A New High Order Accurate Shock Capture Method with Wave Booster

A new kind of shock capturing method is developed. Before applying the high order accurate traditional scheme which is called as base scheme in this paper the fluid parameters are preconditioned in order to control the group velocity. The newly constructed scheme is high order accurate, simple, has high resolution of the shock, and less computer time consumed.

Impact of difference accuracy on computational properties of vertical grids for a nonhydrostatic model

Starting from nonhydrostatic Boussinesq approximation equations, a general method is introduced to deduce the dispersion relationships. A comparative investigation is performed on inertia-gravity wave with horizontal lengths of 100, 10 and 1 km. These are examined using the second-order central difference scheme and the fourth-order compact difference scheme on vertical grids that are currently available from the perspectives of frequency, horizontal and vertical component of group velocity. These findings are compared to analytical solutions. The obtained results suggest that whether for the second-order central difference scheme or for the fourth-order compact difference scheme, Charny-Phillips and Lorenz ( L) grids are suitable for studying waves at the above-mentioned horizontal scales; the Lorenz time-staggered and Charny-Phillips time staggered (CPTS) grids are applicable only to the horizontal scales of less than 10 km, and N grid ( unstaggered grid) is unsuitable for simulating waves at any horizontal scale. Furthermore, by using fourth-order compact difference scheme with higher difference precision, the errors of frequency and group velocity in horizontal and vertical directions produced on all vertical grids in describing the waves with horizontal lengths of 1, 10 and 100 km cannot inevitably be decreased. So in developing a numerical model, the higher-order finite difference scheme, like fourth-order compact difference scheme, should be avoided as much as possible, typically on L and CPTS grids, since it will not only take many efforts to design program but also make the calculated group velocity in horizontal and vertical directions even worse in accuracy.

青藏高原横波速度与各向异性结构及其壳幔形变印迹

As the most spectacular and youngest case of continental collision on the Earth, to investigate the crust and mantle of Tibetan plateau, and then to reveal its characters of structure and deformation, are most important to understand its deformation mechanism and deep process. A great number of surface wave data were initially collected from events occurred between 1980 and 2002, which were recorded by 13 broadband digital stations in Eurasia and India. Up to 1,525 source-station Rayleigh waveforms and 1,464 Love wave trains were analysed to obtain group velocity dispersions, accompanying with the detail and quantitative assessment of the fitness of the classic Ray Theory, errors from focal and measurements. Assuming the model region covered by a mesh of 2ox2o-sized grid-cells, we have used the damped least-squares approach and the SVD to carry out tomographic inversion, SV- and SH-wave velocity images of the crust and upper mantle beneath the Tibetan Plateau and surroundings are obtained, and then the radial anisotropy is computed from the Love-Rayleigh discrepancy. The main results demonstrate that follows, a) The Moho beneath the Tibetan Plateau presents an undulating shape that lies between 65 and 74 km, and a clear correlation between the elevations of the plateau and the Moho topography suggests that at least a great part of the highly raised plateau is isostatically compensated. b) The lithospheric root presents a depth that can be substantiated at ~140 km (Qiangtang Block) and exceptionally at ~180 km (Lhasa Block), and exhibits laterally varying fast velocity between 4.6 and 4.7 km/s, even ~4.8 km/s under northern Lhasa Block and Qiangtang Block, which may be correlated with the presence of a shield-like upper mantle beneath the Tibetan Plateau and therefore looked as one of the geophysical tests confirming the underthrusting of India, whose leading edge might have exceeded the Bangong-Nujiang Suture, even the Jinsha Suture. c) The asthenosphere is depicted by a low velocity channel at depths between 140 and 220 km with negative velocity gradient and velocities as low as 4.2 km/s; d) Areas in which transverse radial anisotropy is in excess of ~4% and 6% on the average anisotropy are found in the crust and upper mantle underlying most of the Plateau, and up to 8% in some places. The strength, spatial configuration and sign of radial anisotropy seem to indicate the existence of a regime of horizontal compressive forces in the frame of the convergent orogen at the same time that laterally varying lithospheric rheology and a differential movement as regards the compressive driving forces. e) Slow-velocity anomalies of 12% or more in southern Tibet and the eastern edge of the Plateau support the idea of a mechanically weak middle-to-lower crust and the existence of crustal flow in Tibet.

旋转轴对称弱各向异性介质模型的射线追踪方法

Ray tracing is a rapid and effective method for wave field calculation. Not only in the field of seismic-wave theory, but also in the field of seismic inversion and migration imaging,the seismic ray tracing method has become one of the most important methods. In anisotropic media, group velocity and phase velocity have different propagation directions. The seismic wave propagates along the direction of group velocity , it does not depend on the direction of phase velocity. Ray angle is a complex function with respect to phase angle, it is difficult to measure and calculate. But most rocks are weak anisotropic, so the expression of phase velocity can be simplified greatly. Based on the approximate expression of phase velocity this thesis for rotating axisymmetric weak anisotropic media deduces an expression of the partial derivative of phase velocity and an expression of group velocity with the method of linear approximation. This paper uses the fourth order Runge-Kutta method together with the two-dimensional interpolation and linear interpolation to obtain the parameters of the physical locations. At last the paths of seismic wave in rotating axisymmetric weak anisotropic media are computed. According to the analysis of the computational results, it indicates that the method developed in this paper has strong adaptability, high computational efficiency and high accuracy for rotating axisymmetric weak anisotropic media.

A review of X-ray laser development at Rutherford Appleton Laboratory

Recent experiments undertaken at the Rutherford Appleton Laboratory to produce X-ray lasing over the 5-30 nm wavelength range are reviewed. The efficiency of lasing is optimized when the main pumping pulse interacts with a preformed plasma. Experiments using double 75-ps pulses and picosecond pulses superimposed on 300-ps background pulses are described. The use of travelling wave pumping with the approximately picosecond pulse experiments is necessary as the gain duration becomes comparable to the time for the X-ray laser pulse to propagate along the target length. Results from a model taking account of laser saturation and deviations from the speed of light c of the travelling wave and X-ray laser group velocity are presented. We show that X-ray laser pulses as short as 2-3 ps can be produced with optical pumping pulses of approximate to1-ps.

Rising time of entanglement between scattering spins

We investigate the time evolution of entanglement in a process where a mobile particle is scattered by static spins. We show that entanglement increases monotonically during a transient and then saturates to a steady-state value. For a quasimonochromatic mobile particle, the transient time depends only on the group velocity and width of the incoming wave packet and is insensitive to the interaction strength and spin number of the scattering particles. These features do not depend on the interaction model and can be seen in various physical settings.

Electromagnetic beam profile dynamics in collisional plasmas

The compression of a finite extent Gaussian laser pulse in collisional plasma is investigated. An analytical model is employed to describe the spatiotemporal evolution of a laser pulse propagating through the plasma medium. The pulse geometry is modeled via an appropriate ansatz which takes into account both beam radius (in space) and pulse width (in time). Compression and self-focusing are taken into account via appropriated group velocity dispersion and nonlinearity terms. The competition among the collisional nonlinearity in the plasma and the effect of divergence due to diffraction is pointed out and investigated numerically. Our results suggest that laser pulse compression and intensity localization is enhanced by plasma collisionality. In specific, a pulse width compression by an order of magnitude approximately is observed, for typical collisional laser plasma parameters, along with a significant increase in the intensity.

Modulational instability and localized excitations involving two nonlinearly coupled upper-hybrid waves in plasmas

The nonlinear coupling between two perpendicularly propagating ( with respect to the external magnetic field direction) upper-hybrid ( UH) waves in a uniform magnetoplasma is considered, taking into account quasi-stationary density perturbations which are driven by the UH wave ponderomotive force. This interaction is governed by a pair of coupled nonlinear Schrodinger equations ( CNLSEs) for the UH wave envelopes. The CNLSEs are used to investigate the occurrence of modulational instability. Waves in the vicinity of the UH resonance are considered, so that the group dispersion terms for both waves are approximately equal, but the UH wave group velocities may be different. It is found that a pair of unstable UH waves ( obeying anomalous group dispersion) yields an increased instability growth rate, while a pair of stable UH waves ( individually obeying normal group dispersion) remains stable for equal group velocities, although it is destabilized by a finite group velocity mismatch. Stationary nonlinear solutions of the CNLSEs are presented.

Stability of dust lattice modes in the presence of charged dust grain polarization in plasmas

We discuss the effect of the attractive force associated with overlapping Debye spheres on the dispersion properties of the longitudinal and transverse dust lattice waves in strongly coupled dust crystals. The dust grain attraction is shown to contribute to a destabilization of the longitudinal dust lattice oscillations. The (optic-like) transverse mode dispersion law is shown to change. due to the Debye sphere dressing effect, from the known inverse-dispersive ("backward wave") form into a normal dispersive law (i.e. the group velocity changes sign). The stability of one-dimensionless bi-layers, consisting of (alternating) negatively and positively charged dust particles, is also discussed. The range of parameter values (mainly in terms of the lattice parameter kappa) where the above predictions are valid, are presented. (c) 2005 Elsevier B.V. All rights reserved.

Nonlinearly modulated dust lattice wave packets in two-dimensional hexagonal dust crystals

The amplitude modulation of dust lattice waves (DLWs) propagating in a two-dimensional hexagonal dust crystal is investigated in a continuum approximation, accounting for the effect of dust charge polarization (dressed interactions). A dusty plasma crystalline configuration with constant dust grain charge and mass is considered. The dispersion relation and the group velocity for DLWs are determined for wave propagation in both longitudinal and transverse directions. The reductive perturbation method is used to derive a (2+1)-dimensional nonlinear Schrodinger equation (NLSE). New expressions for the coefficients of the NLSE are derived and compared, for a Yukawa-type potential energy and for a

Evolution of linearly polarized electromagnetic pulses in laser plasmas

An analytical and numerical investigation is presented of the behavior of a linearly polarized electromagnetic pulse as it propagates through a plasma. Considering a weakly relativistic regime, the system of one-dimensional fluid-Maxwell equations is reduced to a generalized nonlinear Schrodinger type equation, which is solved numerically using a split step Fourier method. The spatio-temporal evolution of an electromagnetic pulse is investigated. The evolution of the envelope amplitude of density harmonics is also studied. An electromagnetic pulse propagating through the plasma tends to broaden due to dispersion, while the nonlinear frequency shift is observed to slow down the pulse at a speed lower than the group velocity. Such nonlinear effects are more important for higher density plasmas. The pulse broadening factor is calculated numerically, and is shown to be related to the background plasma density. In particular, the broadening effect appears to be stronger for dense plasmas. The relation to existing results on electromagnetic pulses in laser plasmas is discussed. (c) 2008 American Institute of Physics.

High contrast plasma mirror: spatial filtering and second harmonic generation at 10(19)Wcm(-2)

Recently, the use of plasma optics to improve temporal pulse contrast has had a remarkable impact on the field of high- power laser-solid density interaction physics. Opening an avenue to previously unachievable plasma density gradients in the high intensity focus, this advance has enabled researchers to investigate new regimes of harmonic generation and ion acceleration. Until now, however, plasma optics for fundamental laser reflection have been used in the sub-relativistic intensity regime (10(15) - 10(16)Wcm(-2)) showing high reflectivity (similar to 70%) and good focusability. Therefore, the question remains as to whether plasma optics can be used for such applications in the relativistic intensity regime (> 10(18)Wcm(-2)). Previous studies of plasma mirrors (PMs) indicate that, for 40 fs laser pulses, the reflectivity fluctuates by an order of magnitude and that focusability of the beam is lost as the intensity is increased above 5 x 10(16)Wcm(-2). However, these experiments were performed using laser pulses with a contrast ratio of similar to 10(7) to generate the reflecting surface. Here, we present results for PM operation using high contrast laser pulses resulting in a new regime of operation - the high contrast plasma mirror (HCPM). In this regime, pulses with contrast ratio > 10(10) are used to form the PM surface at > 10(19)Wcm(-2), displaying excellent spatial filtering, reflected near- field beam profile of the fundamental beam and reflectivities of 60 +/- 5%. Efficient second harmonic generation is also observed with exceptional beam quality suggesting that this may be a route to achieving the highest focusable harmonic intensities. Plasma optics therefore offer the opportunity to manipulate ultra-intense laser beams both spatially and temporally. They also allow for ultrafast frequency up-shifting without detrimental effects due to group velocity dispersion (GVD) or reduced focusability which frequently occur when nonlinear crystals are used for frequency conversion.

Modulational instability in asymmetric coupled wave functions

The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schrödinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and the group velocity dispersion terms) and the nonlinearity and coupling coefficients, on which no assumption is made. A generalized dispersion relation is obtained, relating the frequency and wave-number of a small perturbation around a coupled monochromatic (Stokes') wave solution. Explicitly stability criteria are obtained. The analysis reveals a number of possibilities. Two (individually) stable systems may be destabilized due to coupling. Unstable systems may, when coupled, present an enhanced instability growth rate, for an extended wave number range of values. Distinct unstable wavenumber windows may arise simultaneously.

High-energy monoenergetic proton beams from two stage acceleration with a slow laser pulse

We present a new regime to generate high-energy quasimonoenergetic proton beams in a "slow-pulse" regime, where the laser group velocity vg<c is reduced by an extended near-critical density plasma. In this regime, for properly matched laser intensity and group velocity, ions initially accelerated by the light sail (LS) mode can be further trapped and reflected by the snowplough potential generated by the laser in the near-critical density plasma. These two acceleration stages are connected by the onset of Rayleigh-Taylor-like (RT) instability. The usual ion energy spectrum broadening by RT instability is controlled and high quality proton beams can be generated. It is shown by multidimensional particle-in-cell simulation that quasimonoenergetic proton beams with energy up to hundreds of MeV can be generated at laser intensities of 1021W/cm².

Comprehensive numerical modelling of the performance of a second harmonic generation stage coupled with a low-gain optical parametric amplifier

We present a comprehensive model for predicting the full performance of a second harmonic generation-optical parametric amplification system that aims at enhancing the temporal contrast of laser pulses. The model simultaneously takes into account all the main parameters at play in the system such as the group velocity mismatch, the beam divergence, the spectral content, the pump depletion, and the length of the nonlinear crystals. We monitor the influence of the initial parameters of the input pulse and the interdependence of the two related non-linear processes on the performance of the system and show its optimum configuration. The influence of the initial beam divergence on the spectral and the temporal characteristics of the generated pulse is discussed. In addition, we show that using a crystal slightly longer than the optimum length and introducing small delay between the seed and the pump ensures maximum efficiency and compensates for the spectral shift in the optical parametric amplification stage in case of chirped input pulse. As an example, calculations for bandwidth transform limited and chirped pulses of sub-picosecond duration in beta barium borate crystal are presented.