Impact of free electron degeneracy on collisional rates in plasmas

Degenerate plasmas, in which quantum effects dictate the behavior of free electrons, are ubiquitous on earth and throughout space. Transitions between bound and free electron states determine basic plasma properties, yet the effects of degeneracy on these transitions have only been theorized. Here, we use an x-ray free electron laser to create and characterize a degenerate plasma. We observe a core electron fluorescence spectrum that cannot be reproduced by models that ignore free electron degeneracy. We show that degeneracy acts to restrict the available electron energy states, thereby slowing the rate of transitions to and from the continuum. We couple degeneracy and bound electron dynamics in an existing collisional-radiative code, which agrees well with observations. The impact of the shape of the cross section, and hence the magnitude of the correction due to degeneracy, is also discussed. This study shows that degeneracy in plasmas can significantly influence experimental observables such as the emission spectra, and that these effects can be included parametrically in well-established atomic physics codes. This work narrows the gap in understanding between the condensed-matter and plasma phases, which coexist in myriad scenarios.

Figure 1

(a) The fluence scan data (blue circles) with fitted curve (dashed blue line) and corresponding peak electron temperatures (solid red line) of the XFEL focal spot radial profile. The spot is separated into 10 radial volumes for modeling, labeled $R$, that absorb the same number of XFEL photons, and four such regions are shown by vertical black lines. (b) The XFEL pulse intensity profile in time (black dash-dotted curve) and corresponding electron temperatures for two heating delays of 20 fs (dashed curves) and 40 fs (solid curves) for four plasma volumes from $R1$ (top curves) to $R10$ (bottom curves). (c) The corresponding hot electron densities, $n_e$.

Figure 2

The correction factor ($\mathit{CF}$) plotted against the plasma degeneracy $\mathrm{\Theta }=\mu /\left(k_B{T}_e\right)$ at solid density. $\mathit{CF}$ is shown for three-body recombination (green shaded curve) and collisional ionization (dash-dotted green curve) for three cross sections for a transition of energy $dE\gg T_e$ (details in text). The $\mathit{CF}$ values for the analytical cross sections are shown for three-body recombination (solid red curve) and ionization (dashed red curve). The range of $\mathit{CF}$ values for the hot and bulk electrons is shown by solid black arrows. The hot electrons are unaffected by degeneracy, and $CF\approx 1$. Conversely, the bulk electrons remain degenerate throughout the XFEL pulse. The $\mathit{CF}$ values for the bulk electrons corresponding to the two heating delays used in Fig. 1 are indicated by black dash-dotted lines with arrows.

Figure 3

The experimental $K\alpha$ fluorescence spectrum of XFEL irradiated aluminium showing the three ionization stages IV, V, and VI for 300 and 600 nm foil thickness (noisy solid black lines). Each shaded region is calculated using a different treatment of $\mathit{CF}$ according to Fig. 2. The spectra of two heating delays, and three cross sections are calculated for each treatment of $\mathit{CF}$. The spectra using MB statistics and no correction (shaded blue region with short-dashed line: bottom), FD statistics with the standard $\mathit{CF}$ values (shaded green region with dashed line: middle), and FD statistics with the analytical approximation (shaded red region, with dash-dotted line: top) are shown.