My DPhil research project (Oxford)

Coming to the end of my DPhil (PhD) people often ask me what it is actually that I do. I believe that all Physics can be explained in the simplest terms and since this particular one actually has some exciting applications (at least I think so) in many fields including Astrophysics and thermonuclear fusion, I feel like this could be of an interest to the wider general public. So here it is ...

Inferring The Equation of State of Shocked Liquid Deuterium Under Conditions Relevant to the Interiors of Giant Planets and Inertial Confinement Fusion

A detailed understanding of the thermodynamics of light elements under extreme conditions is essential for the modeling of the evolution and inner structure of many astrophysical objects including Jovian planets and brown dwarfs [1]. A knowledge of the equation of state (EOS) of hydrogen and its isotopes is also important for inertial confinement fusion (ICF) research. Under such conditions, with high pressures (in the Mbar region) and temperatures of the order of 0.1 to 1 eV (thousands of degrees), quantum degeneracy and strong inter-particle forces play an important role. The theoretical description of the EOS in this regime, often referred to as warm dense matter (WDM), is thus very challenging. Thanks to recent technological advances, such extreme condition can be produced in the laboratory using fast shocks created by laser ablation at high power laser facilities giving us a unique opportunity to directly study these extraordinary astrophysical objects here on Earth. Such experiments are very challenging, but some of the latest diagnostics developments have now given us the tools to obtain highly accurate measurements.

Phase diagram for the WDM regime. WDM lies between condensed matter (CM), hot dense matter (HDM) and ideal plasma (low densities), and overlaps the planar laser generated shocks in matter as well as the astrophysical conditions. Inserted images show the internal layers of Jupiter and laser irradiation of a golden holhraum during a inertial confinement fusion (ICF) implosion.

In my research I combine a range of experimental techniques and theoretical models used to characterize warm dense deuterium in a project that I have now been working for more than two years. The OMEGA laser at the Laboratory for Laser Energetics (LLE) at the University of Rochester was used to directly drive a shock wave in a planar liquid-deuterium target through ablation of the laser-heated material similar to the rocket propulsion, which creates very dense hot plasma within the target [2].

Schematic of the Omega laser system (a), photograph of the target chamber (b), schematic of port locations on the target chamber (c), and target set up with the laser drive and backlighter/scattering configuration (d).

The shocked D2 conditions were diagnosed using x-ray scattering and shock velocity measurements made by use of a velocity interferometer system for any reflector (VISAR) in conjunction with complementary temperature measurement inferred from streaked optical pyrometry (SOP) [3, 4, 5, 6]. My analysis is based on three different theoretical EOS models: i) the SESAME tables, widely used for ICF applications [7]; ii) the model by Saumon and Chabrier that spans a wide range of conditions and is often used for astrophysical purposes [8]; and iii) density-functional molecular dynamics (DFT-MD) simulations of fluid hydrogen developed by our collaborators at the University of Warwick [9].

Schematic of the target set up with the laser drive with VISAR laser set up (a) and the backlighter/scattering configuration (b). A constant intensity 6 ns laser drive incident on the CH ablator compresses and heats the material inside a planar layer of liquid deuterium target, like a rocket, creating WDM. When VISAR is used, the laser drive 1013 W/cm2 comes from the left side. In the scattering experiment, sixteen tightly focused beams irradiate a saran backlighter from the left side creating the x-ray probe emission, while the laser drive comes from the right side. The scattered x-ray emission scattered at 90 degrees and is detected with a crystal spectrometer. 

VISAR has previously been used to obtain the pressure and density of the shocked deuterium by use of impedance matching (IM) techniques using a pressure standard. This technique has recently been proven to introduce significant errors into the EOS of hydrogen and its isotopes. I was however able to develop an alternative approach, which bypasses the need for a pressure reference by a direct comparison of the shock velocity measured by VISAR with theoretical models and simultaneous validation of the EOS inferred temperature with the SOP measurement and inferred reflectivity [10]. It was found that EOS tables based on ab initio DFT-MD simulations can provide such consistency whereas other EOS models fail to produce a consistent description of all measured data. 

VISAR results: (a) image from one of the interferometer arms in the VISAR system, (b) calculated velocity measurement from the two VISAR arms (red and blue traces) and the temperature of the emitting shock front calculated from the SOP measurement fitted with the grey body approximation using reflectivity of 0.45 obtained from DFT-MD simulation (black solid line). The shock forms at t = 0 ns as soon as the laser pulse hits the surface of the target, which is instantly observed by SOP. The shockwave becomes reflective ∼1.5 ns later when VISAR records the signal. (c) Hugoniot curves as function of compression ratio ρ/ρ0 calculated from the SESAME 5263 table [7] (red dot-dashed line), SESAME 5265 (yellow thin dashed line), S&C [8] (green thick dashed line) and our DFT-MD [9] (solid blue line) EOS models for deuterium. The initial conditions are: P0 ∼ 1.38 × 10^5 Pa, ρ0 = 0.175 g/cm3 and T0 = 18 K. The conditions extracted from each model for the shockwave travelling at Us = 16.9 km/s are marked by red, green, and blue circles, respectively.

This experimental campaign also introduced the first x-ray Thomson scattering data from shocked deuterium, a new powerful technique capable of inferring the density, temperature and ionization state of studied sample from a single spectrum [11]. This complementary data provided an excellent agreement with the VISAR and SOP as well as the DFT-MD theoretical model making this a unique self-consistent EOS measurement [10]. Our findings suggest a higher compressibility of hydrogen in the measured regime, which has serious implications for Jupiter’s structure, in particular on the size of its core, the required concentration of heavier elements, and the location of the molecular to metallic transition. 

Measurement of (a) Cl Ly-α emission incident on shocked liquid deuterium and (b) Cl Ly-alpha emission scattered from shocked liquid deuterium. The scattered spectrum has a strong Rayleigh peak around 2960 eV and a Compton downshifted feature. The splitting of the Cl Lyα emission is observed in the scattered spectrum, but not in the incident spectrum, due to differences in the amount of source broadening in each measurement. The scattered spectrum was fitted with the X-ray scattering code (XRS) code and Te = 3±2 eV, Z ~ 0.35±0.15 and ne = 0.4±0.2 x 10^23cm^-3 were inferred [4].

I also work on static compression using diamond anvil cells that compress the samples statically to very high densities can be used to create steady state conditions which are more representative of the planetary interiors than laser-shock experiments. In this technique, two perfectly polished diamond anvils are used to create extreme pressures in the GPa regime. I am using various diagnostic techniques including x-ray scattering and diffraction carried out at the Diamond Light Source synchrotron facility as well as laser Raman spectroscopy to study the microscopic structure of the fluid and solid hydrogen and deuterium as well as H or D miscibility with He in mixtures relevant to the interior of Jupiter.

Diamond experiment layout including (a) a schematic of the apparatus  arrangement with the cylindrically bend HAPG crystal spectrometer in Von Hamos  geometry, (b) photograph of the Oxford cell holding the diamond anvils with hydrogen gas load, (c) photograph of the Diamond synchrotron facility (RAL) and (d)  microscope view of the compressed H DAC gasket interior with colourful birefringence effect resulting from the strain within the diamond anvils. 

In one of our DAC experiments we have managed to obtain a measurement of inelastic scattering spectra across the liquid to solid phase transition in hydrogen. The scattering signal from statically compressed hydrogen inside diamond anvil cells at 2.8 GPa and 6.4 GPa was measured at the Diamond Light Source synchrotron facility in the UK. The first direct measurement of the local field correction (G) to the Coulomb interactions in degenerate plasmas was obtained from spectral shifts in the inelastic scattering peak and compared to predictions by the Utsumi-Ichimaru theory for degenerate electron liquids [12, 13]. This is important since the local field correction can be linked to dynamic properties of the compressed material, namely the isothermal compressibility and conductivity.

Normalized plots of the electron-electron feature of the scattering spectrum for H at 2.8 GPa. There is a noticeable shift of 17±1 eV between the peaks of the calculated spectrum using the Utsumi-Ichimaru theory and the data obtained from experiment (assuming a nearly free electron gas for the solid H), which is a result of our assumptions breaking down in the case of liquid hydrogen, where the electrons are no longer free and short range correlations can become important. The calculated response overlaps with the experimental data for G(k = 5.59 ± 0.19 x 10^10 m^−1, \omega = 130 eV) = −9 ± 1.5 (red dots).

The full thesis can be downloaded here:
https://ora.ox.ac.uk/objects/uuid:9aa33691-48f0-430f-a8cf-48795ad8f7c7
References:

[1] T. Guillot, Science 286, 72‐77 (1999).
[2] S. P. Regan et al., J. Phys.: Conf. Ser. 244 042017 (2010).
[3] S. H. Glenzer & R. Redmer, Rev. Mod. Phys. 81, 1625 (2009).
[4] G. Gregori et al., Phys. Rev. E 67, 026412 (2003).
[5] P. M. Celliers et al., Rev. Sci. Instrum. 75, 11 (2004).
[6] J. E. Miller et al., Rev. Sci. Instrum. 78, 0349903 (2007).
[7] G. I. Kerley, Phys. Earth Planet. Interiors 6, 78‐82 (1972).
[8] D. Saumon and G. Chabrier, Phys. Rev. A 46, 4 (1992).
[9] J. Vorberger et al., Phys. Rev. B 75, 024206 (2007).
[10] K. Falk et al., HEDP 8 (1), 76-80 (2012).
[11] S. P. Regan, K. Falk, G. Gregori, et al., Phys. Rev. Lett. (2012).
[12] Ichimaru S 1982 Rev. Mod. Phys 54, 4 (1982).
[13] K. Falk et al., J. Phys.: Conf. Ser. 244, 042014 (2010).

More info can be found on:

http://www.physics.ox.ac.uk/users/gregorig/research/xrts/eos/eos.html
http://www.lle.rochester.edu/
http://www.diamond.ac.uk/