Influence of atomic radiative and collisional processes on the plasma modeling of Mg^{10+} at low electron densities

Abstract

In this paper, we report on theoretical calculations of electron-impact excitation cross sections and radiative transition rates for ${\mathrm{Mg}}^{10+}.$ The excitation cross sections were calculated using semirelativistic close-coupling and fully relativistic distorted-wave theory and the radiative rates were determined using semirelativistic and fully relativistic atomic-structure theory. After the solution of the corresponding collisional-radiative equations, the $K{\ensuremath{\alpha}}_{2}/K{\ensuremath{\alpha}}_{1}$ $(1s2p{ }^{3}{P}_{1}\ensuremath{\rightarrow}{1s}^{2}{ }^{1}{S}_{0}$ over $1s2p{ }^{1}{P}_{1}\ensuremath{\rightarrow}{1s}^{2}{ }^{1}{S}_{0})$ emission line ratio and the $K{\ensuremath{\beta}}_{2}/K{\ensuremath{\beta}}_{1}$ $(1s3p{ }^{3}{P}_{1}\ensuremath{\rightarrow}{1s}^{2}{ }^{1}{S}_{0}$ over $1s3p{ }^{1}{P}_{1}\ensuremath{\rightarrow}{1s}^{2}{ }^{1}{S}_{0})$ emission line ratio were calculated as a function of electron temperature and density. The various scattering calculations involving different numbers of levels enabled us to study the influence of resonance structures and cascades from highly excited levels on the collisional-radiative modeling and we found that they have little effect on the level populations. However, even in this ten-times ionized species, the effects of orbital relaxation are found to be important in the determination of accurate electric-dipole radiative transition rates. Both line ratios were found to be strongly affected by whether the magnetic-dipole radiative transition from the $1s2s$ ${}^{3}{S}_{1}$ level to the ground state was included or not. At very low electron densities, the $1s2s$ ${}^{1}{S}_{0}$ two-photon transition to the ground state also has an effect on the $K{\ensuremath{\alpha}}_{2}/K{\ensuremath{\alpha}}_{1}$ line ratio. In addition, we found that the line ratios are enhanced at high temperatures by radiative and dielectronic recombination from the hydrogenic ${\mathrm{Mg}}^{11+}$ ion. However, the dielectronic satellite lines have no effect on the line ratios for the low-density astrophysical, solar, and magnetic-fusion plasmas considered in this paper.