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

Abstract

Over the last decade the electron density of plasmas has been measured using X-ray laser interferometers in the 14 to 47 nm wavelength regime. With the same formula used in decades of experiments with optical interferometers, the data analysis assumes the index of refraction is due only to the free electrons, which makes the index less than one. Over the last several years, interferometer experiments in C, Al, Ag, and Sn plasmas have observed plasmas with index of refraction greater than one at 14 or 47 nm and demonstrated unequivocally that the usual formula for calculating the index of refraction is not always valid as the contribution from bound electrons can dominate the free electrons in certain cases. In this paper we search for other materials with strong anomalous dispersion that could be used in X-ray laser interferometer experiments to help understand this phenomena. An average atom code is used to calculate the plasma properties. This paper discusses the calculations of anomalous dispersion in Ne and Na plasmas near 47 nm and Xe plasmas near 14 nm. With the advent of the FLASH X-ray free electron laser in Germany and the LCLS X-FEL coming online at Stanford in 2 years the average atom code will be an invaluable tool to explore plasmas at higher X-ray energy to identify potential experiments for the future. During the next decade X-ray free electron lasers and other X-ray sources will be used 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.

Ultrafast X-Ray Scattering of Xenon Nanoparticles: Imaging Transient States of Matter

“…Cluster-specific effects increasing the charge states on the cluster surface have been theoretically proposed [20] but could not yet experimentally be verified due to a lack of suitable and fast enough measurement techniques. Similarly, the plasma environment can lead to anomalous dispersion and a strong enhancement of absorption [21].…”

Ionization and Plasma Dynamics of Single Large Xenon Clusters in Superintense XUV Pulses

“…A strong screening gradient resulting from the radial density distribution of the quasifree electrons falls together with the radial distribution of Xe 3+ . For this charge state, strong oscillations of the real part of the refractive index close to the excitation energy have been reported [159]. Both effects in combination might transform the strong oscillations of n within a short energy range into spatial oscillations of the real part of the refractive index.…”

“…This indicates that also the bound electrons make a contribution to the real part of the refractive index which further decreases n . The atomic scattering factor f 1 for the example of Xe 3+ [159], displayed in Fig. 4.36, can give a striking example.…”

“…2.11d in chapter 2.2.2. By using the Kramers-Kronig relations, f 1 was calculated by Nilsen [159]. A pronounced oscillatory structure with excitation energy can be observed in Fig.…”

“…In plasma physics where mostly low density plasmas are investigated, the standard method to determine the electron density is to measure the phase shift of light propagating through the plasma [159].…”