Quantum effects on plasma screening for thermonuclear reactions in laser-generated plasmas

A quantum plasma screening model based on the density matrix formalism is used to investigate theoretically the thermonuclear reactions ${}^{13}\mathrm{C}(\alpha ,$ $n){}^{16}\mathrm{O}$ and ${}^2\mathrm{H}(d,$ $n){}^3\mathrm{He}$ in laser-generated plasmas over a large range of densities and temperatures. For cold and dense (solid-state density) plasmas, our results show that quantum effects can enhance the plasma screening for thermonuclear reactions up to one order of magnitude compared with the classical case. This result can have impact on nuclear astrophysics predictions and also may play a role for fusion energy gain prospects. Our simulations allow us to identify the laser-generated plasma experimental setting in which the quantum effects on plasma screening could be confirmed at existing high-intensity laser facilities.

Figure 1

Plasma screening enhancement factor $g_{\mathrm{scr}}$ for the ${}^{13}\mathrm{C}(\alpha$, $n){}^{16}\mathrm{O}$ reaction as a function of the He plasma temperature for weak screening [8] (black solid curve), the Mitler formula [9] (brown dashed curve), the SVH interpolation [11] (magenta dotted curve), the GDGC interpolation [13] (gray dash-dotted curve), and the DMF model (orange filled circles). We consider the plasma density ${10}^{24}{\mathrm{cm}}^{-3}$ (${10}^{21}{\mathrm{cm}}^{-3}$ for the inset).

Figure 2

Plasma screening enhancement factor $g_{\mathrm{scr}}$ for the ${}^{13}\mathrm{C}(\alpha$, $n){}^{16}\mathrm{O}$ reaction as a function of helium plasma density at temperature $200\mathrm{eV}$ for the same models as in Fig. 1.