, whereas the contribution from the magnetic field is negligible. To resolve the deflection-counteracting problem, the spatial spectrum of the electric field energy is found to be related to the deflection velocity of the probe beam by theoretical analyses. The strength and wavelength of the electric field are then obtainable from the proton flux on the detection plane, whereas the strength and wavelength of the magnetic field can be deduced through the equilibrium between the electric field and the magnetic field pressure gradient after the linear growth stage of the instability. Both numerical and experimental verifications suggest that our method performs well in extracting the strength and wavelength of the spontaneous electric and magnetic fields of the Weibel instability from proton radiography.
PIC simulations of the temperature anisotropy-driven Weibel instability: analysing the perpendicular mode