Understanding the anomalous dispersion of doubly ionized carbon plasmas near 47nm

Abstract

Over the last several years we have predicted and observed plasmas with an index of refraction greater than one in the soft X-ray regime. These plasmas are usually a few times ionized and have ranged from low-Z carbon plasmas to mid-Z tin plasmas. Our main calculational tool has been the average atom code. We have recently observed C 2+ plasmas with an index of refraction greater than one at a wavelength of 46.9 nm (26.44 eV). In this paper we compare the average atom method, AVATOMKG, against two more detailed methods, OPAL and CAK, for calculating the index of refraction for the carbon plasmas and discuss the different approximations used. We present experimental measurements of carbon plasmas that display this anomalous dispersion phenomenon. It is shown that the average atom calculation is a good approximation when the strongest lines dominate the dispersion. However, when weaker lines make a significant contribution, the more detailed calculations such as OPAL and CAK are essential. During the next decade X-ray free electron lasers and other X-ray sources will be available to probe a wider variety of plasmas at higher densities and shorter wavelengths so understanding the index of refraction in plasmas will be even more essential. With the advent of tunable X-ray lasers the frequency dependent interferometer measurements of the index of refraction may enable us to determine the absorption coefficients and line-shapes and make detailed comparisons against our atomic physics codes.

Extreme ultraviolet interferometry of laser plasma material between the critical and ablation surfaces

“…The low values of refractive index observed with our interferometry act as a signature of the presence of lowly ionized material at high density between the absorption and ablation surface. Sample calculations of our procedure for evaluating h(E) agree with results by Nilsen et al [29,32] carried out for low density (10 20 ions cm À3 ) carbon plasmas at temperatures of 2, 5, 10 and 20 eV. At late times, as the plasma expands, see Fig.…”

Average-atom treatment of relaxation time in x-ray Thomson scattering from warm dense matter

“…The present version of the average-atom model was used in Refs. [17][18][19][20][21] to investigate anomalous dispersion in C, Al, Ag, and other plasmas in the soft X-ray region of the spectrum and has been used to investigate Thomson scattering in Refs. [22][23][24][25][26][27][28][29][30].…”