Prevention of trajectory crossings in proton radiography and the reconstruction of a sheath electric field

The sheath electric field is localized with a thickness of only several Debye lengths. It widely exists at plasma boundaries and in some cases can be very intense. Previous diagnoses of an intense, localized sheath electric field could only deliver the spatially averaged amplitude of the field. The sheath’s spatial structures remain unresolved. In this paper, we numerically demonstrate the three-dimensional reconstruction of a cylindrically symmetric sheath electric field by means of the Abel inversion in combination with a correction of the spatial dislocation in the inversion process. By employing a divergent or/and relativistic proton beam for radiography of the sheath region, it is found that the crossings of the proton trajectories can be prevented and the linearity requirement for the Abel inversion can be satisfied. A sheath electric field with an amplitude of about 1×1011 V/m and a thickness of sub-μm level is well reconstructed with a 120 MeV proton beam. The inter dependences of the reconstruction on the proton beam energy, energy spread, beam divergence, and the amplitude of the sheath are discussed.