X-ray line shift as a high-density diagnostic for laser-imploded plasmas

Abstract

The frequency shift of x-ray spectral lines has been theoretically studied for possible application as a density diagnostic in high-compression laser-fusion experiments. Neon was found to have line-shift characteristics ideal for near-term experiments and could be used as a diagnostic seed material for the fuel. At densities above \ensuremath{\sim}4 g/${\mathrm{cm}}^{3}$, the shift of neon Lyman $\ensuremath{\alpha}$ was found to be roughly proportional to density ($\ensuremath{\Delta}\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}\ensuremath{-}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}{n}_{e}$ eV). The calculations were done by solving the Schr\"odinger equation for energy levels, in a self-consistent potential determined by the nonlinear Poisson equation for electrons and neighboring ions. The computer simulation of a possible laser-compression experiment was used to calculate the line spectrum that might be seen in the laboratory and to illustrate how the shift could be used to estimate density. Unfortunately, this diagnostic was found to be applicable only when the average charge of target materials was less than about 6; i.e., it is applicable to plastic microballoons but not to glass. When higher-$Z$ material is present, then the amount of background radiation and line attenuation reduce neon Lyman $\ensuremath{\alpha}$ to the level of noise and preclude an accurate measure of the frequency shift. Alternatively, given other diagnostics for density, such experiments could be used to test the theory of line shifts and to examine the physics of ions in a high-density plasma.