Fig. 4: Simulated distribution of longitudinal electric field and proton beam density during beam transport in experimentally used ionized target, and the resulting proton beam energy spectra shift after passing through the sample.

a Longitudinal electric field driven by proton beam, moving along the Z direction with a beam density of 8 × 10¹⁶ cm⁻³. The beam density profile is indicated by the red solid curve. b The same situation as in (a) but the initial beam density is reduced to 8 × 10¹¹ cm⁻³. c Normalized energy spectra. The energy spectra of protons without target are represented by the black solid curve. The colored lines indicate the energy spectra of protons passing through the plasma target for varying beam densities of 8 × 10¹¹ cm⁻³ (red solid line), 8 × 10¹⁵ cm⁻³ (green dashed line), and 8 × 10¹⁶ cm⁻³ (blue solid line).