Charge Equilibrium of a Laser-Generated Carbon-Ion Beam in Warm Dense Matter

Using ion carbon beams generated by high intensity short pulse lasers we perform measurements of single shot mean charge equilibration in cold or isochorically heated solid density aluminum matter. We demonstrate that plasma effects in such matter heated up to 1 eV do not significantly impact the equilibration of carbon ions with energies $0.045–0.5\mathrm{MeV}/\mathrm{nucleon}$. Furthermore, these measurements allow for a first evaluation of semiempirical formulas or ab initio models that are being used to predict the mean of the equilibrium charge state distribution for light ions passing through warm dense matter.

Figure 1

Experimental setup.

Figure 2

$Z_{\mathrm{mean}}$ for carbon ions as measured by the “reference” TP1 and “transmission” TP2 after 100 nm of aluminum target at 300 K. The error is $\pm 0.005\mathrm{MeV}/\mathrm{nucl}$ for the energy and the uncertainty is $\pm 0.1$ for the mean charge.

Figure 3

Comparison between $Z_{\mathrm{mean}}$ from our experiment with (a) the effective charge from Refs. 4, 12, 24, 25 and $Z_{\mathrm{mean}}$ from Betz [7]; (b) $Z_{\mathrm{mean}}$ from Shima [26] and from ETACHA.

Figure 4

Density and temperature of the heated aluminum target as simulated by ESTHER using the measured heating proton parameters.

Figure 5

$Z_{\mathrm{mean}}$ of the carbon ion beam as measured by the TP2 through 100 nm of aluminum cold or heated to 1 eV. The shot was timed such that the ion beam with energy $0.41–0.53\mathrm{MeV}/\mathrm{nucl}$ came to equilibrium through the warm dense aluminum plasma (see Fig. 4).