A demonstration of extracting the strength and wavelength of the magnetic field generated by the Weibel instability from proton radiography

The Weibel instability and the induced magnetic field are of great importance for both astrophysics and inertial confinement fusion.Because of the stochasticity of this magnetic field,its main wavelength and mean strength,which are key characteristics of the Weibel instability,are still unobtainable experimentally.In this paper,a theoretical model based on the autocorrelation tensor shows that in proton radiography of the Weibel-instability-induced magnetic field,the proton flux density on the detection plane can be related to the energy spectrum of the magnetic field.It allows us to extract the main wavelength and mean strength of the two-dimensionally isotropic and stochastic magnetic field directly from proton radiography for the first time.Numerical calculations are conducted to verify our theory and show good consistency between pre-set values and the results extracted from proton radiography.