Understanding the dramatic role of anomalous dispersion on the measurement of electron densities in plasmas using interferometers

For decades the electron density of plasmas has been measured using optical interferometers. With the availability of good X-ray laser sources in the last decade interferometers have been extended into the wavelength range 14-47 nm, which has enabled researchers to probe even higher density plasmas. The data analysis assumes the index of refraction is due only to the free electrons, which makes the index less than one. Recent interferometer experiments in Al plasmas observed plasmas with index of refraction greater than one at 14 nm and brought into question the validity of the usual formula for calculating the index. In this paper we show how the anomalous dispersion from bound electrons can dominate the free electron contribution to the index of refraction in many plasmas and make the index greater than one or enhance the contribution to the index such that one would greatly overestimate the density of the plasma using interferometers. Using a new average-atom code we calculate the index of refraction in many plasmas at different temperatures for photon energies from 0 to 100 eV and compare against calculations done with OPAL. We also present examples of other plasmas that may have index of refraction greater than one at X-ray laser energies. 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