Femtosecond visualization of lattice dynamics in shock-compressed matter

Science 342 (2013) 220-223

D Milathianaki, S Boutet, GJ Williams, A Higginbotham, D Ratner, AE Gleason, M Messerschmidt, MM Seibert, DC Swift, P Hering, J Robinson, WE White, JS Wark

The ultrafast evolution of microstructure is key to understanding high-pressure and strain-rate phenomena. However, the visualization of lattice dynamics at scales commensurate with those of atomistic simulations has been challenging. Here, we report femtosecond x-ray diffraction measurements unveiling the response of copper to laser shock-compression at peak normal elastic stresses of ∼73 gigapascals (GPa) and strain rates of 10 9 per second. We capture the evolution of the lattice from a one-dimensional (1D) elastic to a 3D plastically relaxed state within a few tens of picoseconds, after reaching shear stresses of 18 GPa. Our in situ high-precision measurement of material strength at spatial ( < 1 micrometer) and temporal ( < 50 picoseconds) scales provides a direct comparison with multimillion-atom molecular dynamics simulations.

Implosion and heating experiments of fast ignition targets by Gekko-XII and LFEX lasers

EPJ Web of Conferences 59 (2013)

H Shiraga, S Fujioka, M Nakai, T Watari, H Nakamura, Y Arikawa, H Hosoda, T Nagai, M Koga, H Kikuchi, Y Ishii, T Sogo, K Shigemori, H Nishimura, Z Zhang, M Tanabe, S Ohira, Y Fujii, T Namimoto, Y Sakawa, O Maegawa, T Ozaki, KA Tanaka, H Habara, T Iwawaki, K Shimada, M Key, P Norreys, J Pasley, H Nagatomo, T Johzaki, A Sunahara, M Murakami, H Sakagami, T Taguchi, T Norimatsu, H Homma, Y Fujimoto, A Iwamoto, N Miyanaga, J Kawanaka, T Kanabe, T Jitsuno, Y Nakata, K Tsubakimoto, K Sueda, R Kodama, K Kondo, N Morio, S Matsuo, T Kawasaki, K Sawai, K Tsuji, H Murakami, N Sarukura, T Shimizu, K Mima, H Azechi

The FIREX-1 project, the goal of which is to demonstrate fuel heating up to 5 keV by fast ignition scheme, has been carried out since 2003 including construction and tuning of LFEX laser and integrated experiments. Implosion and heating experiment of Fast Ignition targets have been performed since 2009 with Gekko-XII and LFEX lasers. A deuterated polystyrene shell target was imploded with the 0.53- μm Gekko-XII, and the 1.053- μm beam of the LFEX laser was injected through a gold cone attached to the shell to generate hot electrons to heat the imploded fuel plasma. Pulse contrast ratio of the LFEX beam was significantly improved. Also a variety of plasma diagnostic instruments were developed to be compatible with harsh environment of intense hard x-rays (γ rays) and electromagnetic pulses due to the intense LFEX beam on the target. Large background signals around the DD neutron signal in time-of-flight record of neutron detector were found to consist of neutrons via (γ,n) reactions and scattered gamma rays. Enhanced neutron yield was confirmed by carefully eliminating such backgrounds. Neutron enhancement up to 3.5 × 10 7 was observed. Heating efficiency was estimated to be 10-20% assuming a uniform temperature rise model. © Owned by the authors, published by EDP Sciences, 2013.

The role of collisions on mode competition between the two-stream and Weibel instabilities

Journal of Plasma Physics 79 (2013) 987-989

KA Humphrey, RMGM Trines, DC Speirs, P Norreys, R Bingham

We present results from numerical simulations conducted to investigate a potential method for realizing the required fusion fuel heating in the fast ignition scheme to achieving inertial confinement fusion. A comparison will be made between collisionless and collisional particle-in-cell simulations of the relaxation of a non-thermal electron beam through the two-stream instability. The results presented demonstrate energy transfer to the plasma ion population from the laser-driven electron beam via the nonlinear wave-wave interaction associated with the two-stream instability. Evidence will also be provided for the effects of preferential damping of competing instabilities such as the Weibel mode found to be detrimental to the ion heating process. © Cambridge University Press 2013.

Laminar shocks in high power laser interactions

40th EPS Conference on Plasma Physics, EPS 2013 2 (2013) 850-853

RA Cairns, R Bingham, PA Norreys, RMGM Trines

Ultrafast three-dimensional imaging of lattice dynamics in individual gold nanocrystals.

Science 341 (2013) 56-59

JN Clark, L Beitra, G Xiong, A Higginbotham, DM Fritz, HT Lemke, D Zhu, M Chollet, GJ Williams, M Messerschmidt, B Abbey, RJ Harder, AM Korsunsky, JS Wark, IK Robinson

Key insights into the behavior of materials can be gained by observing their structure as they undergo lattice distortion. Laser pulses on the femtosecond time scale can be used to induce disorder in a "pump-probe" experiment with the ensuing transients being probed stroboscopically with femtosecond pulses of visible light, x-rays, or electrons. Here we report three-dimensional imaging of the generation and subsequent evolution of coherent acoustic phonons on the picosecond time scale within a single gold nanocrystal by means of an x-ray free-electron laser, providing insights into the physics of this phenomenon. Our results allow comparison and confirmation of predictive models based on continuum elasticity theory and molecular dynamics simulations.

Diffusive shock acceleration at laser-driven shocks: Studying cosmic-ray accelerators in the laboratory

New Journal of Physics 15 (2013)

B Reville, AR Bell, G Gregori

The non-thermal particle spectra responsible for the emission from many astrophysical systems are thought to originate from shocks via a first order Fermi process otherwise known as diffusive shock acceleration. The same mechanism is also widely believed to be responsible for the production of high energy cosmic rays. With the growing interest in collisionless shock physics in laser produced plasmas, the possibility of reproducing and detecting shock acceleration in controlled laboratory experiments should be considered. The various experimental constraints that must be satisfied are reviewed. It is demonstrated that several currently operating laser facilities may fulfil the necessary criteria to confirm the occurrence of diffusive shock acceleration of electrons at laser produced shocks. Successful reproduction of Fermi acceleration in the laboratory could open a range of possibilities, providing insight into the complex plasma processes that occur near astrophysical sources of cosmic rays. © IOP Publishing and Deutsche Physikalische Gesellschaft.

Molecular dynamics simulations of shock-induced deformation twinning of a body-centered-cubic metal

PHYSICAL REVIEW B 88 (2013) ARTN 104105

A Higginbotham, MJ Suggit, EM Bringa, P Erhart, JA Hawreliak, G Mogni, N Park, BA Remington, JS Wark

Simulation of X-ray scattering diagnostics in multi-dimensional plasma

High Energy Density Physics 9 (2013) 510-515

I Golovkin, JJ MacFarlane, P Woodruff, I Hall, G Gregori, J Bailey, E Harding, T Ao, S Glenzer

X-ray scattering is a powerful diagnostic technique that has been used in a variety of experimental settings to determine the temperature, density, and ionization state of warm dense matter. In order to maximize the intensity of the scattered signal, the x-ray source is often placed in close proximity to the target plasma. Therefore, the interpretation of the experimental data can become complicated by the fact that the detector records photons scattered at different angles from points within the plasma volume. In addition, the target plasma that is scattering the x-rays can have significant temperature and density gradients. To address these issues, we have developed the capability to simulate x-ray scattering for realistic experimental configurations where the effects of plasma non-uniformities and a range of x-ray scattering angles are included. We will discuss the implementation details and show results relevant to previous and ongoing experimental investigations. © 2013 Elsevier B.V.

Radiative shocks produced from spherical cryogenic implosions at the National Ignition Facility

Physics of Plasmas 20 (2013)

A Pak, L Divol, G Gregori, S Weber, J Atherton, R Bennedetti, DK Bradley, D Callahan, DT Casey, E Dewald, T Döppner, MJ Edwards, JA Frenje, S Glenn, GP Grim, D Hicks, WW Hsing, N Izumi, OS Jones, MG Johnson, SF Khan, JD Kilkenny, JL Kline, GA Kyrala, J Lindl, OL Landen, S Le Pape, T Ma, A Macphee, BJ Macgowan, AJ Mackinnon, L Masse, NB Meezan, JD Moody, RE Olson, JE Ralph, HF Robey, HS Park, BA Remington, JS Ross, R Tommasini, RPJ Town, V Smalyuk, SH Glenzer, EI Moses

Spherically expanding radiative shock waves have been observed from inertially confined implosion experiments at the National Ignition Facility. In these experiments, a spherical fusion target, initially 2 mm in diameter, is compressed via the pressure induced from the ablation of the outer target surface. At the peak compression of the capsule, x-ray and nuclear diagnostics indicate the formation of a central core, with a radius and ion temperature of ∼20 μm and ∼ 2 keV, respectively. This central core is surrounded by a cooler compressed shell of deuterium-tritium fuel that has an outer radius of ∼40 μm and a density of > 500 g/cm 3 . Using inputs from multiple diagnostics, the peak pressure of the compressed core has been inferred to be of order 100 Gbar for the implosions discussed here. The shock front, initially located at the interface between the high pressure compressed fuel shell and surrounding in-falling low pressure ablator plasma, begins to propagate outwards after peak compression has been reached. Approximately 200 ps after peak compression, a ring of x-ray emission created by the limb-brightening of a spherical shell of shock-heated matter is observed to appear at a radius of ∼100 μm. Hydrodynamic simulations, which model the experiment and include radiation transport, indicate that the sudden appearance of this emission occurs as the post-shock material temperature increases and upstream density decreases, over a scale length of ∼10 μm, as the shock propagates into the lower density (∼1 g/cc), hot (∼250 eV) plasma that exists at the ablation front. The expansion of the shock-heated matter is temporally and spatially resolved and indicates a shock expansion velocity of ∼300 km/s in the laboratory frame. The magnitude and temporal evolution of the luminosity produced from the shock-heated matter was measured at photon energies between 5.9 and 12.4 keV. The observed radial shock expansion, as well as the magnitude and temporal evolution of the luminosity from the shock-heated matter, is consistent with 1-D radiation hydrodynamic simulations. Analytic estimates indicate that the radiation energy flux from the shock-heated matter is of the same order as the in-flowing material energy flux, and suggests that this radiation energy flux modifies the shock front structure. Simulations support these estimates and show the formation of a radiative shock, with a precursor that raises the temperature ahead of the shock front, a sharp μ m-scale thick spike in temperature at the shock front, followed by a post-shock cooling layer. © 2013 AIP Publishing LLC.

Numerical modeling of the sensitivity of x-ray driven implosions to low-mode flux asymmetries

Physical Review Letters 110 (2013)

RHH Scott, DS Clark, DK Bradley, DA Callahan, MJ Edwards, SW Haan, OS Jones, BK Spears, MM Marinak, RPJ Town, PA Norreys, LJ Suter

The sensitivity of inertial confinement fusion implosions, of the type performed on the National Ignition Facility (NIF), to low-mode flux asymmetries is investigated numerically. It is shown that large-amplitude, low-order mode shapes (Legendre polynomial P 4 ), resulting from low-order flux asymmetries, cause spatial variations in capsule and fuel momentum that prevent the deuterium and tritium (DT) "ice" layer from being decelerated uniformly by the hot spot pressure. This reduces the transfer of implosion kinetic energy to internal energy of the central hot spot, thus reducing the neutron yield. Furthermore, synthetic gated x-ray images of the hot spot self-emission indicate that P 4 shapes may be unquantifiable for DT layered capsules. Instead the positive P 4 asymmetry "aliases" itself as an oblate P 2 in the x-ray images. Correction of this apparent P 2 distortion can further distort the implosion while creating a round x-ray image. Long wavelength asymmetries may be playing a significant role in the observed yield reduction of NIF DT implosions relative to detailed postshot two-dimensional simulations. © 2013 American Physical Society.

Comparison between x-ray scattering and velocity-interferometry measurements from shocked liquid deuterium

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 87 (2013)

K Falk, SP Regan, J Vorberger, BJB Crowley, SH Glenzer, SX Hu, CD Murphy, PB Radha, AP Jephcoat, JS Wark, DO Gericke, G Gregori

The equation of state of light elements is essential to understand the structure of Jovian planets and inertial confinement fusion research. The Omega laser was used to drive a planar shock wave in the cryogenically cooled deuterium, creating warm dense matter conditions. X-ray scattering was used to determine the spectrum near the boundary of the collective and noncollective scattering regimes using a narrow band x-ray source in backscattering geometry. Our scattering spectra are thus sensitive to the individual electron motion as well as the collective plasma behavior and provide a measurement of the electron density, temperature, and ionization state. Our data are consistent with velocity-interferometry measurements previously taken on the same shocked deuterium conditions and presented by K. Falk. This work presents a comparison of the two diagnostic systems and offers a detailed discussion of challenges encountered. ©2013 American Physical Society.

X-ray scattering from warm dense iron

High Energy Density Physics 9 (2013) 573-577

S White, G Nersisyan, B Kettle, TWJ Dzelzainis, K McKeever, CLS Lewis, A Otten, K Siegenthaler, D Kraus, M Roth, T White, G Gregori, DO Gericke, R Baggott, DA Chapman, K Wünsch, J Vorberger, D Riley

We have carried out X-ray scattering experiments on iron foil samples that have been compressed and heated using laser-driven shocks created with the VULCAN laser system at the Rutherford-Appleton Laboratory. This is the highest Z element studied in such experiments so far and the first time scattering from warm dense iron has been reported. Because of the importance of iron in telluric planets, the work is relevant to studies of warm dense matter in planetary interiors. We report scattering results as well as shock breakout results that, in conjunction with hydrodynamic simulations, suggest the target has been compressed to a molten state at several 100GPa pressure. Initial comparison with modelling suggests more work is needed to understand the structure factor of warm dense iron. © 2013.

Visualizing electromagnetic fields in laser-produced counter-streaming plasma experiments for collisionless shock laboratory astrophysics

Physics of Plasmas 20 (2013)

NL Kugland, JS Ross, PY Chang, RP Drake, G Fiksel, DH Froula, SH Glenzer, G Gregori, M Grosskopf, C Huntington, M Koenig, Y Kuramitsu, C Kuranz, MC Levy, E Liang, D Martinez, J Meinecke, F Miniati, T Morita, A Pelka, C Plechaty, R Presura, A Ravasio, BA Remington, B Reville, DD Ryutov, Y Sakawa, A Spitkovsky, H Takabe, HS Park

Collisionless shocks are often observed in fast-moving astrophysical plasmas, formed by non-classical viscosity that is believed to originate from collective electromagnetic fields driven by kinetic plasma instabilities. However, the development of small-scale plasma processes into large-scale structures, such as a collisionless shock, is not well understood. It is also unknown to what extent collisionless shocks contain macroscopic fields with a long coherence length. For these reasons, it is valuable to explore collisionless shock formation, including the growth and self-organization of fields, in laboratory plasmas. The experimental results presented here show at a glance with proton imaging how macroscopic fields can emerge from a system of supersonic counter-streaming plasmas produced at the OMEGA EP laser. Interpretation of these results, plans for additional measurements, and the difficulty of achieving truly collisionless conditions are discussed. Future experiments at the National Ignition Facility are expected to create fully formed collisionless shocks in plasmas with no pre-imposed magnetic field. © 2013 AIP Publishing LLC.

Comparison between x-ray scattering and velocity-interferometry measurements from shocked liquid deuterium.

Phys Rev E Stat Nonlin Soft Matter Phys 87 (2013) 043112-

K Falk, SP Regan, J Vorberger, BJ Crowley, SH Glenzer, SX Hu, CD Murphy, PB Radha, AP Jephcoat, JS Wark, DO Gericke, G Gregori

The equation of state of light elements is essential to understand the structure of Jovian planets and inertial confinement fusion research. The Omega laser was used to drive a planar shock wave in the cryogenically cooled deuterium, creating warm dense matter conditions. X-ray scattering was used to determine the spectrum near the boundary of the collective and noncollective scattering regimes using a narrow band x-ray source in backscattering geometry. Our scattering spectra are thus sensitive to the individual electron motion as well as the collective plasma behavior and provide a measurement of the electron density, temperature, and ionization state. Our data are consistent with velocity-interferometry measurements previously taken on the same shocked deuterium conditions and presented by K. Falk et al. [High Energy Density Phys. 8, 76 (2012)]. This work presents a comparison of the two diagnostic systems and offers a detailed discussion of challenges encountered.

A Monte Carlo algorithm for degenerate plasmas

Journal of Computational Physics 249 (2013) C

AE Turrell, M Sherlock, SJ Rose

Electron–positron pair creation in burning thermonuclear plasmas

High Energy Density Physics 9 (2013) 480-483

SJ Rose

Kinetic simulations of the heating of solid density plasma by femtosecond laser pulses

High Energy Density Physics 9 (2013) 38-41

M Sherlock, EG Hill, SJ Rose

X-ray scattering by many-particle systems

New Journal of Physics 15 (2013)

BJB Crowley, G Gregori

This paper reviews the treatment of high-frequency Thomson scattering in the non-relativistic and near-relativistic regimes with the primary purpose of understanding the nature of the frequency redistribution correction to the differential cross-section. This correction is generally represented by a factor involving the ratio ω α /ω β of the scattered (α) to primary (β) frequencies of the radiation. In some formulae given in the literature, the ratio appears squared, in others it does not. In Compton scattering, the frequency change is generally understood to be due to the recoil of the particle as a result of energy and momentum conservation in the photon-electron system. In this case, the Klein-Nishina formula gives the redistribution factor as . In the case of scattering by a many-particle system, however, the frequency and momentum changes are no longer directly interdependent but depend also upon the properties of the medium, which are encoded in the dynamic structure factor. We show that the redistribution factor explicit in the quantum cross-section (that seen by a photon) is ω α /ω β, which is not squared. Formulae for the many-body cross-section given in the literature, in which the factor is squared, can often be attributed to a different (classical) definition of the cross-section, though not all authors are explicit about which definition they are using. What is shown not to be true is that the structure factor simply gives the ratio of the many-electron to one-electron differential cross-sections, as is sometimes supposed. Mixing up the cross-section definitions can lead to errors when describing x-ray scattering. We illustrate the nature of the discrepancy by deriving the energy-integrated angular distributions, with first-order relativistic corrections, for classical and quantum scattering measurements, as well as the radiative opacity for photon diffusion in a Thomson-scattering medium, which is generally considered to be governed by quantum processes. © IOP Publishing and Deutsche Physikalische Gesellschaft.

Fourier-transform inelastic X-ray scattering from time- and momentum-dependent phonon-phonon correlations

Nature Physics (2013)

M Trigo, M Fuchs, J Chen, MP Jiang, AM Lindenberg, DA Reis, K Gaffney, S Ghimire, ME Kozina, G Ndabashimiye, M Cammarata, DM Fritz, H Lemke, D Zhu, S Fahy, A Higginbotham, JS Wark, SL Johnson, J Larsson, F Quirin, K Sokolowski-Tinten, C Uher, G Wang

The macroscopic characteristics of a material are determined by its elementary excitations, which dictate the response of the system to external stimuli. The spectrum of excitations is related to fluctuations in the density-density correlations and is typically measured through frequency-domain neutron or X-ray scattering. Time-domain measurements of these correlations could yield a more direct way to investigate the excitations of solids and their couplings both near to and far from equilibrium. Here we show that we can access large portions of the phonon dispersion of germanium by measuring the diffuse scattering from femtosecond X-ray free-electron laser pulses. A femtosecond optical laser pulse slightly quenches the vibrational frequencies, producing pairs of high-wavevector phonons with opposite momenta. These phonons manifest themselves as time-dependent coherences in the displacement correlations probed by the X-ray scattering. As the coherences are preferentially created in regions of strong electron-phonon coupling, the time-resolved approach is a natural spectroscopic tool for probing low-energy collective excitations in solids, and their microscopic interactions.

Orbital-free density-functional theory simulations of the dynamic structure factor of warm dense aluminum

Physical Review Letters 111 (2013)

TG White, S Richardson, BJB Crowley, LK Pattison, JWO Harris, G Gregori

Here, we report orbital-free density-functional theory (OF DFT) molecular dynamics simulations of the dynamic ion structure factor of warm solid density aluminum at T=0.5 eV and T=5 eV. We validate the OF DFT method in the warm dense matter regime through comparison of the static and thermodynamic properties with the more complete Kohn-Sham DFT. This extension of OF DFT to dynamic properties indicates that previously used models based on classical molecular dynamics may be inadequate to capture fully the low frequency dynamics of the response function. © 2013 American Physical Society.