Stopping power of hot dense deuterium-tritium plasmas mixed with impurities to charged particles

In this work, we studied the stopping power of deuterium-tritium (DT) plasmas mixed with impurities to the injected charged particles. Based on the Brown-Preston-Singleton model, the analytical expression for the change ratio of stopping power (denoted by η) induced by impurities in DT plasmas is developed, in which both classical short-distance collision part and quantum correction contribution are purely linear response to the impurity concentration ξ_{X}, while the classical long-range collision brings about higher-order nonlinear response to ξ_{X}. Furthermore, the expression for change ratio of deposition depth (denoted by χ) of charged particles induced by impurities in DT plasmas is also derived. As applications, we systemically investigated the energy loss of α particles deposited into a hot dense DT plasma mixed with impurity X(X=C, Si, Ge), where the temperature and density of DT are smaller than 10 keV and 500 g/cm^{3} and the concentration of Xξ_{X} is less than 5%. The numerical results suggest that (i) for the case of C mixed into DT, both change ratios of stopping power and deposition depth of α particles (i.e., η and χ) are linear response to the concentration of C ξ_{C}; (ii) for the case of Si mixed into DT, the second-order nonlinear response of η and χ to ξ_{Si} cannot be ignored when the densities of DT are larger than 200 g/cm^{3}; and (iii) for the case of Ge mixed into DT, the second- and third-order nonlinear response of η and χ to ξ_{Ge} are very remarkable because of the higher ionization degree and heavier atomic mass of Ge. The formulas and findings in this work may be helpful to the research of internal confinement fusion (ICF) related implosion physics and may provide useful theoretical guidance and data for the design of ICF target.