Hot electron production using the Texas Petawatt Laser irradiating thick gold targets

We present data for relativistic hot electron production by the Texas Petawatt Laser irradiating solid Au targets with thickness between 1 and 4 mm. The experiment was performed at the short focus target chamber TC1 in July 2011, with intensities on the order of several ×10¹⁹ W/cm² and laser energies around 50 J. We discuss the design of an electron-positron magnetic spectrometer to record the lepton energy spectra ejected from the Au targets and present a deconvolution algorithm to extract the lepton energy spectra. We measured hot electron spectra out to ～50 MeV, which show a narrow peak around 10–20 MeV, plus high energy exponential tail. The hot electron spectral shapes appear significantly different from those reported for other PW lasers.     

Towards laboratory produced relativistic electron–positron pair plasmas

We review recent experimental results on the path to producing electron–positron pair plasmas using lasers. Relativistic pair-plasmas and jets are believed to exist in many astrophysical objects and are often invoked to explain energetic phenomena related to Gamma Ray Bursts and Black Holes. On earth, positrons from radioactive isotopes or accelerators are used extensively at low energies (sub-MeV) in areas related to surface science positron emission tomography and basic antimatter science. Experimental platforms capable of producing the high-temperature pair-plasma and high-flux jets required to simulate astrophysical positron conditions have so far been absent. In the past few years, we performed extensive experiments generating positrons with intense lasers where we found that relativistic electron and positron jets are produced by irradiating a solid gold target with an intense picosecond laser pulse. The positron temperatures in directions parallel and transverse to the beam both exceeded 0.5 MeV, and the density of electrons and positrons in these jets are of order 10¹⁶ cm⁻³ and 10¹³ cm⁻³, respectively. With the increasing performance of high-energy ultra-short laser pulses, we expect that a high-density, up to 10¹⁸ cm⁻³, relativistic pair-plasma is achievable, a novel regime of laboratory-produced hot dense matter.     

Tungsten L transition line shapes and energy shifts resulting from ionization in warm dense matter

Spectra of the W L transitions in the energy range 8–12 keV from warm dense plasmas generated by the Naval Research Laboratory's Gamble II pulsed power machine were recorded by a newly developed high-resolution transmission-crystal X-ray spectrometer with ±2 eV accuracy. The discharges have up to 2 MV voltage, 0.5 MA current, and produce up to 2.4 MJ/cm^?3 energy density. The plasma-filled rod pinch (PFRP) diode produces a plasma with N_e ≈ 10²² cm^?3 and T_e ≈ 50 eV during the time of maximum X-ray emission. By analyzing the line shapes, it was determined that the Lβ₂ inner-shell transition from the 4d_5/2 level was shifted to higher energy by up to 23 eV relative to nearby Lβ transitions from n = 3 levels. In addition, the Lβ₂ transition was significantly broader and asymmetric compared to the n = 3 transitions. The energy shift of the Lβ₂ transition results from the ionization of electrons outside the 4d shell that perturbs the transition energies in the ions to higher values. The increased line width and asymmetry result from unresolved transitions from a range of ionization states up to +28. The ionization distribution was determined by comparison of the measured energy shifts and widths to calculated transition energies in W ions, and the ionization was correlated with Gamble discharge parameters such as the anode type and the high voltage delay time. This work demonstrates a new hard X-ray spectroscopic diagnostic technique for the direct measurement of the ionization distribution in warm dense plasmas of the heavy elements W through U that is independent of the other plasma parameters and does not require interpretation by hydrodynamic, atomic kinetics, and radiative simulation codes.     

Ground shock from the detonation of buried explosives

New nonlinear empirical relationships are given for predicting peak radial soil particle velocity and maximum radial displacement at various standoff distances from buried chemical and nuclear explosive detonations. Experimental test data in soil and rock, and for yields ranging from 0.03 pounds (0.01 kg) of explosive to blast yields of 19.2 kilotons (17.5 kilotonnes), are used to demonstrate the validity of these results. The scaled energy releases W/πc²R³ range over nine orders of magnitude in this study from approximately 4.4 × 10⁻¹¹ to 4.4 × 10⁻²; whereas, previous efforts generally covered three orders of magnitude. A soil impedence term is added to handle the troublesome problem of nondimensionalized displacements and particle velocities scaling for different soils. The paper ends by presenting a few nondimensionalized test results which can be used to predict ground motions from buried line explosive sources, an area of little previous discussion.     

Quantitative measurement of hard X-ray spectra from laser-driven fast ignition plasma

Absolute Kα line spectroscopy is proposed for studying laser–plasma interactions taking place in the Au cone-guided fast ignition targets. X-ray spectra ranging from 20 to 100 keV were quantitatively measured with a Laue spectrometer composed of a cylindrically curved crystal and a filter-absorption method for Bremsstrahlung continuum emission. The absolute sensitivities of the Laue spectrometer systems were calibrated using pre-characterized laser-produced X-ray sources and radioisotopes. The integrated reflectivity for the crystal is in good agreement with predictions by an X-ray diffraction code. The energy transfer efficiency from incident laser beams to hot electrons, as the energy transfer mechanism, is derived from this work. The absolute yield of Au and Ta Kα lines were measured in the fast ignition experimental campaign performed at Institute of Laser Engineering, Osaka University. Applying the hot electron spectrum information from electron spectrometer and scaling laws, the energy transfer efficiency from the incident LFEX, a kJ-class PW laser, to hot electrons was derived for the first time.     

Simultaneous imaging of K-α radiation and coherent transition radiation from relativistic-intensity laser-irradiated solid target plasmas

Laser acceleration of hot electrons and their transport through 12-32 μm thick Ti foils was explored experimentally using two complementary diagnostics, a bent crystal imaging the Ti K_α emission and optical imaging of the coherent transition radiation (CTR) produced by the exit of the hot electrons from the foil. The spatial extent of the hot electron production measured by these two diagnostics is dramatically different. Electrons producing CTR emerge in a spot of less than 7 μm and appear to maintain a high degree of collimation during transport through the foil while electrons that produce K_α emission appear to diverge to sizes of 50-100 μm as viewed from the back surface of the foil. These results indicate that there is a large difference in the transport of the highest energy electrons contributing to CTR signal as compared with the bulk of the hot electron population generating K_α signal.     

Simulations of hot, dense iron plasma opacity at 89 eV and comparison with experiment

Predictions of hot, dense iron plasma opacity at 89 eV photon energy are compared with experimental determinations from the transmission of laser-heated iron to extreme ultra-violet (EUV) laser radiation. The EUV laser was pumped using six beams of an Nd-Yag laser in a refraction compensating geometry, while another beam irradiated a tamped solid iron target with an intensity of 10¹⁴ W cm⁻². The Ehybrid hydrodynamic and atomic physics code was used to predict temperatures, densities and ionisation throughout the evolving iron plasma. The iron opacities were deduced taking into account free–free, bound–free and bound–bound absorption. Bound–bound absorption was considered using atomic data generated by the Opacity Project. Reasonable overall agreement between theory and experiment was obtained for the iron layer transmission. The simulations indicated the dominance of bound–bound absorption throughout most regions of the iron plasma, but also the potential importance of photoionisation from core levels where energetically possible.     

Strain fields caused by doughnut-like and tubular inclusions with uniform eigenstrains

Inclusion problems for elongated toroidal inclusions are solved to discuss the strain fields caused by eigenstrained doughnut-like and tubular inclusions. For an infinitely long tubular inclusion, uniform eigenstrains do not generate elastic strains in the matrix region inside the tube. Effects of tube length on the elastic strains are shown for the purely dilatational eigenstrain ^*. For the tubular inclusion with the length 2b, the elastic strain at the center of the matrix region inside the tube becomes the maximum as much as ≈(a/b)^* when the tubular inclusion has the inner diameter ≈2(b−a) and the outer diameter ≈2(b+a).     

Hard X-ray spectroscopy of inner-shell K transitions generated by MeV electron propagation from intense picosecond laser focal spots

The propagation of energetic electrons from the focal spots of intense picosecond laser pulses was studied using targets consisting of planar foils and fine metal wires. High-resolution K-shell spectra of elements with atomic numbers in the range 46–74 (Pd to W) and with energies from 21 keV to 69 keV were recorded by a Cauchois-type spectrometer using a curved transmission crystal. The K-shell spectra resulted from the collisional ionization of 1 s electrons by energetic electrons that were generated in the laser focal spot and propagated into the planar foil region beyond the focal spot or into the metal wires adjacent to an irradiated wire. The lateral spread of the energetic electrons from the focal spot was determined from the source broadening of the K spectral lines and from the relative intensities of the K spectra from an irradiated wire and neighboring wires of different metals. The propagation distances up to 1 mm in a variety of materials indicated electron energies up to 1 MeV were generated in the laser focal spot. Inhibited propagation in an electrically insulating material was observed that results from a weak return current and incomplete space charge neutralization.     

Free-stream turbulence effects on vortex-induced vibration of two side-by-side elastic cylinders

The effect of free-stream turbulence on vortex-induced vibration of two side-by-side elastic cylinders in a cross-flow was investigated experimentally. A turbulence generation grid was used to generate turbulent incoming flow with turbulence intensity around 10%. Cylinder displacements in the transverse direction at cylinder mid-span were measured in the reduced velocity range 1.45<U_r0<12.08, corresponding to a range of Reynolds number (Re), based on the mean free-stream velocity and the diameter of the cylinder, between Re=5000–41 000. The focus of the study is on the regime of biased gap flow, where two cylinders with pitch ratio (T/D) varying from 1.17 to 1.90 are considered. Results show that the free-stream turbulence effect is to enhance the vortex-induced force, thus to restore the large-amplitude vibration associated with the lock-in resonance. However, the enhancement is significant at a different Strouhal number (St) for different pitch ratios. When the spacing between two cylinders is relatively small (1.17<T/D<1.50), the enhancement is significant at St≈0.1. When the spacing is increased, the Strouhal number at which the enhancement is significant shifts to St≈0.16. This enlarges the range of reduced velocity to be concerned. An energy analysis showed that free-stream turbulence feeds energy to the cylinder at multiple frequencies of vortex shedding. Therefore, the lock-in region is still of main concern when the approach flow is turbulent.     

Stress evolution to steady state in ion bombardment of silicon

Low temperature ion bombardment of initially crystalline, defect-free silicon with 700 eV ion beam energy creates a highly-damaged stressed layer a few nanometers thick on the surface. An apparent steady state in structure is achieved at a fluence of 2 × 10¹⁴–3 × 10¹⁴ ions/cm². In this work, the stresses are computed using the interatomic force definition of stress. The stress evolution is studied as a function of argon implantation into the target. Stress per implanted argon atom is observed to reach a nearly constant value between 20 MPa and 25 MPa at a fluence of 1.2 × 10¹⁴ ions/cm².     

TOF-OFF: A method for determining focal positions in tightly focused free-electron laser experiments by measurement of ejected ions

Pulse intensities greater than 10¹⁷ Watt/cm² were reached at the FLASH soft X-ray laser in Hamburg, Germany, using an off-axis parabolic mirror to focus 15 fs pulses of 5–70 μJ energy at 13.5 nm wavelength to a micron-sized spot. We describe the interaction of such pulses with niobium and vanadium targets and their deuterides. The beam produced craters in the solid targets, and we measured the kinetic energy of ions ejected from these craters. Ions with several keV kinetic energy were observed from craters approaching 5 μm in depth when the sample was at best focus. We also observed the onset of saturation in both ion acceleration and ablation with pulse intensities exceeding 10¹⁶ W/cm², when the highest detected ion energies and the crater depths tend to saturate with increasing intensity.A general difficulty in working with micron and sub-micron focusing optics is finding the exact focus of the beam inside a vacuum chamber. Here we propose a direct method to measure the focal position to a resolution better than the Rayleigh length. The method is based on the correlation between the energies of ejected ions and the physical dimensions of the craters. We find that the focus position can be quickly determined from the ion time-of-flight (TOF) data as the target is scanned through the expected focal region. The method does not require external access to the sample or venting the vacuum chamber. Profile fitting employed to analyze the TOF data can extend resolution beyond the actual scanning step size.     

Micro/macro-crack growth due to creep–fatigue dependency on time–temperature material behavior

The implicit character of micro-structural degradation is determined by specifying the time history of crack growth caused by creep–fatigue interaction at high temperature. A dual scale micro/macro-equivalent crack growth model is used to illustrate the underlying principle of multiscaling which can be applied equally well to nano/micro. A series of dual scale models can be connected to formulate triple or quadruple scale models. Temperature and time-dependent thermo-mechanical material properties are developed to dictate the design time history of creep–fatigue cracking that can serve as the master curve for health monitoring.In contrast to the conventional procedure of problem/solution approach by specifying the time- and temperature-dependent material properties as a priori, the desired solution is then defined for a class of anticipated loadings. A scheme for matching the loading history with the damage evolution is then obtained. The results depend on the initial crack size and the extent of creep in proportion to fatigue damage. The path dependent nature of damage is demonstrated by showing the range of the pertinent parameters that control the final destruction of the material. A possible scenario of 20 yr of life span for the 38Cr2Mo2VA ultra-high strength steel is used to develop the evolution of the micro-structural degradation. Three micro/macro-parameters μ^*, d^* and σ^* are used to exhibit the time-dependent variation of the material, geometry and load effects. They are necessary to reflect the scale transitory behavior of creep–fatigue damage. Once the algorithm is developed, the material can be tailor made to match the behavior. That is a different life span of the same material would alter the time behavior of μ^*, d^* and σ^* and hence the micro-structural degradation history. The one-to-one correspondence of the material micro-structure degradation history with that of damage by cracking is the essence of path dependency. Numerical results and graphs are obtained to demonstrate how the inherently implicit material micro-structure parameters can be evaluated from the uniaxial bulk material properties at the macroscopic scale.The combined behavior of creep and fatigue can be exhibited by specifying the parameter ξ with reference to the initial defect size a₀. Large ξ (0.90 and 0.85) gives critical crack size a_cr = 11–14 mm (at t < 20 yr) for a₀ about 1.3 mm. For small ξ (0.05 and 0.15), there results critical a_cr = 6–7 mm (at t < 20 yr) for a₀ about 0.7–0.8 mm. The initial crack is estimated to increase its length by an order of magnitude before triggering global to the instability. This also applies ξ ≈ 0.5 where creep interacts severely with fatigue. Fine tuning of a_cr and a₀ can be made to meet the condition oft = 20 yr.Trade off among load, material and geometric parameters are quantified such that the optimum conditions can be determined for the desired life qualified by the initial–final defect sizes. The scenario assumed in this work is indicative of the capability of the methodology. The initial–final defect sizes can be varied by re-designing the time–temperature material specifications. To reiterate, the uniqueness of solution requires the end result to match with the initial conditions for a given problem. This basic requirement has been accomplished by the dual scale micro/macro-crack growth model for creep and fatigue.     

Equilibrium states in homogeneous turbulence with baroclinic instability

The evolution of energies and fluxes in homogeneous turbulence with baroclinic instability is analyzed using the linear theory. The mean flow corresponds to a vertical shear having a uniform mean velocity gradient, ?U _i /?x _j  = S δ _i1 δ _j3, a system rotation about the vertical axis with rate Ω, Ω _i  = Ωδ _i3, and uniform buoyancy gradients in the spanwise ${(\partial B{/}\partial x_2\,{=}\, N_h^2\,{=}\,-2\Omega S)}The evolution of energies and fluxes in homogeneous turbulence with baroclinic instability is analyzed using the linear theory. The mean flow corresponds to a vertical shear having a uniform mean velocity gradient, ∂U _i /∂x _j  = S δ _i1 δ _j3, a system rotation about the vertical axis with rate Ω, Ω _i  = Ωδ _i3, and uniform buoyancy gradients in the spanwise (?B/?x₂ = N_h² = -2WS){(\partial B{/}\partial x_2\,{=}\, N_h^2\,{=}\,-2\Omega S)} and vertical (?B/?x₃ = N_v²){(\partial B{/}\partial x_3\,{=}\,N_v^2)} directions. Computations based on the rapid distortion theory (RDT) are performed for several values of the rotation number R = 2Ω/S and the Richardson number R_i = N_v²/S² < 1{R_i\,{=}\,N_v^2/S^2 <1 }. It is shown that, during an initial phase, the energies and the buoyancy fluxes are sensitive to the effects of pressure and viscosity. At large time, the ratios of energies, as well as the normalized fluxes, evolve to an asymptotically constant value, while the pressure–strain correlation scaled with the product of the turbulent kinetic energy by the shear rate approaches zero. Accordingly, an analytical parametric study based on the “pressure-less” approach (PLA) is also presented. The analytical study indicates that, when R _i  < 1, there is an exponential instability and equilibrium states of turbulence, in agreement with RDT. The energies and the buoyancy fluxes grow exponentially for large times with the same rate (γ in St units). The asymptotic value of the ratios of energies yielded by RDT is well described by its PLA counterpart derived analytically. At R _i  = 0, the asymptotic value of γ increases with increasing R approaching 2 for high rotation rates. At low rotation rates, an important contribution to the kinetic energy comes from the streamwise kinetic energy, whereas, at high rotation rates, the contribution of the vertical kinetic energy is dominant. When 0 < R _i  < 1 and R 1 0{R\ne 0}, the asymptotic value of γ decreases as R _i increases so as it becomes zero at R _i  = 1.     

Transport properties in mixtures involving carbon dioxide at low and moderate density: test of several intermolecular potential energies and comparison with experiment

It is the purpose of this paper to extract unlike intermolecular potential energies of five carbon dioxide-based binary gas mixtures including CO₂–He, CO₂–Ne, CO₂–Ar, CO₂–Kr, and CO₂–Xe from viscosity data and compare the calculated potentials with other models potential energy reported in literature. Then, dilute transport properties consisting of viscosity, diffusion coefficient, thermal diffusion factor, and thermal conductivity of aforementioned mixtures are calculated from the calculated potential energies and compared with literature data. Rather accurate correlations for the viscosity coefficient of afore-cited mixtures embracing the temperature range 200 K < T < 3273.15 K is reproduced from the present unlike intermolecular potentials energy. Our estimated accuracies for the viscosity are to within ±2%. In addition, the calculated potential energies are used to present smooth correlations for other transport properties. The accuracies of the binary diffusion coefficients are of the order of ±3%. Finally, the unlike interaction energy and the calculated low density viscosity have been employed to calculate high density viscosities using Vesovic–Wakeham method.     

Thin-layer drying of tomato (<Emphasis Type="Italic">Lycopersicum esculentum Mill. cv. Rio Grande</Emphasis>) slices in a convective hot air dryer

The effects of different drying temperatures on the drying kinetics of tomato slices were investigated using a cabinet-type dryer. The experimental drying data were fitted best to the to the Page and Modified Page models apart from other theoretical models to predict the drying kinetics. The effective moisture diffusivities varied from 1.015 × 10⁻⁹ to 2.650 × 10⁻⁹ m² s⁻¹over the temperature range studied, and activation energy was 22.981 kJ mol⁻¹.     

Effect of the parameters of an electron beam on the process of accumulation of hot electrons in a mirror trap

A study is made of the mechanism of generation and accumulation of hot electrons during the interaction of an electron beam with a cold plasma in a mirror machine. The energy density distribution of the hot component of the plasma (nT) along the radius of the system, the time dependence of the diamagnetism, and the escape of fast electrons from the beam region into the loss cone are measured. It is established that there is a considerable difference in the processes of accumulation of hot electrons depending on whether the beam current or beam energy is varied. It is concluded that under the conditions of these experiments the hot component of the plasma is formed from the beam electrons.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 49–54, July–August, 1974.The authors are grateful to L. I. Rudakov for valuable remarks.     

Non-linear oscillation of circular cylindrical shells

The method of multiple scales is used to analyze the non-linear forced response of circular cylindrical shells in the presence of a two-to-one internal (autoparametric) resonance to a harmonic excitation having the frequency Ω. If ω_r and a_r denote the frequency and amplitude of a flexural mode and ω_b and a_b denote the frequency and amplitude of the breathing mode, the steady-state response exhibits a saturation phenomenon when ω_b ≈ 2ω_r, if the excitation frequency Ω is near ω_b. As the amplitude ƒ of the excitation increases from zero, a_b increases linearly whereas a_r remains zero until a threshold is reached. This threshold is a function of the damping coefficients and ω_b−2ω_r. Beyond this threshold a_b remains constant (i.e. the breathing mode saturates) and the extra energy spills over into the flexural mode. In other words, although the breathing mode is directly excited by the load, it absorbs a small amount of the input energy (responds with a small amplitude) and passes the rest of the input energy into the flexural mode (responds with a large amplitude). For small damping coefficients and depending on the detunings of the internal resonance and the excitation, the response exhibits a Hopf bifurcation and consequently there are no steadystate periodic responses. Instead, the responses are amplitude- and phase-modulated motions. When Ω ≈ ω_r, there is no saturation phenomenon and at close to perfect resonance, the response exhibits a Hopf bifurcation, leading again to amplitude- and phase-modulated or chaotic motions.     

Mesoscopic dynamics of polymer chains in high strain rate extensional flows

We take a step towards accessing the physics of viscoelastic liquid breakup in high speed, high strain rate flows by performing Brownian dynamics computations of dilute uniaxial, equibiaxial, and ellipsoidal polymeric extensional flows. Our computational implementation of the bead-spring model, when tailored to the DNA molecule, consistently with recent works of Larson and co-workers, is shown: (a) to predict a coil-stretch transition at Deborah number De≈0.5, and (b) to reproduce the experimental longest relaxation time. Furthermore, after adapting the model parameters to represent the polyethylene oxide (PEO) chain (for M=10⁶ Da), we find it possible to reproduce our own experimental data of the longest relaxation time, the transient extensional viscosity of dilute solutions at small Deborah numbers, and a coil-stretch transition at Deborah number De≈0.5. Extended to large Deborah numbers, the model predicts that polymer stretching is controlled by: (a) the randomness of the initial conditions that, in combination with rapid kinematically imposed compression, lead to the formation of initially frozen chain-folds, and (b) the speed with which thermo-kinematic processes relax these folds. The slowest fold relaxation occurs during uniaxial extension. As expected, the introduction of stretching along a second direction enhances the efficiency of fold relaxation mechanisms. Even for Deborah numbers (based on the chain longest relaxation time) of the order of one thousand, there is a large variation in the time a polymer needs in order to extend fully, and the effects of Brownian motion cannot be ignored. The computed Trouton ratios and polymer contributions to the total stress as functions of Hencky strain provide information about the relative importance of elastic effects during polymeric liquid stretching. At high strain rates, the steady state elastic stresses increase linearly with the Deborah number, resembling at that stage an anisotropic Newtonian fluid (constant extensional viscosity).     

Ion acceleration in the radiation pressure regime with ultrashort pulse lasers

Numerical simulations of the interaction between 100 TW ultrashort (<50 fs) laser pulses and nanometre scale carbon targets have been performed using the 2D3V PIC code OSIRIS. Different focusing geometries (f/2 and f/0.8) were investigated, along with varying target thickness and laser polarisation, to see the effect on the accelerated carbon ions and protons. The ions are found to be accelerated either directly by the radiation pressure of the incident radiation on the plasma, by bulk heating in the relativistic transparency regime, or a combination of both. Optimum target thicknesses for maximum carbon energies were found to be ～ 10 nm for the f/2 configuration and ～ 30 nm for the f/0.8 configuration. Despite this greater optimum target thickness, the faster focusing f/0.8 can result in a greater than doubling in maximum ion and proton energy. Circular polarisation was found to give only a marginal advantage in maintaining radiation pressure acceleration due to the deformation of the target during acceleration.