Modeling of the oscillating field effects on the Heβ line emission in short pulse laser-produced plasmas

Strong oscillating fields may induce strong modifications of the emission spectra of ions. We discuss here the possibility of observing such effects in actual laser experiments where space- and time-integration effects can easily mask their existence. Focusing on the Al He_β transition, we first discuss the calculation of its spectral broadening in the presence of a strong laser field. Then, starting from 1D hydro-simulations of short, intense, laser pulse-produced plasmas that provide the density, temperature and laser intensity profiles as a function of time, full integrated collisional-radiative calculations of the laser field-dependent emissivity of the Al He_β line, are presented.     

Investigation of the influence of inner-shell photoionization and photoexcitation on the Heα spectrum in photoionized plasmas

The present paper investigates the influence of inner shell photoionization and photoexcitation on the He_α, i.e., the 1s² to 1s2p transition in He-like ions, and the associated satellite spectra in photoionized plasmas. A comparison of the importance of these processes is made relative to other atomic processes as a function of the electron temperature and irradiation conditions. For the formation of the He_α and the satellite spectra, the K-shell photoionization is found to have significant contribution under low radiation temperature and/or intensity, when lithium- and beryllium-like ions have high abundance, but highly ionized H-like ions are rare.     

Crack size and speed interaction characteristics at micro-, meso- and macro-scale

The motivation to examine physical events at even smaller size scale arises from the development of use-specific materials where information transfer from one micro- or macro-element to another could be pre-assigned. There is the growing belief that the cumulated macroscopic experiences could be related to those at the lower size scales. Otherwise, there serves little purpose to examine material behavior at the different scale levels. Size scale, however, is intimately associated with time, not to mention temperature. As the size and time scales are shifted, different physical events may be identified. Dislocations with the movements of atoms, shear and rotation of clusters of molecules with inhomogeneity of polycrystals; and yielding/fracture with bulk properties of continuum specimens. Piecemeal results at the different scale levels are vulnerable to the possibility that they may be incompatible. The attention should therefore be focused on a single formulation that has the characteristics of multiscaling in size and time. The fact that the task may be overwhelmingly difficult cannot be used as an excuse for ignoring the fundamental aspects of the problem.Local nonlinearity is smeared into a small zone ahead of the crack. A “restrain stress” is introduced to also account for cracking at the meso-scale.The major emphasis is placed on developing a model that could exhibit the evolution characteristics of change in cracking behavior due to size and speed. Material inhomogeneity is assumed to favor self-similar crack growth although this may not always be the case. For relatively high restrain stress, the possible nucleation of micro-, meso- and macro-crack can be distinguished near the crack tip region. This distinction quickly disappears after a small distance after which scaling is no longer possible. This character prevails for Mode I and II cracking at different speeds. Special efforts are made to confine discussions within the framework of assumed conditions. To be kept in mind are the words of Isaac Newton in the Fourth Regula Philosophandi:

“Men are often led into error by the love of simplicity which disposes us to reduce things to few principles, and to conceive a greater simplicity in nature than there really is … We may learn something of the way in which nature operates from fact and observation; but if we conclude that it operates in such a manner, only because to our understanding that operates to be the best and simplest manner, we shall always go wrong.”––Isaac Newton

Understanding the Piche evaporimeter as a simple integrating mass transfer meter

Results are presented of a comparison of measured and calculated evaporation rates of the Piche evaporimeter under indoor and outdoor (within a meteorological screen) conditions. In both cases, application of mass transfer formulae in use for horizontal (turbulent) flow to the evaporating blotting paper of the instrument yield very good results under pure forced convection conditions. For mixed convection regimes, comparisons using either pure free (combined heat and mass transfer) or pure forced convection equations give as expected too low calculated values. Reasons for such differences with measured values are reviewed. Our forced convection results confirm that main stream turbulence is only of influence on mass transfer to a zero incidence flow in combination with pressure gradient (bluff body) effects, which under our conditions appear to be absent around the Piche surfaces. The same results prove absence of any influence of the particular temperature distribution over the blotting paper on the mass transfer. The understanding and importance of these conclusions in relation to the use of the Piche evaporimeter as a simple integrating mass transfer meter under actual farming conditions are discussed. The importance to obtain such mass transfer data is explained in the introduction.Nomenclature A Numerical constant in free convection Sherwood number - Coefficient of thermal expansion (K^–1) - C _{(s, b)} Water vapour concentration average at the evaporating surface (s) and in the bulk air (b) (g m^–3) - D Coefficient of molecular diffusion of water vapour in air (m² s^–1) - d Characteristic dimension of the paper disc in the direction of flow (m) - E _{(c, m)} Evaporation rates of the Piche evaporimeter, calculated (c) and measured (m) (units in text) - e _{(s, b)} Partial water vapour pressure average at the evaporating surface (s) and in the bulk air (b) (mbar) - Gr Grashof number - g Acceleration of gravity (m s^–2) - m Number of measuring periods - n Numerical constant in free convection Sherwood number - Coefficient of kinematic viscosity of air (m² s^–1) - P Atmospheric pressure (mbar) - Re Reynolds number - _{(s, b)} Air density average at the evaporating surface (s) and of the bulk air (b) (g m^–3) - Sh Sherwood number - T _{(s, b)} Temperature average of the evaporating surface (s) and in the bulk air (b) (K) - T _{(vs, vb)} Virtual temperature average at the evaporating surface (s) and in the bulk air (b) (K) - U Wind speed (air movement) average of the bulk air (m s^–1)     

Effect of material nonhomogeneities on the HRR dominance

This work studies the asymptotic stress and displacement fields near the tip of a stationary crack in an elastic–plastic nonhomogeneous material with the emphasis on the effect of material nonhomogeneities on the dominance of the crack tip field. While the HRR singular field still prevails near the crack tip if the material properties are continuous and piecewise continuously differentiable, a simple asymptotic analysis shows that the size of the HRR dominance zone decreases with increasing magnitude of material property gradients. The HRR field dominates at points that satisfy |α⁻¹ ∂α/∂x_δ|1/r, |α⁻¹ ∂²α/(∂x_δ ∂x_γ)|1/r², |n⁻¹ ∂n/∂x_δ|1/[r|ln(r/A)|] and |n⁻¹ ∂²n/(∂x_δ ∂x_γ)|1/[r²|ln(r/A)|], in addition to other general requirements for asymptotic solutions, where α is a material property in the Ramberg–Osgood model, n is the strain hardening exponent, r is the distance from the crack tip, x_δ are Cartesian coordinates, and A is a length parameter. For linear hardening materials, the crack tip field dominates at points that satisfy |E_tan⁻¹ ∂E_tan/∂x_δ|1/r, |E_tan⁻¹ ∂²E_tan/(∂x_δ ∂x_γ)|1/r², |E⁻¹ ∂E/∂x_δ|1/r, and |E⁻¹ ∂²E/(∂x_δ ∂x_γ)|1/r², where E_tan is the tangent modulus and E is Young’s modulus.     

Time- and space-resolved spectroscopy of dynamic hohlraum interiors

A dynamic hohlraum is created when an annular z-pinch plasma implodes onto a cylindrical 0.014 g/cc 6-mm-diameter CH₂ foam. The impact launches a radiating shock that propagates toward the axis at 350 μm/ns. The radiation trapped by the tungsten z-pinch plasma forms a 200 eV hohlraum that provides X-rays for indirect drive inertial confinement fusion capsule implosion experiments. We are developing the ability to diagnose the hohlraum interior using emission and absorption spectroscopy of Si atoms added as a tracer to the central portion of the foam. Time- and space-resolved Si spectra are recorded with an elliptical crystal spectrometer viewing the cylindrical hohlraum end-on. A rectangular aperture at the end of the hohlraum restricts the field of view so that the 1D spectrometer resolution corresponds approximately to the hohlraum radial direction. This enables distinguishing between spectra from the unshocked radiation-heated foam and from the shocked foam. Typical spectral lines observed include the Si Lyα with its He-like satellites and the He-like resonance sequence including Heα, Heβ, and Heγ, along with some of their associated Li-like satellites. Work is in progress to infer the hohlraum conditions using collisional–radiative modeling that accounts for the radiation environment and includes both opacity effects and detailed Stark broadening calculations. These 6-mm-scale radiation-heated plasmas might eventually also prove suitable for testing Stark broadening line profile calculations or for opacity measurements.     

Measurement and simulations of hollow atom X-ray spectra of solid-density relativistic plasma created by high-contrast PW optical laser pulses

K-shell spectra of solid Al excited by petawatt picosecond laser pulses have been investigated at the Vulcan PW facility. Laser pulses of ultrahigh contrast with an energy of 160 J on the target allow studies of interactions between the laser field and solid state matter at 10²⁰ W/cm². Intense X-ray emission of KK hollow atoms (atoms without n = 1 electrons) from thin aluminum foils is observed from optical laser plasma for the first time. Specifically for 1.5 μm thin foil targets the hollow atom yield dominates the resonance line emission. It is suggested that the hollow atoms are predominantly excited by the impact of X-ray photons generated by radiation friction to fast electron currents in solid-density plasma due to Thomson scattering and bremsstrahlung in the transverse plasma fields. Numerical simulations of Al hollow atom spectra using the ATOMIC code confirm that the impact of keV photons dominates the atom ionization. Our estimates demonstrate that solid-density plasma generated by relativistic optical laser pulses provide the source of a polychromatic keV range X-ray field of 10¹⁸ W/cm² intensity, and allows the study of excited matter in the radiation-dominated regime. High-resolution X-ray spectroscopy of hollow atom radiation is found to be a powerful tool to study the properties of high-energy density plasma created by intense X-ray radiation.     

Backlighter development at the National Ignition Facility (NIF): Zinc to zirconium

K-shell X-ray emission from laser-irradiated planar Zn, Ge, Br, and Zr foils was measured at the National Ignition Facility for laser irradiances in the range of 0.6–9.5 × 10¹⁵ W/cm². The incident laser power had a pre-pulse to enhance the laser-to-X-ray conversion efficiency (CE) of a 2–5 ns constant-intensity pulse used as the main laser drive. The measured CE into the 8–16 keV energy band ranged from 0.43% to 2%, while the measured CE into the He-like resonance 1s2–1s2p(1P) and intercombination 1s2–1s2p(3P) transitions, as well as from their 1s2(2s,2p)l–1s2p(2s,2p)l satellite transitions for l = 1, 2, 3, corresponding to the Li-, Be-, and B-like resonances, respectively, ranged from 0.3% to 1.5%. Absolute and relative CE measurements are consistent with X-ray energy scaling of (hν)^?3 to (hν)^?5, where hν is the X-ray energy. The temporal evolution of the broadband X-ray power was similar to the main laser drive for ablation plasmas having a critical density surface.     

K-shell spectroscopy of plasmas created by intense laser irradiation of micron-scale pyramid and sphere targets

K-shell spectra of targets with microstructured features irradiated by an intense femtosecond laser have been studied. Examination of K_α emission from laser irradiated Si targets coated with micron-scale polystyrene spheres indicates that the emission is enhanced by a factor of 3 over emission from planar solids. Sphere-coated targets also emit K-shell He-like Si radiation indicating the presence of a hot dense plasma beneath the microspheres. Furthermore, K_α from Ti foils coupled to micro-tipped reentrant pyramid and wedge shaped targets has been studied, however, no significant enhancement of the K_α yield is observed for these kinds of targets. These studies illustrate that, with correct tailoring of the target surface, field enhancements can be used to increase X-ray emission from intensely irradiated targets.     

Symmetry and secondary bifurcation of elastic structures

We consider non-linear bifurcation problems for elastic structures modeled by the operator equation F[w;α]=0 where F:X×R^k→Y,X,Y are Banach spaces and XY. We focus attention on problems whose bifurcation equations are of the form

f_i(α₁,α₂;λ,μ)=(a_iμ+b_iλ)α_i+p_iα_i³+q_iα_i∑_j=1,j≠i^kα_j+1²+α_ih_i(λ,μ;α₁,α₂,…α_k) i=1,2,…k

which emanates from bifurcation problems for which the linearization of F is Fredholm operators of index 0. Under the assumption of F being odd we prove an important theorem of existence of secondary bifurcation. Under this same assumption we prove a symmetry condition for the reduced equations and consequently we got an existence result for secondary bifurcation. We also include a stability analysis of the bifurcating solutions.     

Investigation of active media for a short-wave gas dynamic laser

The process of formation of an active medium on the visible and ultraviolet intervals in a recombining plasma flow through a supersonic nozzle has been investigated theoretically and experimentally. The conditions of onset of inversion over its interval of existence have been theoretically determined. A highly ionized xenon plasma, generated by a pulsed gas dynamic source of the shock tube with nozzle type, was used in the experiments. Amplification of the emission in the blue—green region of the spectrum was obtained for the 6p ⁴ D ₅ ^2/° —6s ⁴ P _3/2 (wavelength 0.5419 m) and 6p' ² P _3/25d ² D _5/2(0.4973m) transitions of the Xe II ion.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 165–173, March–April, 1992.     

Oblique stagnation-point flow of a viscoelastic fluid with heat transfer

The two-dimensional forced convection stagnation-point flow and heat transfer of a viscoelastic second grade fluid obliquely impinging on an infinite plane wall is considered as an exact solution of the full partial differential equations. This oblique flow consists of an orthogonal stagnation-point flow to which a shear flow whose vorticity is fixed at infinity is added. The relative importance of these flows is measured by a parameter γ. The viscoelastic problem is reduced to two ordinary differential equations governed by the Weissenberg number W_e, two parameters α and β, the later being a free parameter β, introduced by Tooke and Blyth [A note on oblique stagnation-point flow, Physics of Fluids 20 (2008) 033101-1–3], and the Prandtl number Pr. The two cases when α=β and α≠β are, respectively, considered. Physically the free parameter may be viewed as altering the structure of the shear flow component by varying the magnitude of the pressure gradient. It is found that the location of the separation point x_s of the boundary layer moves continuously from the left to the right of the origin of the axes (x_s<0).     

Mixed convection flow over a vertical plate with localized heating (cooling), magnetic field and suction (injection)

An analysis is carried out to study the effects of localized heating (cooling), suction (injection), buoyancy forces and magnetic field for the mixed convection flow on a heated vertical plate. The localized heating or cooling introduces a finite discontinuity in the mathematical formulation of the problem and increases its complexity. In order to overcome this difficulty, a non-uniform distribution of wall temperature is taken at finite sections of the plate. The nonlinear coupled parabolic partial differential equations governing the flow have been solved by using an implicit finite-difference scheme. The effect of the localized heating or cooling is found to be very significant on the heat transfer, but its effect on the skin friction is comparatively small. The buoyancy, magnetic and suction parameters increase the skin friction and heat transfer. The positive buoyancy force (beyond a certain value) causes an overshoot in the velocity profiles.A mass transfer constant - B magnetic field - C_fx skin friction coefficient in the x-direction - C_p specific heat at constant pressure, kJ.kg^–1.K - C_v specific heat at constant volume, kJ.kg^–1.K^–1 - E electric field - g acceleration due to gravity, 9.81 m.s^–2 - Gr Grashof number - h heat transfer coefficient, W.m².K^–1 - Ha Hartmann number - k thermal conductivity, W.m^–1.K - L characteristic length, m - M magnetic parameter - Nu_x local Nusselt number - p pressure, Pa, N.m^–2 - Pr Prandtl number - q heat flux, W.m^–2 - Re Reynolds number - Re_m magnetic Reynolds number - T temperature, K - T_o constant plate temperature, K - u,v velocity components, m.s^–1 - V characteristic velocity, m.s^–1 - x,y Cartesian coordinates - thermal diffusivity, m².s^–1 - coefficient of thermal expansion, K^–1 - , transformed similarity variables - dynamic viscosity, kg.m^–1.s^–1 - ₀ magnetic permeability - kinematic viscosity, m².s^–1 - density, kg.m^–3 - buoyancy parameter - electrical conductivity - stream function, m².s^–1 - dimensionless constant - dimensionless temperature, K - w, conditions at the wall and at infinity     

Flow between parallel walls containing the lines of neutrally buoyant circular cylinders

The motions of a single and two lines of neutrally buoyant circular cylinders in fluid between flat parallel walls are numerically investigated over the range of the Reynolds number of 12 < Re < 96, the ratio of the diameter of the cylinder D_s to the channel width D of 0.25≤D_s/D≤0.5, and the ratio of the streamwise spacing of the cylinders L to the channel width of 0.75≤L/D≤2. The lattice Boltzmann method is used for computations of the fluid phase and the cylinders are moved according to Newton’s law of motion. The Segré–Silberberg effect is found for both a single and two lines of cylinders. It is also found that for two lines of cylinders with D_s/D=0.25 and L/D=1, the equilibrium positions of the two lines are arranged to be staggered with respect to each other in the flow direction. The effects of the Reynolds number Re, D_s/D, and L/D on the equilibrium position of the lines of cylinders and on the friction factor of the cylinder–fluid mixture are presented and discussed.     

Strain-rate history effects and microstructural aspects in lithium fluoride and aluminium single crystals after dynamic loading

Single crystals of LiF and Al are deformed in shear at a number of constant strain-rates in the range 10^–4 to 1600 s^–1. These constant rate tests are supplemented by a series of jump tests in which a sharp increment in strain rate is imposed during the quasi-static straining. Dislocation arrangements are observed by etch-pits technique for LiF crystals and by TEM for Al crystals. It is shown that cell sizes vary inversely with flow stress and strain-rate sensitivity.     

Crack repair using an elastic filler

The effect of repairing a crack in an elastic body using an elastic filler is examined in terms of the stress intensity levels generated at the crack tip. The effect of the filler is to change the stress field singularity from order 1/r^1/2 to 1/r^(1-λ) where r is the distance from the crack tip, and λ is the solution to a simple transcendental equation. The singularity power (1-λ) varies from (the unfilled crack limit) to 1 (the fully repaired crack), depending primarily on the scaled shear modulus ratio γ_r defined by G₂/G₁=γ_rε, where 2πε is the (small) crack angle, and the indices (1, 2) refer to base and filler material properties, respectively. The fully repaired limit is effectively reached for γ_r≈10, so that fillers with surprisingly small shear modulus ratios can be effectively used to repair cracks. This fits in with observations in the mining industry, where materials with G₂/G₁ of the order of 10^-3 have been found to be effective for stabilizing the walls of tunnels. The results are also relevant for the repair of cracks in thin elastic sheets.     

Synthesis and electrorheological properties of polar molecule-dominated TiO 2 particles with high yield stress

Two types of amorphous TiO₂ particles with different particle sizes were synthesized by a simple sol–gel method and were characterized by X-ray diffraction analysis, field emission scanning electron microscopy, and Fourier transform infrared spectrometry. The electrorheological (ER) results show that the TiO₂/silicone oil suspensions exhibited a remarkable ER effect. The static shear stress can be up to 130 kPa (shear rate 0.2 s^− 1) under the DC electric field of 4 kV/mm at room temperature. The polar molecules present on the particles’ surface play a decisive role for the observed giant ER effect, which arises from the alignment of polar molecules in the gap between neighboring particles.     

Using waste to treat waste: Red mud induced hierarchical porous γ-AlOOH and γ-Al2O3 microspheres as superior Pd support for catalytic reduction of 4-nitrophenol

Toward the imperative treatment of the industrial wastewater containing 4-nitrophenol (4-NP) and industrial solid waste red mud (RM), an innovative approach of “Using waste to treat waste” is developed. Valuable element Al is leached from the RM first, the resultant NaAlO₂ solution is hydrothermally converted to γ-AlOOH hierarchical porous microspheres (RM γ-AlOOH HPMSs, average diameter: 2.0 μm, S_BET: 77.81 m² g⁻¹, pore volume: 0.38 cm³ g⁻¹) in the presence of urea. The subsequent mild thermal conversion results in γ-Al₂O₃ hierarchical porous microspheres (RM γ-Al₂O₃ HPMSs). Both of the RM γ-AlOOH and RM γ-Al₂O₃ HPMSs are employed as the Pd catalyst support for the catalytic reduction of 4-NP. Particularly, the as-obtained composite Pd/RM γ-AlOOH and Pd/RM γ-Al₂O₃ exhibit excellent catalytic activities with superior k_nor as 8204.5 and 4831.4 s⁻¹ g⁻¹, respectively, significantly higher than that of most Pd based catalysts. Moreover, the excellent catalytic stability and durability of the Pd/RM γ-AlOOH and Pd/RM γ-Al₂O₃ within 10 successive cycles of reduction enable the present industrial solid waste RM induced γ-AlOOH and γ-Al₂O₃ HPMSs as great promising Pd catalyst support for the reduction of the industrial wastewater containing 4-NP.     

A specific slit die rheometer for extruded starchy products. Design,validation and application to maize starch

A novel in-line rheometer, called Rheopac, has been designed and built in order to study the rheological behaviour of starchy products or, more generally, of products sensitive to a thermomechanical treatment. It is based on the principle of a twin channel, using a balance of feed rate between each of them, in order to make local shear rate vary in the measuring section without changing the flow conditions into the extruder. A wide range of shear rate could be reached and measurements were performed more swiftly than with a classical slit die. The viscous behaviour of maize starch was studied by taking into account the influence of the thermomechanical history, which modified the starch degradation and thus led to important variations in the viscosity. Experimental results were satisfactorily compared to previously published models.Nomenclature E activation energy (J · mol^–1) - h channel depth (m) - h ₁ depth under the piston valve in channel 1 (m) - h ₂ depth under the piston valve in channel 2 (m) - K consistency (Pa·s ⁿ ) - K ₀ reference consistency (Pa·s ⁿ ) - L total channel length (m) - L _p length of the piston valve (m) - MC moisture content (wet basis) - n power law index - N screw rotation speed (rpm) - P ₀ entrance pressure (Pa) - P _e pressure at the entry of the piston valve (Pa) - Q ₁ flow rate in channel 1 (m3 · s^–1) - Q ₂ flow rate in channel 2 m³·s^–1) - Q _T total flow rate (m3 · s^–1) - R constant of perfect gas (8.314 J·mol^–1·K^–1) - SME specific mechanical energy (kWh · t^–1) - T temperature (°C) - T _a absolute temperature (K) - T _b barrel temperature (°C) - T _d die temperature (°C) - T _p product temperature (°C) - w channel width (m) - W energetical term (J·m^–3) - viscosity (Pa · s) - [gh ₀] intrinsic viscosity of native starch (ml·g^–1) - [] intrinsic viscosity (ml·g^–1) - shear rate (s^–1) - shear rate in measuring section (s^–1) - maximum shear rate (s^–1)     

New Explicit Expression of Barnett-Lothe Tensors for Anisotropic Linear Elastic Materials

The three Barnett-Lothe tensors H, L, S appear often in the Stroth formalism of two-dimensional deformations of anisotropic elastic materials [1–3]. They also appear in certain three-dimensional problems [4, 5]. The algebraic representation of H, L, S requires computation of the eigenvalues p^v(v=1,2,3) and the normalized eigenvectors (a, b). The integral representation of H, L, S circumvents the need for computing p ^v(v=1,2,3) and (a, b), but it is not simple to integrate the integrals except for special materials. Ting and Lee [6] have recently obtained an explicit expression of H for general anisotropic materials. We present here the remaining tensors L, S using the algebraic representation. They key to our success is the obtaining of the normalization factor for (a, b) in a simple form. The derivation of L and S then makes use of (a, b) but the final result does not require computation of (a, b), which makes the result attractive to numerical computation. Even though the tensor H given in [6] is in terms of the elastic stiffnesses C^μ v while the tensors L, S presented here are in terms of the reduced elastic compliances s′ _μv , the structure of L, S is similar to that of H. Following the derivation of H, we also present alternate expressions of L, S that remain valid for the degenerate cases p ₁ p ₂ and p₁=p₂ = p ₃. One may want to compute H, L, S using either C _μv or s′ _μv v, but not both. We show how an expression in C^μ v can be converted to an expression in s′ _μv v, and vice versa. As an application of the conversion, we present explicit expressions of the extic equation for p in C^μ v and s′ _μv v. This revised version was published online in August 2006 with corrections to the Cover Date.