In the field of laser-plasma interactions, proton radiography has become a key diagnostic technique for high-energy density and transient electromagnetic fields that typically relies on the deflection of proton beams due to the Lorentz force to obtain the information. However, in regions of higher-density plasma, the effects of scattering on the deflection of the probing proton beam have not been thoroughly studied, limiting the application of proton radiography in these environments.

This study presents a theoretical and simulation-based approach to quantifying the effects of plasma scattering and electromagnetic field deflection. We introduce a new method for calculating the path integral of the electric and magnetic field in consideration of plasma scattering. This method requires knowledge of the plasma density, and the results remain accurate enough even when the input density information deviates by 50%. The calculation also maintains good accuracy when the detection distance away from the target rear surface changes. Our findings contribute to a better understanding of the effects of scattering on proton diagnostic deflection and provide theoretical guidance for the application of proton radiography in higher-density plasma regions.