Ionization rate coefficients in warm dense plasmas

We recast the atomic processes in a warm, dense plasma using Fermi-Dirac statistics and compare them to the rates of the usual Maxwell-Boltzmann approach of many collisional-radiative models. Population calculations show insignificant differences to calculations assuming nondegenerate free electrons of plasmas at solid density close to local thermodynamic equilibrium, but show departures in average ionization in the presence of strong photoionization. For example, we show that electron degeneracy affects the evolution of plasmas created by ultraviolet free electron laser interaction with solid targets.

Figure 1

(a) Ratio of the photoionization cross section of atoms in a dense plasma with Pauli blocking factors from the value of a free atom. Here $\mathrm{\Delta }E=E_{\gamma }-E_i$ and electron densities are as indicated. (b) Comparison of the three-body recombination rate of singly ionized carbon, with electron densities as indicated, of Maxwell-Boltzmann (dashed line) to Fermi-Dirac (solid line) statistics.

Figure 2

Comparison of the differential collisional ionization cross section due to Mott (dashed) to the modified Mott used in this work (solid) plotted as a function of the fraction of its domain $x={\epsilon }_1/({\epsilon }_0-E_i)$ for the first ionization stage of carbon and (a) ${\epsilon }_0=50$, (b) ${\epsilon }_0=100$.

Figure 3

Comparison of the steady state ionization fraction of a carbon plasma (density of 2.23 g ${\mathrm{cm}}^{-3}$, corresponding to graphite) for Fermi-Dirac (solid) and Maxwell-Boltzmann (dashed) statistics, irradiated by 50 eV photons at intensities indicated.

Figure 4

Evolution of the electron temperature and ionization fraction of carbon (density of 3.53 g ${\mathrm{cm}}^{-3}$, corresponding to diamond) irradiated by a laser beam with photon energies of 14 eV and Gaussian intensity as shown shaded with a full-width half maximum of 1 fs and peak intensity of ${10}^{14}$ W ${\mathrm{cm}}^{-2}$ with Maxwell-Boltzmann (dashed line) and Fermi-Dirac (solid line) statistics as indicated.