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 T, 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.
The preliminary experimental results of Z-pinch dynamic hohlraums conducted on the Primary Test Stand (PTS) facility are presented herein. Six different types of dynamic hohlraums were used in order to study the influence of load parameters on radiation characteristics and implosion dynamics, including dynamic hohlraums driven by single and nested arrays with different array parameters and different foams. The PTS facility can deliver a current of 6–8 MA in the peak current and 60–70 ns in the 10%–90% rising time to dynamic hohlraum loads. A set of diagnostics monitor the implosion dynamics of plasmas, the evolution of shock waves in the foam and the axial/radial X-ray radiation, giving the key parameters characterizing the features of dynamic hohlraums, such as the trajectory and related velocity of shock waves, radiation temperature, and so on. The experimental results presented here put our future study on Z-pinch dynamic hohlraums on the PTS facility on a firm basis.
A theoretical model of Z-pinch driven magneto-Rayleigh-Taylor instability is proposed based on the particle drift point of view, which can explain the helical instability structure observed in premagnetized imploding liner experiments. It is demonstrated that all possible drift motions, including polarization drift, gradient drift, and curvature drift, which can lead to charge separations, each will attribute to an effective gravity acceleration. Theoretical predictions given by this model are dramatically different from those given by previous theories which have been readily recovered in the theory presented here as a limiting case. The theory shows qualitative agreement with available experimental data of the pitch angle and provides certain predictions to be verified.
Particular attention was placed on observations of dynamic properties of the azimuthally correlated structures of axial instability of wire-array Z pinches, which were conducted at 10-MA (for short circuit load) pulsed power generator-the Primary Test Stand facility. Not well fabricated loads, which were expected to preset bubble or spike in plasma, were used to degrade the implosion symmetry in order to magnify the phenomenon of instability. The side-view sequence of evolution of correlation given by laser shadowgraphy clearly demonstrates the dynamic processes of azimuthal correlation of the bubble and spike. A possible mechanism presented here suggests that it is the substantial current redistribution especially in regions surrounding the bubble/spike resulting from change of inductance due to the presence of the bubble/spike that plays an essential part in establishment of azimuthal correlation of wire array and liner Z pinches.
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