• planetology
• high intensity lasers
• high energy density physics
• experimental physics
• equation of state
• plasma physics
• shock physics
• warm dense matter

The study of planetary interiors is a key concern for the purpose of providing a unified framework about planets' formation, evolution and structure.
Today this purpose also acquires new significance because of the active effort of research and discovery of extrasolar planets.
Reliable classication methods are needed if we want to be able of distinguish habitable Earth-like planets in the remote case of their finding.
Planets of our Solar System are thus studied for both their specific interest and their role as better-known prototypes for classification and modeling of exoplanets.
A major obstacle for this kind of study is represented by the substantial impossibility to directly probe the planets interiors. While the internal structure of our Earth can be inferred by means of analysis of seismic waves, for the other solar planets probing is limited to the surface (Mars) or even to a fly-by in the upper atmosphere (giant planets). In the last case, the only data in our possession are measurements of mass, magnetic and gravitational fields, luminosity, radii etc.
Therefore, a model is needed to couple these observables in a self-consistent way with the interior structure and dynamics.
In this context, an accurate modeling requires a precise knowledge of structural and transport properties of some key elements (e.g. iron for our Earth), such as the equation of state (EoS), phase diagram, conductivity, diffusion coefficients, chemical reactions' rates, etc.
Conductivity is a crucial variable for dynamo action, a magneto-hydrodynamic
mechanism trough which the internal currents of a planet can self-consistently produce a magnetic field.
The equation of state of a material links its pressure, density and temperature and is thus a key ingredient for interior structure models.
It should be pointed that even small uncertainties on the measurement or computation of these physical properties can significantly affect the inferred structures and evolution models and lead to unsolvable dichotomies. This is the case for the EoS of hydrogen/helium with respect to the internal structure of Jupiter and Saturn. For example, the uncertainty of H EoS is at the base of the debate whether these planets have a core or not [Saumon and Guillot (2004)].
Matter in planetary interiors lies in very extreme conditions of several Mbar pressures and 0.1 - 1 eV temperature. These exotic states, at the interface between a classic plasma and condensed matter, are referred to as Warm Dense Matter (WDM).
Establish equation of state and transport properties in this regime is a real challenge from both theoretical and experimental point of view. Indeed, at these thermodynamical conditions matter is a highly coupled and degenerate plasma.
On one side, many useful approximations typical of ideal plasmas cannot be worked out. On the other side, quantum effects have to be accounted for. These two effects extremely complicate the treatment of WDM.
Very complex ab initio calculations from the very first principles of quantum mechanics have thus to be employed to model these peculiar conditions, with a dramatic increase of the computational cost. The available data are therefore limited in number and do not span the totality of the pertinent thermodynamical conditions for planetary modeling.
On the other side, experiments have to deal with difficulties in both recreate extreme planetary interiors Mbar pressures and eV temperatures and characterize these states with pertinent diagnostics.
There are two approaches to generate the high required pressures: static techniques, based on diamond anvil cells (DAC) and dynamic methods which employ the propagation of a shock wave. In this last case, the EoS of the shocked sample can be inferred from a shock velocity measurement using the Rankine-Hugoniot relations [Rankine (1870); Hugoniot (1887)], which express the conservation of mass, momentum and energy when a shock wave - an abrupt change of thermodynamical variables – propagates in a material.
DAC studies are technically limited to a few Mbar and too low temperatures, while dynamic compressions reach very high pressures, up to 100 Mbar, but too high temperatures because of the dissipative nature of this process.
Alternative approaches can combine the two methods to attain a wider range of thermodynamical conditions.
There are many ways to generate a shock wave, among which we cite chemical and nuclear explosions, Z-pinches, light-gas gun impact and high power lasers.
In this work, we make use of laser-driven shock waves to study the EoS and reflectivity of C-H-N-O mixtures that simulate the atomic composition of the mantle of the icy giants in the Solar System, namely Uranus and Neptune.
These data will bring key elements on the behaviour of these mixtures at extreme pressures useful for a better understanding of the two planets.
Indeed, only few data exist in literature and are limited to 1 Mbar. Our goal was to extend them to higher pressures and obtain reflectivity measurements useful for the understanding of Uranus' and Neptune's magnetic field and structure.
Our experimental campaign took place in January 2016 at the GEKKO XII laser facility in Osaka, Japan. We obtained 11 shots available for the analysis: 5 on the C-H-N-O mixture, 5 on a C-H-O mixture and one on pure water. The samples, starting from ambient conditions, were compressed via a single shock.
Optical diagnostics allowed the time-resolved measurement of the self-emission of the shocked sample, of the shock velocity (via Doppler interferometry) and of the reflectivity of the shock front.
We were able to obtain the pressure of the shocked sample, its fluid velocity and its density by means of the impedance mismatching technique [Benuzzi (1997)] from the analysis of the shock velocity in the sample and in a well known reference material.
Temperature was obtained from self-emission and reflectivity data using the Planck's law with a grey-body hypothesis.
The errors on the extracted variables were estimated by means of Monte-Carlo codes.
We obtained the equation of state and reflectivity of C-H-O and C-H-N-O (synthetic Uranus) mixtures along the principal Hugoniot up to 3 Mbar.
A single shot on water, principally aimed at validating calibrations and methods of the entire experimental campaign, has given EoS and reflectivity results in full agreement with the available literature.
The equation-of-state data obtained in this up to now uncharted region allow us to better characterize the structural properties of these planetary mixtures in a wider area of the phase plane. From a practical point of view, a more precise relation between shock velocity and pressure achieved in this work permits to get pressure-dependent measurements using shock velocity measured with precision by Doppler interferometry.
Furthermore, we can conclude that, while water EoS and carbon-bearing mixtures (C-H-O, C-H-N-O) EoS display signicative differences at high pressures, those between the EoS of C-H-O and C-H-N-O mixtures are negligible. These data suggest that the small amount of nitrogen present in synthetic Uranus does not impact the EoS. Similar results have been obtained for reflectivity [Ozaki (2016)]. We should clarify whether this low impact of nitrogen on EoS and reflectivity behaviour is due to its small amount or this is the case even for higher concentrations, as suggested by
Bethkenhagen et al. (2015). This will be done by experimental investigation
of mixtures with different nitrogen concentrations.
On the contrary, the chemical reasons of the highly relevant effect of carbon on the equation of state and optical properties, such as polymerization [Chau et al. (2011)], must be investigated by means of further ab initio calculations.