Minimal dielectric polarization stopping power in white dwarfs

Abstract

In this paper, we investigate the energy loss of ions by arbitrarily degenerate electron fluid, in the framework of hydrodynamic model by incorporating the generalized relativistic degeneracy pressure, Wigner–Seitz cell Coulomb interactions, and electron spin-exchange pressures for a wide range of electron number-density regimes relevant to the solid density (SD), inertial confinement fusion (ICF), warm dense matter (WDM), and super-dense astrophysical objects, such as white dwarf (WD) stars. It is found that the use of non-relativistic degeneracy pressure for electron fluid, instead of the exact Chandrasekhar relativistic degeneracy pressure, for the ICF density regime and beyond can introduce significant relative error to the stopping power calculation. Therefore, current study may introduce a significant change to the ICF scheme of super-compressed fuel. It is further revealed that the relativistic degeneracy parameter, R ₀, and the atomic number of constituent ions, Z, significantly affect the maximum stopping power velocity of ions. We also discover that the velocity-averaged energy loss function becomes minimal in electron number density typical of white dwarf stars, n ₀≃2×10³⁰ cm⁻³. It is found that the characteristic density for the minimal ion beam energy loss does not depend on the value of other plasma parameters, such as the ion–electron collision rate and the ion temperature or its atomic number. The latter finding, in particular, may help in better understanding of fusion-burning waves in dense compact stars and their cooling mechanisms.