THE laser experiments team knew they had to scramble. The dismantling of Nova, the world's largest laser, was on the agenda. Lawrence Livermore's even larger laser facility, the National Ignition Facility (NIF), needed Nova's space for support facilities as NIF construction was progressing. The two-beam laser target area necessary for the experiment was scheduled to be shut down imminently, and the Nova schedule was very full. But a place in line suddenly became available. Team members knew this was their opportunity to repeat some important but difficult work using new diagnostic techniques with the Nova facility. They were going to perform another round of experiments to laser-shock and compress deuterium, an isotope of hydrogen, and turn the element most familiar in a gaseous form into a metal.|
For this experiment, Nova would be used to create conditions not very different from the atmospheres of giant planets and the outer envelopes of low-mass, largely hydrogen stars. The laser would subject hydrogen to extreme and hitherto unexplored pressure regimes. It would pulverize deuterium samples, allowing experimenters to collect, analyze, and verify thermodynamic and optical information about how hydrogen goes metallic.
The results would establish a substantially improved equation of state for the element hydrogen. They would also add to our understanding of large planets and stars, make it easier to design fusion targets for NIF's 192 laser beams, and prove important for DOE's stockpile stewardship mission by providing new high-pressure deuterium data critical to safety and reliability assurances of the nation's nuclear weapons.
Simplicity Poses Difficulties
Experimentation to Guide Theory
Tools for Shock Experiments
It Took Three Laser Beams|
The experiments were conducted with three simultaneous laser beams: two from Nova (Figure 2) and the third from a tabletop laser. One Nova beam was used for shocking the deuterium. The laser shot blasted the target's polystyrene layer, which heated up rapidly to drive a shock wave into the pusher and compress the deuterium. Aimed at the target cell, the laser's high energies produced a long and steady shock wave. The beam was smoothed by a phase plate to ensure a spatially planar and uniform shock front, critical for accurate measurements. If the shock had been delivered as a small, nonuniform laser spot, experimental data would have been difficult or impossible to interpret, and "edge effects" would interfere with the results as well.
The second Nova laser beam was used to create an x-ray source for transverse radiography by irradiating a nearby iron foil. X rays from the iron plasma illuminated the target cell from the side. The shocked deuterium absorbed and refracted the x-ray light differently because it had been changed by the propagating shock wave. The
x rays transmitted through the cell were collected by a Kirkpatrick-Baez microscope, which improved data resolution, and were then focused onto a streak camera. In this way, the experimenters tracked the propagation of the shock front to find the shock speed. The pusher-deuterium interface, which moved at the particle speed, was tracked to determine that speed. Combining these speeds produced a single Hugoniot data point.|
An example of a streaked radiograph of shock-compressed deuterium is shown in Figure 3. Because the pusher is opaque and the liquid deuterium is transparent, the interface between them is the boundary between the light and dark regions. When the laser-driven shock crossed the interface at 2 nanoseconds, the pusher surface accelerated to a steady speed, i.e., the particle speed. As the shock wave headed into the deuterium, a shock front (visible as a dark line because the backlight x rays refract at density differences) moved ahead of the interface. The shock and particle speeds were determined from the film. The shock propagated steadily until a second, stronger shock, caused by shock reverberation in the pusher, entered the deuterium at 6 nanoseconds.
The third laser beam was used for optical interferometric measurements. In the earlier set of laser-shock experiments, this third beam was configured as a Michelson interferometer to monitor how much the target cell heated up before the arrival of the shock wave. This "preheat" had to be accounted for, or calculations of the shocked material's initial density would be inaccurate. The experiments would determine the compression (the ratio of shocked to unshocked deuterium densities), so knowledge of the initial, unshocked density was extremely important.
The Michelson interferometer beam was directed through the sapphire window at the bottom of the target cell. Its function was to monitor the movement of the pusher surface, indicative of expansion from radiative heating. The interferometer imaged this movement by splitting its beam into two arms: a reference arm and a sample arm that bounced off the pusher surface. When the two arms were recombined, their phase differences resulted in light fringes (bands caused by diffraction) that revealed, through measurements as small as a few tens of nanometers, what motion was detected in the pusher surface. The incorporation of a polystyrene coat on top of the pusher kept its bottom surface temperature below the detection limit of 400 kelvin.
The Michelson interferometer measurements had one additional use. Its reference beam verified the planarity and uniformity of the arriving shock wave. Experimenters saw that the shock front was uniform and planar to within 2.5 micrometers over a lateral region of 350 micrometers.
With concerns over preheat and shock-wave quality out of the way, it was unnecessary to repeat the Michelson interferometer measurements for the second set of laser experiments. Instead, the third beam was set up for velocity interferometry to determine the velocity and, importantly, reflectivity of the shock front. Because of its relationship to electrical conductivity, the reflectivity measurement established the occurrence of metallization.
Then There Were Measurements|
The velocity interferometer used in these experiments was a particularly accurate instrument for measuring motion-in this case, the speed of the reflecting surface of a moving shock front. Unlike a conventional interferometer that first splits a laser beam into two arms, this interferometer shot the whole beam onto the experimental sample and split the beam after it exited the sample. Then one beam was passed through a piece of glass, called an etalon, which slowed it down. Because of this induced time delay in one arm, recombining the beams generated light fringes. The fringes changed when the shock front moved, doing so in proportion to shock speed.
Figure 4 shows a streak velocity interferogram. For times before t = 0, the fringes are reflections of the stationary pusher surface. For t > 0, the reflection is from the shock front in the deuterium. The amount of the fringe shift at t = 0 is proportional to the speed of the shock front.
The difference in reflected light intensity originating from the motionless pusher surface and that from the shock front moving in the deuterium reveals the reflectivity of the shock. The pressure at which a change in reflectivity occurs can be determined because particle and shock speeds can be measured. The measured reflectivity at low shock pressure (0.2 megabar) is only a few percent. Above 0.55 megabar, however, the measured reflectivity is about 60 percent-characteristic of a poorly reflecting metal. This measurement proves that the deuterium changed from an insulating state to a conducting one. The data also show that the transition occurs simultaneously with the earlier observed high compression. These effects are linked: the high compression is a result of the transition.
In addition to these measurements, the temperature of the shock was determined by recording the light emission of the shock front in several wavelength bands. An optical pyrometer viewed the shock through the sapphire window in the cell. Temperature is a fundamental component of the EOS, but it cannot be derived from the Hugoniot relations. It must be found separately. Because the form of the wavelength-dependent light intensity is a known function of temperature, fitting the emission data into that formula allowed the experimenters to find the value of temperature.
Implications for Hydrogen's EOS|
The experimental team was tired but elated with their results. The data obtained from the latest round of effort would once again recharge their work on hydrogen theory and, furthermore, bring experimentation to another level. Their work had provided the first direct evidence on the Hugoniot to support the hypothesis that liquid deuterium transforms from a molecular fluid into a monatomic metallic fluid at lower pressures than postulated by earlier theoretical models.
Figure 5 shows the measured Hugoniot as pressure versus density. The figure compares Hugoniot curves for the laser data with a linear mixing model proposed by Livermore scientist Marvin Ross, an earlier model in the SESAME EOS library, the prediction of Saumon and Chabrier, and the Livermore light-gas-gun data. At the lowest compression, the laser data are in agreement with the gas-gun results, while at higher compressions, the data significantly deviate from the SESAME prediction. The data at 0.25 megabar are significant because they overlap the gas-gun data, providing confidence in current results. The current data show an enhanced compressibility similar to that of the Ross linear mixing model in the region where strong molecular dissociation is predicted. Although the shocked density at 1 megabar is close to that of Saumon and Chabrier, the data do not show the abrupt transition predicted by their model. The conclusion is that molecular dissociation and ionization are significant factors in hydrogen isotopes compressed to megabar pressures. Reflectivity measurements, using the measured Hugoniot to find the pressure, are shown in Figure 6.
The current data provide an important benchmark for a revised EOS model of hydrogen and its isotopes in a regime relevant to high-energy-density physics applications. Additionally, the experiments demonstrate that laser-driven shock waves can effectively be used for EOS studies at pressures beyond those attainable by traditional techniques. The new hydrogen EOS will change the way planets such as Jupiter are modeled, especially the size of its metallic core. For fusion occurring on Earth, the higher compressibility of deuterium will make the goal of laboratory thermonuclear fusion easier to achieve than previously thought.
Prize-Winning Basic Science
*Results apply to deuterium, hydrogen, and tritium; the experiment used deuterium for convenience.
Key Words: equation of state (EOS), gas gun, high-energy density, Hugoniot, metallized hydrogen, Nova laser.
1. L. B. Da Silva et al., Physical Review Letters, Vol. 78, No. 3 (January 1997), pp. 483-486.
For further information contact Robert C. Cauble (925) 422-4724 (firstname.lastname@example.org).
ABOUT THE SCIENTIST
ROBERT C. CAUBLE received his B.S. in physics in 1974 from the University of Arizona and his Ph.D. in nuclear engineering from the University of Michigan in 1980. In 1980, Cauble worked at the Naval Research Laboratory on theoretical predictions of the effects of high-density plasma on atomic transitions and particle transport. He came to Lawrence Livermore in 1985 to work on projects to produce atomic models for plasma simulations and to design and analyze experiments to use laboratory x-ray lasers as high-density-plasma probes and interferometers. More recently, he has worked on large-scale simulations and designs of experiments to elicit material properties, mainly equation-of-state data at extreme pressures using intense, laser-driven shocks.