Dynamic properties of the energy loss of multi-MeV charged particles traveling in two-component warm dense plasmas

The energy loss of multi-MeV charged particles moving in two-component warm dense plasmas (WDPs) is studied theoretically beyond the random-phase approximation. The short-range correlations between particles are taken into account via dynamic local field corrections (DLFC) in a Mermin dielectric function for two-component plasmas. The mean ionization states are obtained by employing the detailed configuration accounting model. The Yukawa-type effective potential is used to derive the DLFC. Numerically, the DLFC are obtained via self-consistent iterative operations. We find that the DLFC are significant around the maximum of the stopping power. Furthermore, by using the two-component extended Mermin dielectric function model including the DLFC, the energy loss of a proton with an initial energy of $\sim 15$ MeV passing through a WDP of beryllium with an electronic density around the solid value $n_e\approx 3\times {10}^{23}{\mathrm{cm}}^{-3}$ and with temperature around $\sim 40$ eV is estimated numerically. The numerical result is reasonably consistent with the experimental observations [A. B. Zylsta et al., Phys. Rev. Lett. 111, 215002 (2013)]. Our results show that the partial ionization and the dynamic properties should be of importance for the stopping of charged particles moving in the WDP.

Figure 1

(a) The mean ionization degree $〈Z〉$ of an average ion, (b) the number densities of electrons, and (c) the chemical potential as a function of temperature of Be at solid density of ${\rho }_{\text{Be}}=1.85\mathrm{g}/{\mathrm{cm}}^3$.

Figure 2

Real part (solid curves) and imaginary part (dotted curves) of the DCF $\nu \left(\omega \right)$ as a function of the frequency $\omega$. (a) is for the Be plasmas with electron density $n_e={10}^{23}{\mathrm{cm}}^{-3}$ and temperatures $T=1,10$, and 100 eV, and (b) is for the Be plasmas with temperature $T=10$ eV and electron densities $n_e={10}^{23},{10}^{24}$, and ${10}^{25}{\mathrm{cm}}^{-3}$. Mean ionization degree $〈Z〉$ is considered in all calculations.

Figure 3

Electron-electron SLFC $G_{ee}\left(k,0\right)$ (thick curves) and ion-ion SLFC $G_{ii}\left(k,0\right)$ (thin curves) as a function of the $k{a}_e$ for Be plasmas at three different temperatures $T=10$, 50, and 100 eV and electron density $n_e={10}^{23}{\mathrm{cm}}^{-3}$. In the calculations, the mean ionization degree and chemical potential of Be plasma shown in Fig. 1 were used.

Figure 4

Proton particle moving the WDP of Be. The stopping power splitting into separate (a) electron component $d{E}_{\text{ele}}/dx$ and (b) ion component $d{E}_{\text{ion}}/dx$ are plotted vs particle velocity $v_p$ (in units of thermal velocity of electron ${\overline{v}}_e$). Different inverse dielectric function models, including the RPA model (black open circles), the Mermin model with DCF $\nu \left(\omega \right)$ (blue solid squares), and the EMDF with both DCF $\nu \left(\omega \right)$ and DLFCs $G_{\alpha \alpha }\left(k,\omega \right)$ with $\alpha =e,i$ (red open stars) were considered. The temperature of Be plasma is chosen as $T=40$ eV, and the electron density is $n_e=2.78\times {10}^{23}{\mathrm{cm}}^{-3}$.

Figure 5

Same as Fig. 4, but the SCF ${\nu }_S$ and SLFCs $G_{\alpha \alpha }\left(k,0\right)$ with $\alpha =e,i$ were used in the Mermin model and the EMDF model. Other parameters are the same as those in Fig. 4.

Figure 6

Stopping power $d{E}_{\text{ele}}/dx$ obtained from the Mermin model (black curve) and the EMDF model (red stars) with DCF $\nu \left(\omega \right)$ and DLFC $G_{ee}(k,\omega )$. The temperature of Be plasma is $T=100$ eV, and the electron density is $n_e=4\times {10}^{23}{\mathrm{cm}}^{-3}$.