Impact of anomalous dispersion on the interferometer measurements of plasmas

Abstract

For many decades optical interferometers have been used to measure the electron density of plasmas. During the last ten years X-ray lasers in the wavelength range 14 to 47 nm have enabled researchers to use interferometers to probe even higher density plasmas. The data analysis assumes that the index of refraction is due only to the free electrons, which makes the index of refraction less than one and the electron density proportional to the number of fringe shifts. Recent experiments in Al plasmas observed plasmas with an index of refraction greater than one and made us question the validity of the usual formula for calculating the index of refraction. Recent calculations showed how the anomalous dispersion from the bound electrons can dominate the index of refraction in many types of plasma and make the index greater than one or enhance the index such that one would greatly overestimate the electron density of the plasma using interferometers. In this work we calculate the index of refraction of C, Al, Ti, and Pd plasmas for photon energies from 0 to 100 eV (12.4 nm) using a new average-atom code. The results show large variations from the free electron approximation under many different plasma conditions. We validate the average-atom code against the more detailed OPAL code for carbon and aluminum plasmas. During the next decade X-ray free electron lasers and other 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.

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

“…Several years ago our calculations showed that the index of refraction of partially ionized C plasma was very complex for photon energies below 40 eV [18]. To understand what C plasmas would display an anomalous index of refraction near 47 nm we first need to look at the absorption characteristics of C. For neutral C the ionization potential is at 11.26 eV.…”

“…Analysis of these experiments showed that the anomalous dispersion from the resonance lines and absorption edges of the bound electrons have a larger contribution to the index of refraction with the opposite sign as the free electrons [10][11][12][13][14][16][17][18] and their influence on the index of refraction extends far from the absorption edges and resonance lines. In all these experiments the familiar dispersion [19] from solid-state physics, which is responsible for glass having an index of refraction between 1.5 and 2.0 and gives us visible optics, appears as an important effect in the plasma regime, where it has traditionally been ignored.…”

Searching for plasmas with anomalous dispersion in the soft x-ray regime

“…The average-atom results [13] have been validated against calculations done with the OPAL code [17][18][19]. The OPAL code was developed at the LLNL to compute opacities of low-to mid-Z elements.…”

“…The original experiments in the Al plasmas were done at the Advanced Photon Research Center at JAERI using the 13.9 nm Ni-like Ag laser [4] and at the COMET laser facility at LLNL using the 14.7 nm Ni-like Pd laser [5]. The analysis of all these experiments show that the anomalous dispersion from the resonance lines and absorption edges of the bound electrons have a large contribution to the index of refraction with the opposite sign as the free electrons and this explains how the index of refraction is greater than one in these plasmas [10][11][12][13][14]. Initially, a surprising result of the calculations is that the influence of the bound electrons on the index of refraction extends far from the absorption edges and resonance lines [12].…”

“…By modifying this code [16], we are now able to calculate the index of refraction for a wide range of plasma conditions. To validate the average atom code [13] we compared with calculations done with the more detailed OPAL code [17][18][19].…”