Plasma Diagnostics Using K‐Line Emission Profiles of Silicon

Abstract

Modifications of K-line profiles due to a warm dense plasma environment are a suitable tool for plasma diagnostics. We focus on Si Kα emissions due to an electron transfer from 2P to 1S shell. Besides 2P fine structure effects we also consider the influence of excited and higher ionized emitters. Generally spoken, a plasma of medium temperature and high density (warm dense matter) is created from bulk Si the greater part of atoms is ionized. The high energy of Kα x-rays is necessary to penetrate and investigate the Si sample. The plasma effect influences the many-particle system resulting in an energy shift due to electron-ion and electron-electron interaction. In our work we focus on pure Si using LS coupling. Non-perturbative wave functions are calculated as well as ionization energies, binding energies and relevant emission energies using the chemical ab initio code Gaussian 03. The plasma effect is considered within a perturbative approach to the Hamiltonian. Using Roothaan-Hartree-Fock wave functions we calculate the screening effect within an ion-sphere model. The different excitation and ionization probabilities of the electronic L-shell and M-shell lead to a charge state distribution. Using this distribution and a Lorentz profile convolution with a Gaussian instrument function we calculate spectral line profiles depending on the plasma parameters.

K$_α$ Emission Profiles of Warm Dense Argon Plasmas

“…Previously, to determine emission and ionization energies of various ionic configurations, we solved the corresponding self-consistent Roothaan-Hartree-Fock equations applying the chemical ab initio code Gaussian 03, see e.g. [8,9]. However the calculations prevent straightforward observation of fine-structure splitting and only a very restricted number of excitation levels could be taken into account.…”

“…In the following we describe the determination of the perturbing Hamiltonian H and calculate shifts of the energy levels caused by the surrounding charges in the plasma environment within the approach described above. To obtain the distribution of the free plasma electrons around the quasi-static ionic emitters, an ion sphere or confined atom model is used [8]. The ion sphere contains a nucleus of charge Z = 18 and the respective number of electrons, so that the system in total is neutral.…”

“…When constructing synthetic X-ray spectra, line components that involve vanishing states have to be removed by hand if there is no steady fade out of its contribution with respect to the plasma parameters [7]. We apply an approach where pressure ionized states shift steadily into the continuum and no extra treatment is needed [8,9].…”