Effect of nonlocal transport on heat-wave propagation

We present the first direct measurements of spatially and temporally resolved temperature and density profiles produced by nonlocal transport in a laser plasma. Absolutely calibrated measurements have been performed by Rayleigh scattering and by resolving the ion-acoustic wave spectra across the plasma volume with Thomson scattering. We find that the electron temperature and density profiles disagree with flux-limited models, but are consistent with nonlocal transport modeling.     

Time-dependent electron thermal flux inhibition in direct-drive laser implosions

We simulate direct-drive CH target implosions with square laser pulses by a one-dimensional Fokker-Planck solver combined with a hydrodynamic code, and compare the results with those simulated by the flux-limited Spitzer-H?rm model. We find that the electron thermal flux inhibition is time dependent, resulting in longer density scale length, larger laser absorption, and smaller growth of Rayleigh-Taylor instability. The time of peak neutron production calculated from Fokker-Planck simulations agrees with experiments for both 1-ns and 400-ps pulses.     

激光聚变黑腔中等离子体的热流研究

辐射流体采用限流的局域Spitzer-Harm(S-H)电子热流近似,在预估等离子体状态时可能与实验观察存在偏差.利用一维(1D3V)含碰撞的粒子模拟程序,研究了激光聚变黑腔中金等离子体的电子分布函数和电子热流.分析表明,在等离子体的冕区,α=Z(νos/νte)^2>1,电子分布函数表现为超高斯分布(m=3.34),克努森数λe/Le=0.011大于局域S-H理论的临界值2×10^-3.这导致了局域S-H电子热流远大于实际热流.这种实际热流受限现象将导致辐射流体模拟给出的冕区电子温度高于神光实验测量值.而在等离子体的高密度区域,电子分布函数仍表现为超高斯分布(m=2.93),克努森数λe/Le=7.58×10^-4小于局域S-H理论的临界值,限流的局域S-H电子热流具有一定的适用性.但电子热流严重依赖于限流因子,辐射流体模拟需要根据不同位置的光强和电子温度调整的大小.     

Chapman-Enskog-maximum entropy method on time-dependent neutron transport equation

The time-dependent neutron transport equation in semi and infinite medium with linear anisotropic and Rayleigh scattering is proposed. The problem is solved by means of the flux-limited, Chapman-Enskog-maximum entropy for obtaining the solution of the time-dependent neutron transport. The solution gives the neutron distribution density function which is used to compute numerically the radiant energy density E(x,t), net flux F(x,t) and reflectivity R_f. The behaviour of the approximate flux-limited maximum entropy neutron density function are compared with those found by other theories. Numerical calculations for the radiant energy, net flux and reflectivity of the proposed medium are calculated at different time and space.     

The Milne problem in a continuous stochastic planar medium with Gaussian statistics

The Milne problem of radiative transfer in a planar medium, with isotropic scattering is considered. The medium is assumed to be continuous stochastic medium, with fluctuations described as Gaussian field. Pomraning-Eddington method is used to obtain an explicit form for the radiation energy density in the deterministic case. It depends on two random variables, namely the optical space variable and the optical thickness of the medium. The Gaussian joint probability density function of these two random variables is defined and used to find the ensemble-averaged energy density and the linear extrapolation distance. It is shown that the statistical nature of the medium leads to two quite different solutions of the Milne problem. Numerical results are implemented for the sake of clarification.     

激光与金靶耦合中非局域电子热传导的影响

 在一维非平衡辐射流体力学程序中,引入非局域电子热传导公式,对三倍频激光与金平面靶耦合产生等离子体状态进行了数值模拟计算。数值结果与加限流处理的Spitzer-Harm公式计算结果的比较表明,非局域电子热传导能够得到更为合理的数值结果和物理图象。     

On the solution of Fokker-Planck equation for electron transport

Two different techniques have been used to solve the Fokker-Planck equation for electron transport in infinite homogeneous medium namely, maximum entropy and flux-limited approach. The solutions obtained for the scalar flux function φ₀(x,s) by both methods are numerically compared.     

The Pomraning-Eddington approximation to diffusion of light in turbid materials

The source-free diffusion problem of light in turbid media with generalized boundary conditions is considered. The intensity of light is considered as a sum of collimated and diffused radiance. In this way the problem is transformed to a source problem with a collimated source (problem 1). This problem is solved in terms of the corresponding source-free problem of simple boundary conditions (problem 2). The Pomraning-Eddington method is used to solve problem 2. Two coupled first-order differential equations are obtained involving the energy density and the radiation net flux. Weight functions are introduced in order to force the boundary conditions to be fulfilled. Numerical results are given and compared with previous calculations. The calculations show that the accuracy depends on the choice of the weight function.     

Albedo problem for pure-triplet scattering in finite planar media

Pure triplet scattering in neutron transport through a finite plane-parallel medium is considered. Galerkin approximation is introduced to calculate some functionals arising in radiative transfer problems such as reflection and transmission coefficients. Some of numerical results are compared with the results calculated by Pomraning-Eddington Variational method.     

用X射线激光M-Z干涉仪诊断点聚焦CH等离子体电子密度

在神光Ⅱ装置上，用软X射线激光Mach-Zehnder干涉仪诊断了点聚焦CH等离子体电子密度N_e分布，介绍了实验结果. 通过Abel变换进行了密度反演， 给出了N_e的2D分布，测得的最高N_e为3.2×10²¹cm^-3. 通过同1.5维JB19程序以及二维XRL2D程序的模拟结果的比较，发现高密度区，限流因子取0.05的理论结果同实验相符，但是低密度区实验得到的N_e分布下降得更快，而且理论模拟的N_e二维分布同实验结果在细节上有比较大的差别. 粗略的误差分析显示，干涉仪面型误差是实验误差的主要来源. 关键词： 类镍银X射线激光 Mach-Zehnder干涉仪 密度反演 Abel变换     

Time-dependent radiation transfer with Rayleigh scattering in finite slab media

The time-dependent radiation transfer equation in a finite plane geometry with Rayleigh scattering is studied. The traveling wave transformation is used to obtain the corresponding stationary-like equation. Pomraning-Eddington approximation is then used to find the solution. Numerical results for reflectivity at the left boundary and transmissivity from the right boundary are presented at different times. The medium is assumed to have specular-reflecting boundaries with angular-dependent externally incident flux. Two different weight functions are introduced to force the boundary conditions to fulfill.     

Polarized radiation transfer in finite binary Markovian random media

The problem of polarized radiation transfer in a finite plane-parallel binary Markovian random medium is studied. Pomraning-Eddington approximation is used for both the total intensity and the difference function of the polarized radiation. The formalism obtained by Levermore et al. and Pomraning is used to average the obtained solution in the deterministic case. The random medium is assumed to have specular-reflecting boundaries with angular-dependent externally incident flux. Numerical results of the average reflectivity and the average transmissivity are calculated for the different degrees of polarization.     

Stochastic radiative transfer in a finite plane-parallel medium with general boundary conditions

The time-independent radiative transfer problem in a scattering and absorbing planar random medium with general boundary conditions and internal energy source is considered. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two-state homogeneous Markov process. The problem is solved in terms of the solution of the corresponding free-source problem with simple boundary conditions which is solved using Pomraning-Eddington approximation in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. The average partial heat fluxes are calculated in terms of the albedoes of the source-free problem. Results are obtained for isotropic and anisotropic scattering for specular and diffused reflecting boundaries.     

Cepheid distance to the virgo cluster

HST data on Cepheid variables in one Virgo Cluster spiral galaxy is re-analyzed, taking into account flux-limited incompleteness in the sample and calibration of the period-luminosity relation in the relevant period range. Distance to the Virgo Cluster is estimated to be 19.6 ± 1.7 (random) ± 2.6 (systematic) Mpc.     

Albedo problem for finite plane-parallel medium

The problem of radiation transfer through a scattering and absorbing finite plane-parallel medium is solved using an efficient and accurate method of analysis which utilizes trial functions based on Case's eigenvalues plus a linear combination of exponential integral functions. The proposed trial functions are used on the integral equation reducing it to a system of algebraic equations to be solved for the expansion coefficients which are used to calculate some interesting physical quantities such as the angular radiation intensity and the reflection and the transmission coefficients. Numerical results are obtained for two different external incidence on the left boundary, x=0. The results are compared with the exact results and with those calculated by the Pomraning-Eddington variational method.     

Multigrid Solution of the Incompressible Navier–Stokes Equations for Density-Stratified Flow past Three-Dimensional Obstacles

The steady incompressible Navier–Stokes equations in three dimensions are solved for neutral and stably stratified flow past three-dimensional obstacles of increasing spanwise width. The continuous equations are approximated using a finite volume discretisation on staggered grids with a flux-limited monotonic scheme for the advective terms. The discrete equations which arise are solved using a nonlinear multigrid algorithm with up to four grid levels using the SIMPLE pressure correction method as smoother. When at its most effective the multigrid algorithm is demonstrated to yield convergence rates which are independent of the grid density. However, it is found that the asymptotic convergence rate depends on the choice of the limiter used for the advective terms of the density equation, and some commonly used schemes are investigated. The variation with obstacle width of the influence of the stratification on the flow field is described and the results of the three-dimensional computations are compared with those of the corresponding computation of flow over a two-dimensional obstacle (of effectively infinite width). Also given are the results of time-dependent computations for three-dimensional flows under conditions of strong static stability when lee-wave propagation is present and the multigrid algorithm is used to compute the flow at each time step.     

Stochastic radiative transfer in a finite plane with anisotropic scattering in a binary Markovian mixture

The time-independent linear transport problem in a stochastic finite-plane medium with linear anisotropic scattering is considered. The medium is assumed to consist of two randomly mixed immiscible fluids, with the mixing statistics described as a two-state homogeneous Markov process. The Pomraning-Eddington approach is used to obtain an explicit solution to the problem in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution for the problem under consideration. In the case of isotropic scattering, explicit analytic results for reflectivity and transmissivity, which show a good agreement with Monte Carlo benchmark results, are given. Results for reflectivity and transmissivity in the case of linear anisotropic scattering are also given.     

On the solution of time-dependent transport equation with time-varying cross sections

The time-dependent neutron transport equation in an infinite medium with time-varying cross sections has been solved by means of two techniques namely, flux-limited approach and maximum entropy method. The behaviour of the distribution function are shown graphically. Knowing the distribution function allows us to calculate directly some physical parametres of special interest such as the reflection function. The results reported in this article provide further evidence of the usefulness of both maximum entropy and flux limited methods for obtaining time-dependent solution of neutron transport in compact form.     

Positivity-preserving high-resolution schemes for systems of conservation laws

A new class of flux-limited schemes for systems of conservation laws is presented that is both high-resolution and positivity-preserving. The schemes are obtained by extending the Steger–Warming method to second-order accuracy through the use of component-wise TVD flux limiters while ensuring that the coefficients of the discretization equation are positive. A coefficient is considered positive if it has all-positive eigenvalues and has the same eigenvectors as those of the convective flux Jacobian evaluated at the corresponding node. For certain systems of conservation laws, such as the Euler equations for instance, this condition is sufficient to guarantee positivity-preservation. The method proposed is advantaged over previous positivity-preserving flux-limited schemes by being capable to capture with high resolution all wave types (including contact discontinuities, shocks, and expansion fans). Several test cases are considered in which the Euler equations in generalized curvilinear coordinates are solved in 1D, 2D, and 3D. The test cases confirm that the proposed schemes are positivity-preserving while not being significantly more dissipative than the conventional TVD methods. The schemes are written in general matrix form and can be used to solve other systems of conservation laws, as long as they are homogeneous of degree one.