Plasma interferometry and how the bound electron contribution can bend fringes in unexpected ways Page: 4 of 22

                                
2

Introduction
Optical interferometers have been used for many decades to measure the electron density
of plasmas [1]. The basic assumption in the data analysis is that the index of refraction of a
plasma can be calculated from the free electron density [1-2]. This implies that the number of
fringe shifts in the interferometer is directly proportional to the electron density of the plasma.
This also makes the index of refraction in the plasma less than one. When X-ray lasers became
available, the same assumptions were used as the interferometer was extended to shorter
wavelengths in order to probe even higher density plasmas. The first X-ray laser interferometer
[3] was demonstrated about 10 years ago using the 15.5 nm Ne-like Y laser at the NOVA facility
at Lawrence Livermore National Laboratory (LLNL). Since then, many X-ray laser
interferometers [4-6], as well as a high order harmonic interferometer [7], have been used in the
wavelength range of 14 to 72 nm. This covers photon energies from 17 to 89 eV.
Experiments recently conducted 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] observed anomalous behavior of fringe lines in interferometer experiments of Al
plasmas where the fringe lines bent in the opposite direction than was expected, indicating the
index of refraction was greater than one. Analysis of the COMET experiments showed that the
bound electrons have a large contribution to the index of refraction with the opposite sign of the
free electrons and explains how the index of refraction is greater than one in some Al plasmas
[8].
The original analysis [8] of the index of refraction in partially ionized Al plasmas was
done only for a single wavelength, 14.7 nm, which is the wavelength of the Ni-like Pd X-ray
laser used in experiments at LLNL [5]. It was done by combining individual calculations of the
photo-ionization cross-section and the dipole allowed lines for each ionization stage of Al. That
analysis assumed all the population was in the ground state of each ionization stage and there
was no distribution of excited states. The analysis adjusted the theoretical calculations so the