The electric and magnetic fields generated by the Weibel instability, most of which have a tube-like structure, are of importance for many relevant physical processes in the astrophysics and the inertial confinement fusion. Experimentally, proton radiography is a commonly used method to diagnose the Weibel instability, where the proton deflection introduced from the self-generated electric field is usually ignored. This assumption, however, is in conflict with the experimental observations by Quinn, Fox and Huntington, et al. because the magnetic field with a tube-like structure cannot introduce parallel flux striations on the deflection plane in the proton radiography.

In this paper, we re-examine the nature of the proton radiography of the Weibel instability numerically. Two symmetric counterstreaming plasma flows are used to generate the electron Weibel instability with the three-dimensional particle-in-cell simulations. The proton radiography of the Weibel instability generated electric and magnetic fields are calculated with the ray tracing method. Three cases are considered andcompared: only the self-generated electric field E is included, only the self-generated magnetic field B is included, both the electric field E and magnetic field B are included.

It is shown that when only E is included, the probe proton flux density perturbation on the detection plane, i.e., δn/n₀, is much larger than that when only B is included. Also, when both E and B are included, δn/n₀ is almost the same as that when only E is included. This suggests that in the proton radiography of the Weibel instability generated electric and magnetic fields, the deflection from the electric field dominates the radiography, whereas the magnetic field has an ignorable influence. Our conclusion is quite different from that obtained on the traditional assumption that the electric field is ignorable in the radiography. This mainly comes from the spatial structure of the Weibel instability generated magnetic field, which is tube-like and points to the azimuthal direction around the current filaments. When the probe protons pass through the field region, the deflection from the azimuthal magnetic field can be compensated for completely by itself along the passing trajectories especially if the deflection distance inside the field region is small. Whereas for the electric field, which is in the radial direction, the deflection to the probe protons will not be totally compensated for and will finally introduce an evident flux density perturbation into the detection plane. This understanding can beconducive to the comprehension of the experimental results about the proton radiography of the Weibel instability.