Aleksei I. Shestakov

Design and modeling of ignition targets for the National Ignition Facility

Several targets are described that in simulations give yields of 1–30 MJ when indirectly driven by 0.9–2 MJ of 0.35 μm laser light. The article describes the targets, the modeling that was used to design them, and the modeling done to set specifications for the laser system in the proposed National Ignition Facility. Capsules with beryllium or polystyrene ablators are enclosed in gold hohlraums. All the designs utilize a cryogenic fuel layer; it is very difficult to achieve ignition at this scale with a noncryogenic capsule. It is necessary to use multiple bands of illumination in the hohlraum to achieve sufficiently uniform x‐ray irradiation, and to use a low‐Z gas fill in the hohlraum to reduce filling of the hohlraum with gold plasma. Critical issues are hohlraum design and optimization, Rayleigh–Taylor instability modeling, and laser–plasma interactions.

Solution of the diffusion equation by finite elements in hydrodynamic codes

Abstract The radiation diffusion equation is solved by the finite element method. The energy densities are point centered. These are integrated into a program architecture which requires zonally averaged quantities. Numerical results are presented which compare the scheme with existing finite difference techniques for zonal variables. Finite elements give better results for transport dominated problems on non-orthogonal meshes such as might be generated by Lagrangian hydrodynamic distortions.

Thinshell symmetry surrogates for the National Ignition Facility: A rocket equation analysis

Several techniques for inferring the degree of flux symmetry in indirectly driven cylindrical hohlraums have been developed over the past several years for eventual application to the National Ignition Facility (NIF) [Paisner et al., Laser Focus World 30, 75 (1994)]. These methods use various ignition capsule surrogates, including non-cryogenic imploded capsules [Hauer et al., Phys. Plasmas 2, 2488 (1995)], backlit aerogel foamballs [Amendt et al., Rev. Sci. Instrum. 66, 785 (1995)], reemission balls [Delamater, Magelssen, and Hauer, Phys. Rev. E 53, 5240 (1996)], and backlit thinshells [Pollaine et al., Phys. Plasmas 8, 2357 (2001)]. Recent attention has focussed on the backlit thinshells as a promising means for detecting higher-order Legendre flux asymmetries, e.g., P6 and P8, which are predicted to be important sources of target performance degradation on the NIF for levels greater than 1% [Haan et al., Phys. Plasmas 2, 2490 (1995)]. A key property of backlit thinshells is the strong amplification of modal flux asymmetry imprinting with shell convergence. A simple single-parameter analytic description based on a rocket model is presented which explores the degree of linearity of the shell response to an imposed flux asymmetry. Convergence and mass ablation effects introduce a modest level of nonlinearity in the shell response. The effect of target fabrication irregularities on shell distortion is assessed with the rocket model and particular sensitivity to shell thickness variations is shown. The model can be used to relate an observed or simulated backlit implosion trajectory to an ablation pressure asymmetry history. Ascertaining this history is an important element for readily establishing the degree of surrogacy of a symmetry target for a NIF ignition capsule.

Evaluation of integrals of the Compton scattering cross-section

Abstract Exact formulae are derived for various integrals of the Compton scattering cross-section. The interaction kernel is integrated over outgoing photon frequency and direction, and over a relativistic Maxwellian distribution for the electrons. The total Compton cross-section, the energy exchange rate, and the transport mean free path are thereby expressed in terms of single integrals of analytic functions. In addition, these integrals produce simple analytic expressions in the limiting cases of either small or large frequency or electron temperature. A numerical method based on Gaussian quadrature is used to compute the transport mean free path. A comparison with previously published results is presented.

Diffusion coefficient for the Compton Fokker-Planck equation☆

Abstract An exact analytical formula for the diffusion coefficient of the Compton Fokker-Planck equation is derived. The formula is valid for arbitrary values of the electron temperature and photon energy. For applications in production-level radiation transport codes, a fast numerical method to compute the coefficient is presented.

Derivation and solution of multifrequency radiation diffusion equations for homogeneous refractive lossy media

Starting from the radiation transport equation for homogeneous, refractive lossy media, we derive the corresponding time-dependent multifrequency diffusion equations. Zeroth and first moments of the transport equation couple the energy density, flux and pressure tensor. The system is closed by neglecting the temporal derivative of the flux and replacing the pressure tensor by its diagonal analogue. The radiation equations are coupled to a diffusion equation for the matter temperature. We are interested in modeling heating and cooling of silica (SiO2), at possibly rapid rates. Hence, in contrast to related work, we retain the temporal derivative of the radiation field. We derive boundary conditions at a planar air-silica interface taking account of reflectivities obtained from the Fresnel relations that include absorption. The spectral dimension is discretized into a finite number of intervals leading to a system of multigroup diffusion equations. Three simulations are presented. One models cooling of a silica slab, initially at 2500K, for 10s. The other two are 1D and 2D simulations of irradiating silica with a CO2 laser, λ=10.59µm. In 2D, a laser beam (Gaussian profile, r0=0.5mm for 1/e decay) shines on a disk (radius=0.4, thickness=0.4cm).

Application of the implicit Fourier-expansion method to the calculation of three-dimensional equilibria by the iterative method

The iterative method of finding solutions to three-dimensional equilibria is discussed. The implicit Fourier-expansion method is briefly described and applied to the linear problems arising in the iterative loops. The paper shows how to efficiently solve for the magnetic field induced by the plasma.

A numerical model for nonaxisymmetric MHD instabilities

Abstract A method is described for studying the stability of two-dimensional equilibria of magnetically confined plasmas. The equations of magnetohydrodynamics (MHD) are linearized and the resulting time-dependent first-order system of equations is solved. Unstable equilibria result in exponentially growing solutions. The plasma is assumed to be incompressible and resistivity is included in the model. The equations are solved in cylindrical coordinates and the perturbations vary as f 1 ( r , z , t )exp( inτ ). Nonaxisymmetric modes ( n ≠0) are considered. Tearing mode results for one-dimensional analytic equilibria are compared with earlier work. A numerically generated equilibrium, modeling the field reversed theta pinch experiment, is shown to be unstable to the n =1 tilting mode.

The role of radiation transport in the thermal response of semitransparent materials to localized laser heating

Lasers are widely used to modify the internal structure of semitransparent materials for a wide variety of applications, including waveguide fabrication and laser glass damage healing. The gray diffusion approximation used in past models to describe radiation cooling is not adequate for these materials, particularly near the heated surface layer. In this paper we describe a computational model based upon solving the radiation transport equation in 1D by the Pn method with ∼500 photon energy bands, and by multi-group radiation diffusion in 2D with fourteen photon energy bands. The model accounts for the temperature-dependent absorption of infrared laser light and subsequent redistribution of the deposited heat by both radiation and conductive transport. We present representative results for fused silica irradiated with 2–12 W of 4.6 or 10.6 µm laser light for 5–10 s pulse durations in a 1 mm spot, which is small compared to the diameter and thickness of the silica slab. We show that, unlike the case for bu...

Fluid simulations of nonlocal dissipative drift‐wave turbulence

A two‐dimensional [2d(x,y)] fluid code has been developed to explore nonlocal dissipative drift‐wave turbulence and anomalous transport. In order to obtain steady‐state turbulence, the y‐averaged fluctuating density 〈n〉 has been forced to be zero in simulations, thus the difficulty of choosing proper sources and sinks in turbulence simulation codes has been avoided. If Ln≫Lc or Lαlc≫Lc, where Ln is the density gradient scale length, Lc the turbulence correlation length Lc, and Lαlc the adiabaticity‐layer width, it has been shown that ‘‘local’’ turbulence simulations give reasonable results. However, for Ln∼Lc, or Lαlc∼Lc ‘‘local’’ turbulence codes are found to overestimate the flux. For a family of hyperbolic tangent background density profiles, n0(x)=nm−n1 tanh[(2x−Lx)/2Δn] with n1<0.5nm, it has been demonstrated that the nonlocality of the turbulence leads to a transition from local gyro‐Bohm (Dlocal≂7.6(Te/eB)[ρs/Ln(x)] [αlc(x)/0.01]−1/3), where αlc(x)=α(x)/κ(x)<1, to nonlocal gyro‐Bohm transport scali...