Monte Carlo simulation of an anharmonic Debye-Waller factor to the T4 order.

In an increasing number of cases the harmonic approximation is incommensurate with the quality of Bragg diffraction data, while results of the anharmonic Debye-Waller factor are not typically available. This paper presents a Monte Carlo computation of a Taylor expansion of an anharmonic Debye-Waller factor with respect to temperature up to the fourth order, where the lattice was a face-centred cubic lattice and the atomic interaction was described by the Lennard-Jones potential. The anharmonic Debye-Waller factor was interpreted in terms of cumulants. The results revealed three significant points. Firstly, the leading term of anharmonicity had a negative contribution to the Debye-Waller factor, which was confirmed by Green's function method. Secondly, the fourth-order cumulants indicated a non-spherical probability density function. Thirdly, up to the melting point of two different densities, the cumulants up to the fourth order were well fitted by the Taylor expansion up to T4, which suggested that the Debye-Waller factor may be calculated by perturbation expansion up to the corresponding terms. In conclusion, Monte Carlo simulation is a useful approach for calculating the Debye-Waller factor.

Diagnosing x-ray power and energy of tungsten wire array z-pinch with a flat spectral response x-ray diode.

Fast z-pinch is a very efficient way of converting electromagnetic energy to radiation. With an 8-10 MA current on primary test stand facility, about 1 MJ electromagnetic energy is delivered to vacuum chamber, which heats z-pinch plasma to radiate soft x-ray. To develop a pulsed high power x-ray source, we studied the applicability of diagnosing x-ray power from tungsten wire array z-pinch with a flat spectral response x-ray diode (FSR-XRD). The detector was originally developed to diagnose radiation of a hohlraum in SG-III prototype laser facility. It utilized a gold cathode XRD and a specially configured compound gold filter to yield a nearly flat spectral response in photon energy range of 0.1-4 keV. In practice, it was critical to avoid surface contamination of gold cathode. It is illustrated that an exposure of an XRD to multiple shots caused a significant change of response. Thus, in diagnosing x-ray power and energy, we used each XRD in only one shot after calibration. In a shot serial, output of FSR-XRD was compared with output of a nickel bolometer. In these shots, the outputs agreed with each other within their uncertainties which were about 12% for FSR-XRD and about 15% for bolometer. Moreover, the ratios between the FSR-XRD and the bolometer among different shots were explored. In 8 shots, the standard deviation of the ratio was 6%. It is comparable to XRD response change of 7%.