Recombination of $\mathrm{W}{}^{18+}$ ions with electrons: Absolute rate coefficients from a storage-ring experiment and from theoretical calculations

We present experimentally measured and theoretically calculated rate coefficients for the electron-ion recombination of ${\mathrm{W}}^{18+}(\left[\mathrm{Kr}\right]4d^{10}4f^{10})$ forming ${\mathrm{W}}^{17+}$. At low electron-ion collision energies, the merged-beam rate coefficient is dominated by strong, mutually overlapping recombination resonances. In the temperature range where the fractional abundance of ${\mathrm{W}}^{18+}$ is expected to peak in a fusion plasma, the experimentally derived Maxwellian recombination rate coefficient is 5 to 10 times larger than that which is currently recommended for plasma modeling. The complexity of the atomic structure of the open-$4f$ system under study makes the theoretical calculations extremely demanding. Nevertheless, the results of the present Breit-Wigner partitioned dielectronic recombination calculations agree reasonably well with the experimental findings. This also gives confidence in the ability of the theory to generate sufficiently accurate atomic data for the plasma modeling of other complex ions.

Figure 1

Populations of the 1671 levels of the $\left[\mathrm{Kr}\right]4d^{10}4f^{10}$ ground configuration and the $\left[\mathrm{Kr}\right]4d^{10}4f^{9}5s$ and $\left[\mathrm{Kr}\right]4d^{10}4f^{9}5p$ first excited configurations of ${\mathrm{W}}^{18+}$ as a function of ion storage time. The thick solid line represents the population of the $\left[\mathrm{Kr}\right]4d^{10}4f^{10}{}^5{I}_8$ ground level and the dashed line denotes the population of the long-lived metastable $\left[\mathrm{Kr}\right]4d^{10}4f^{10}{}^3{F}_2$ level. The thin solid lines represent the remaining 17 levels from Table 1. The dotted line represents the sum of the populations of the 1652 short-lived levels, which are not listed in Table 1.

Figure 2

Lifetime measurements of the stored ion beam with the cooler electron beam off and on, respectively. After 3.5 s, the electron beam was switched on. The symbols represent the measured count rate on the recombination detector. The white solid lines are exponential decay fits to these data points.

Figure 3

Comparison of our measured (symbols) and various calculated merged-beam recombination rate coefficients. The solid curve (labeled IC) is the result of the present intermediate-coupling calculation. The short-dashed curve (labeled PD) is the result of the fully partitioned calculation including autoionizing (and radiative) damping. The long-dashed curve (labeled RR) is the calculated rate coefficient for radiative recombination. Inset: The same data up to 20 eV on a double logarithmic scale. The full circle (labeled ST) is the rate coefficient from the statistical theory by Dzuba et al. [13].

Figure 4

Experimentally derived (thick solid line) and theoretical rate coefficients for electron-ion recombination of ${\mathrm{W}}^{18+}$ in a plasma. The error bars represent the combined statistical and systematic uncertainty (see text) of the experimentally derived rate coefficient. The thin solid line (labeled IC) and the dotted line (labeled PD) are the results of present intermediate-coupling theory and of the present partitioned and damped statistical theory. The dash-dotted line is the plasma recombination rate coefficient from the ADAS database [6, 38]. The dashed curve is the calculated RR plasma rate coefficient. The shaded area indicates the plasma temperature range where ${\mathrm{W}}^{18+}$ is expected to form in a collisionally ionized plasma [39].