Interpretation of proton radiography experiments of hohlraums with three-dimensional simulations

Proton radiography experiments of laser-irradiated hohlraums performed at the OMEGA laser facility are analyzed using three-dimensional (3D) hydrodynamic simulations coupled to a proton trajectography package. Experiments with three different laser irradiation patterns were performed, and each produced a distinct proton image. By comparing these results with synthetic proton images obtained by sending protons through plasma profiles in the hohlraum obtained from 3D radiation hydrodynamic simulations, it is found that the simulated images agree favorably with the experimental images when electric fields, due to the electron pressure gradients that arise from 3D structures occurring during plasma expansion, are included. These comparisons provide quantitative estimates of the electric field present inside the hohlraums.

Figure 1

(a) Experimental setup showing source protons going through the hohlraum and imaged on the detector. Red (solid) and blue (dashed) lines correspond to the geometrical limitation induced by the laser entrance holes (LEHs) of the hohlraums. (b) Laser irradiation used in the experiment: Case A (10 beams grouped by two), Case B (10 beams uniformly spaced), and Case C (five beams uniformly spaced on one side of the hohlraum).

Figure 2

2D maps of electron density $n_e/n_c$ [(a)–(c)] and transverse electric field $|{\mathit{E}}_{\perp }|$ in V/m [(b)–(d)] taken at $t=1.3$ ns from 3D simulations, at $x=0.12$ cm along the hohlraum axis. Panels (a) and (b) are for Case B, (c) and (d) for Case C.

Figure 3

Transverse electric field (in MV/m) from 2D plane simulations as a function of the mesh refinement in arbitrary units. A fit is illustrated with the dashed line.

Figure 4

Proton fluence $\delta n/n_p$ on the detector: experimental [(a), (d), and (g)], simulated with an electric field [(b), (e), and (h)], and with a magnetic field [(c), (f), and (i)]. Proton fluence [(a), (b), and (c)] for Case A, [(d), (e), and (f)] for Case B, and [(g), (h), and (i)] for Case C.