激光腔靶耦合二维辐射输运数值模拟

间接驱动激光聚变过程中,黑腔内物质处于非局域热动平衡(non-LTE)状态,而且辐射传输具有非平衡、各向异性等特点。为了精确描述黑腔辐射场的演化及其与物质的相互作用,最新研制的激光聚变二维总体LARED集成程序,基于non-LTE的多群辐射输运建模,首次实现了激光黑腔靶实验的全过程数值模拟。数值结果表明,辐射输运计算较好地反映了黑腔辐射场均匀性变化,腔壁光斑区与非光斑区X光发射强度比与实验测量值接近,靶丸压缩形状与实验图像定性一致。     

Resonance line transfer and transport of excited atoms—II. Self-consistent solutions (1)

This second part of our study of non-LTE line transfer with convective transport of excited atoms presents self-consistent solutions of the radiative transfer equation and the kinetic equation of the excited two-level atoms, for the limiting case of no elastic velocity-changing collisions of the excited atoms. Pure Doppler broadening of the spectral line is assumed. We investigate reflecting and destroying boundaries for the excited atoms, while the boundary condition for the photons corresponds to free photon escape from the system. Our numerical procedure for solving the two coupled kinetic equations for the excited atoms and the photons is an iterative method using variable Eddington factors, and is described in detail. We present a simple model that considers the gas of excited atoms and the radiation field as two interacting fluids, which yields a straightforward interpretation of the various scale lengths encountered in the numerical results for the hydrodynamic properties (density, flux density, mean velocity) of the gas of excited atoms.     

The effects of gradients on the diagnostic use of spectral features from laser compressed plasmas

The use of spectral features as diagnostics of the plasma temperature and density is studied using a non-LTE radiative transfer model, which solves the coupled statistical equilibrium and radiative transfer equation consistently. The effect of gradients on the hydrodynamic data, i.e. temperature and mass density, is studied to establish the accuracy of the diagnostic procedures.     

Understanding the time dependence of atomic level populations in evolving plasmas

The time dependence of atomic level populations in evolving plasmas is studied using an eigenfunction expansion of the non-LTE rate equations. The work aims to develop understanding without the need for, and as an aid to, numerical solutions. The discussion is mostly limited to linear systems, especially those for optically thin plasmas, but the implicitly non-linear case of non-LTE radiative transfer is briefly discussed. Eigenvalue spectra for typical atomic systems are examined using results compiled by Hearon. Diagonal dominance and sign symmetry of rate matrices show that just one eigenvalue is zero (corresponding to the equilibrium state), that the remaining eigenvalues have negative real parts, and that oscillations, if any, are necessarily damped. Gershgorin's theorems are used to show that many eigenvalues are determined by the radiative lifetimes of certain levels, because of diagonal dominance. With other properties, this demonstrates the existence of both “slow” and “fast” time-scales, where the “slow” evolution is controlled by properties of meta-stable levels. It is shown that, when collisions are present, Rydberg states contribute only “fast” eigenvalues. This justifies use of the quasi-static approximation, in which atoms containing just meta-stable levels can suffice to determine the atomic evolution on time-scales long compared with typical radiative lifetimes. Analytic solutions for two- and three-level atoms are used to examine the basis of earlier intuitive ideas, such as the “ionizing plasma” approximation. The power and limitations of Gershgorin's theorems are examined through examples taken from the solar atmosphere. The methods should help in the planning and interpretation of both experimental and numerical experiments in which atomic evolution is important. While the examples are astrophysical, the methods and results are applicable to plasmas in general.     

A simple new radiative transfer model for simulating the effect of cirrus clouds in the microwave spectral region

The upwelling atmospheric radiation in the millimeter wave spectral range is influenced by the presence of cirrus clouds. A plane parallel radiative transfer model which can take into account the effect of multiple scattering by ice particles in the cirrus has been developed and is used to simulate the brightness temperatures as they would be measured by a satellite instrument. The model uses an iterative procedure to solve the radiative transfer equation. The formulation of the model is such that it can easily be adapted to treat the full specific intensity vector instead of just the scalar total intensity. A convergence test for the model is explained and two cirrus cloud scenarios are simulated. The results illustrate the linearity of microwave radiative transfer for not too strong cirrus clouds in this frequency region.     

Control volume finite element method for radiation

In this paper a new methodology is presented by the authors for the numerical treatment of radiative heat transfer in emitting, absorbing and scattering media. This methodology is based on the utilisation of Control Volume Finite Element Method (CVFEM) and the use, for the first time, of matrix formulation of the discretized Radiative Transfer Equation (RTE). The advantages of the proposed methodology is to avoid problems that confronted when previous techniques are used to predict radiative heat transfer, essentially, in complex geometries and when there is scattering and/or non-black boundaries surfaces. Besides, the new formulation of the discretized RTE presented in this paper makes it possible to solve the algebraic system by direct or iterative numerical methods. The theoretical background of CVFEM and matrix formulation is presented in the text. The proposed technique is applied to different test problems, and the results compared favourably against other published works. Moreover this paper discusses in detail the effects of some radiative parameters, such as optical thickness and walls emissivities on the spatial evolution of the radiant heat flux. The numerical simulation of radiative heat transfer for different cases using the algorithm proposed in this work has shown that the developed computer procedure needs an accurate CPU time and is exempt of any numerical oscillations.     

A rapidly convergent iterative solution of the non-LTE line radiation transfer problem

An iterative scheme has been developed for the solution of the non-LTE line radiation transfer problem. The method uses an approximate operator that is deliberately chosen to be local so that it can be easily extended to multidimensional geometry. The difference between the formal and approximate solutions is used as a driving term for the iterations. In one-dimensional, semiinfinite and free-standing slabs, the technique is found to be very fast, robust, and applicable to a large class of problems.     

Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system

A vector radiative transfer model has been developed for a coupled atmosphere-ocean system. The radiative transfer scheme is based on the discrete ordinate and matrix operator methods. The reflection/transmission matrices and source vectors are obtained for each atmospheric or oceanic layer through the discrete ordinate solution. The vertically inhomogeneous system is constructed using the matrix operator method, which combines the radiative interaction between the layers. This radiative transfer scheme is flexible for a vertically inhomogeneous system including the oceanic layers as well as the ocean surface. Compared with the benchmark results, the computational error attributable to the radiative transfer scheme has been less than 0.1% in the case of eight discrete ordinate directions. Furthermore, increasing the number of discrete ordinate directions has produced computations with higher accuracy. Based on our radiative transfer scheme, simulations of sun glint radiation have been presented for wavelengths of 670 nm and 1.6 μm. Results of simulations have shown reasonable characteristics of the sun glint radiation such as the strongly peaked, but slightly smoothed radiation by the rough ocean surface and depolarization through multiple scattering by the aerosol-loaded atmosphere. The radiative transfer scheme of this paper has been implemented to the numerical model named Pstar as one of the OpenCLASTR/STAR radiative transfer code systems, which are widely applied to many radiative transfer problems, including the polarization effect.     

An approximate analytical solution of the radiative transfer equation in hydrometeors accounting for scattering effects

An iterative method for the radiative transfer equation solution is suggested for the scattering hydrometeors. The method allows to find the layer scattering indicatrix. The method is shown to be more general as compared with the four-flux theory or the perturbation method and differs strongly from these ones because even in the case of the first iteration it gives the results which are very close to ones obtained by numerical methods for all rain scattering angles.     

Radiative transfer equation for graded index medium in cylindrical and spherical coordinate systems

In graded index medium, the ray goes along a curved path determined by Fermat principle, and the curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectory, the methods not based on ray-tracing technique need to be developed for the solution of radiative transfer in graded index medium. For this purpose, in this paper the streaming operator along a curved ray trajectory in original radiative transfer equation for graded index medium is transformed and expressed in spatial and angular ordinates and the radiative transfer equation for graded index medium in cylindrical and spherical coordinate systems are derived. The conservative and the non-conservative forms of radiative transfer equation for three-dimensional graded index medium are given, which can be used as base equations to develop the numerical simulation methods, such as finite volume method, discrete ordinates method, and finite element method, for radiative transfer in graded index medium in cylindrical and spherical coordinate systems.     

Linearization of the interaction principle: Analytic Jacobians in the “Radiant” model

In this paper we present a new linearization of the Radiant radiative transfer model. Radiant uses discrete ordinates for solving the radiative transfer equation in a multiply-scattering anisotropic medium with solar and thermal sources, but employs the adding method (interaction principle) for the stacking of reflection and transmission matrices in a multilayer atmosphere. For the linearization, we show that the entire radiation field is analytically differentiable with respect to any surface or atmospheric parameter for which we require Jacobians (derivatives of the radiance field). Derivatives of the discrete ordinate solutions are based on existing methods developed for the LIDORT radiative transfer models. Linearization of the interaction principle is completely new and constitutes the major theme of the paper. We discuss the application of the Radiant model and its linearization in the Level 2 algorithm for the retrieval of columns of carbon dioxide as the main target of the Orbiting Carbon Observatory (OCO) mission.     

Short characteristic solution of the non-LTE line transfer problem by operator perturbation—I. The one-dimensional planar slab

We present the formal solution of the transfer problem in terms of the exponential short characteristic method and derive approximate operators that allow for the iterative solution of the non-LTE two-level atom problem. An eigenvalue analysis for the convergence rate of these operators and several approximate operators proposed by other authors is presented. The family of operators presented for the short characteristic approach range from local diagonal approximations to tridiagonal and pentadiagonal operators. The extension to multidimensions of the several proposed approximate operators is discussed.     

煤粉炉内弥散介质辐射传热的综合模拟

本文基于辐射传热计算的DT法和颗粒运动计算的随机轨道法,并结合单颗粒的辐射特性模型,构造了能够详细考虑颗粒燃尽、湍流弥散诸因素对炉内空间局部辐射特性及总体辐射传热影响的弥散介质辐射传热计算模型,并将其耦合到炉内过程的总体数值模型中。采用该程序,比较计算了几种颗粒辐射特性模型对某300MW锅炉炉内温度场的预报结果,结果表明：通常采用的均匀颗粒辐射特性模型会导致温度场的极大误差;由于炉内颗粒浓度的不均匀分布,炉内的温度分布呈现高度非均匀状态,在炉膛轴线上有大面积的高温烟气区存在;考虑残炭存在时,温度分布的不均匀性更显著．     

神光Ⅱ间接驱动内爆实验ArX射线谱线模拟研究

ICF内爆物理研究中,示踪元素X射线谱诊断方法是推测内爆压缩温度、 密度以及燃料混合状态的有效方法.针对其中的非平衡物理过程, 研制了非局域热动平衡(non-LTE)下一维谱线输运程序Alpha.程序以辐射流体计算给出的温度、 密度等量为输入条件,求解细致组态(DCA)模型下的原子动力学方程和辐射输运方程, 自洽给出谱线不透明度,和成像面上的X射线谱分布.
利用该程序,模拟了神光Ⅱ装置上的掺Ar靶丸内爆示踪元素X射线谱诊断实验, 研究结果表明,谱线的自吸收效应影响发射的X射线谱的强度和形状, 谱线的宽度对自吸收效应的强弱也有影响.因此,在对X射线谱的数值模拟中应该考虑自吸收效应. 另外,与LTE近似下的发射谱的比较表明, LTE近似下,等离子体电离度大～1, 发射谱的形状与non-LTE的结果不同,且LTE近似下,谱线的强度比non-LTE的谱线强度大5-10倍, 采用LTE近似是不合适的.     

Time-dependent aerodynamic non-LTE radiative transfer

A method is developed for solving simultaneously in one dimension the equation of transfer for non-LTE spectral line radiation and the time-dependent equations specifying conservation of mass, energy and linear momentum. In particular, we illustrate the method on a ‘simple’ time-dependent problem in which a pulsating disturbance at some point in a model homogeneous atmosphere propagates towards the surface and steepens into a shock. The resulting emergent intensities show rather dramatic changes over very small time intervals due to the effect of the velocity, density and temperature distributions on the radiative absorption properties of the gas, and thus emphasises the need to solve the above-mentioned four basic equations if one is to obtain physically realistic model atmospheres experiencing initial disturbances.     

The non-equilibrium Marshak wave problem

An analytic solution to a particular Marshak wave problem is given. The radiative transfer model used is the gray, non-equilibrium diffusion approximation which allows the radiation and material fields to be out of equilibrium. This solution should be useful as a reference problem for validating time-dependent radiative transfer computer codes, as well as investigating the convergence, as a function of space and time step size, for such codes. The coupling of the radiation field to the material field in a multigroup code, a difficult numerical problem, can also be tested against this solution. Typical numerical results are given for surface quantities, integral quantities, and the distribution of radiative energy and material temperature as a function of space and time.     

一维瞬态辐射传输的有限元法模拟

随着超短脉冲激光的快速发展,吸收散射性介质内的瞬态辐射传输引起了人们的广泛关注.本文基于离散坐标法和最小二乘有限元法(LSFEM),提出了模拟多维吸收散射性介质内瞬态辐射传输的数值模型.该模型有效地克服了在标准Galerkin有限元法(GFEM)中发生的伪振荡现象,在时间步长较大的情况下仍然可以得到光滑无振荡的解.而且,最小二乘法产生的求解系数矩阵是对称正定的,与GFEM中的系数矩阵相比,仅需要存储一半的非零系数,可以应用许多高效的迭代求解方法进行求解.为了检验模型,本文研究了一维吸收散射性介质内瞬态辐射传输问题,其结果与蒙特卡洛法(MCM)和积分模型法(IE)的结果进行了比较,结果证实:本文的方法可以精确、高效地模拟参与性介质内的瞬态辐射传输.     

Simultaneous retrieval of aerosols and ocean properties: A classic inverse modeling approach. I. Analytic Jacobians from the linearized CAO-DISORT model

In this paper and the sequel, we investigate the application of classic inverse methods based on iterative least-squares cost-function minimization to the simultaneous retrieval of aerosol and ocean properties from visible and near infrared spectral radiance measurements such as those from the SeaWiFS and MODIS instruments. Radiance measurements at the satellite are simulated directly using an accurate coupled atmosphere-ocean-discrete-ordinate radiative transfer (CAO-DISORT) code as the main component of the forward model. For this kind of cost-function inverse problem, we require the forward model to generate weighting functions (radiance partial derivatives) with respect to the aerosol and marine properties to be retrieved, and to other model parameters which are sources of error in the retrievals.In this paper, we report on the linearization of the CAO-DISORT model. This linearization provides a complete analytic differentiation of the coupled-media radiative transfer theory, and it allows the model to generate analytic weighting functions for any atmospheric or marine parameter. For high solar zenith angles, we give an implementation of the pseudo-spherical (P-S) approach to solar beam attenuation in the atmosphere in the linearized model. We summarize a number of performance enhancements such as the use of an exact single-scattering calculation to improve accuracy. We derive inherent optical property inputs for the linearized CAO-DISORT code for a simple 2-parameter bio-optical model for the marine environment coupled to a 2-parameter bimodal atmospheric aerosol medium.     

一层非球形粒子散射的标量辐射传输迭代解的求逆

给出了一层有下垫反射面的非球形粒子散射的标量辐射传输方程一、二阶迭代解,推导了相函数各阶Legendre展开系数与随机小椭球粒子相函数的对应关系,提出了一层随机小椭球粒子介电常数和单位面积粒子数的迭代反演方法.通过两次各方位角上双站散射测量,反演随机小椭球粒子的介电常数和单位面积粒子数.本方法比现有文献的一些反演方法易于实现,可应用于颗粒性复合材料介电与结构特性以及地表背景参数的反演研究 关键词： 辐射传输方程 迭代解 反演 相函数 介电常数     

Angular quadrature perturbations in radiative transfer theory

A new numerical method is presented for solving the general equation of radiative transfer. The approximation, which replaces the integral term over angle in the transfer equation by a quadrature sum, is studied; an estimate of the error involved is obtained and this error, which may be thought of as a further source or sink of photons (depending upon the sign), can then be used to evaluate a corection to the radiation field originally determined. This process may then be continued as a perturbation series. The method is found to give a final solution, when starting from the Eddington approximation, at least as accurate as that obtained using variable Eddington factors. Furthermore, the technique involves very little extra computing over that required using the Eddington approximation, and may be trivially generalized to any radiative transfer problem. It can also be used in conjunction with any of the existing methods for solving the equation of transfer. Examples are given in the context of spectral line formation in slab geometry.