Measurements of the principal Hugoniots of dense gaseous deuterium-helium mixtures: Combined multi-channel optical pyrometry, velocity interferometry, and streak optical pyrometry measurements , , Zhi-Guo Li, Qi-Feng Chen , Yun-Jun Gu, Jun Zheng, and Xiang-Rong Chen Citation: AIP Advances 6, 105309 (2016); doi: 10.1063/1.4966211 View online: http://dx.doi.org/10.1063/1.4966211 View Table of Contents: http://aip.scitation.org/toc/adv/6/10 Published by the American Institute of Physics AIP ADVANCES 6, 105309 (2016) Measurements of the principal Hugoniots of dense gaseous deuterium−helium mixtures: Combined multi-channel optical pyrometry, velocity interferometry, and streak optical pyrometry measurements Zhi-Guo Li,1,2 Qi-Feng Chen,1,a Yun-Jun Gu,1 Jun Zheng,1 and Xiang-Rong Chen2,a National Key Laboratory for Shock Wave and Detonation Physics, Institute of Fluid Physics, P.O Box 919-102, Mianyang, Sichuan, People’s Republic of China College of Physical Science and Technology, Sichuan University, Chengdu 610064, People’s Republic of China (Received 30 January 2016; accepted 13 October 2016; published online 20 October 2016) The accurate hydrodynamic description of an event or system that addresses the equations of state, phase transitions, dissociations, ionizations, and compressions, determines how materials respond to a wide range of physical environments To understand dense matter behavior in extreme conditions requires the continual development of diagnostic methods for accurate measurements of the physical parameters Here, we present a comprehensive diagnostic technique that comprises optical pyrometry, velocity interferometry, and time-resolved spectroscopy This technique was applied to shock compression experiments of dense gaseous deuterium–helium mixtures driven via a two-stage light gas gun The advantage of this approach lies in providing measurements of multiple physical parameters in a single experiment, such as light radiation histories, particle velocity profiles, and time-resolved spectra, which enables simultaneous measurements of shock velocity, particle velocity, pressure, density, and temperature and expands understanding of dense high pressure shock situations The combination of multiple diagnostics also allows different experimental observables to be measured and cross-checked Additionally, it implements an accurate measurement of the principal Hugoniots of deuterium☞helium mixtures, which provides a benchmark for the impedance matching measurement technique © 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4966211] I INTRODUCTION The unique behaviors of deuterium and helium under high pressures and temperatures are always of great scientific interest related to several significant problems in modern physics In particular, modeling giant planets, developing inertial confinement fusion, and synthesizing hydrogenium are strongly related to the properties of deuterium and helium under extreme conditions.1 The key to solving these problems is the accurate measurement and determination of the equation of state (EOS) of deuterium, helium, and their mixtures over a wide range of pressures and temperatures.2 In the past several decades, much experimental effort has been directed towards deuterium or helium on aspects such as the two-stage light gas gun,3,4 convergent explosives,5–7 magnetically launched flyer 8–11 and laser-driven shock experiments.12–20 In shock experiments, a single shock drives the material to a point on the principal Hugoniot, and the Rankine–Hugoniot conservation equations relate the states of the material before and after a Authors to whom correspondence should be addressed Electronic addresses: chenqf01@gmail.com and xrchen@scu.edu.cn 2158-3226/2016/6(10)/105309/10 6, 105309-1 © Author(s) 2016 105309-2 Li et al AIP Advances 6, 105309 (2016) shock compression by P − P0 = ρ0 Us − Up , (1) ρ ρ = Us Us − Up , (2) where P0 and ρ0 are the initial pressure and density, whereas P and ρ are the corresponding parameters after shock compression Apparently, the measurements of the single shock pressure and density need simultaneously measurement of shock velocity U s , particle velocity U p , and initial density ρ0 Measurements of the particle velocity behind the shock front are really difficult Therefore, most experiments use the impedance matching (IM) method to determine the pressure and density of the shocked deuterium or helium This technique requires a shock pusher with well-known EOS that transfers the shock into the sample and is used to determine the Hugoniot A few attempts to measure the Hugoniot by by-passing the need for shock pushers have been reported In 1997 and 1998, Da Silva et al developed side-on radiography for absolute measurements of the Hugoniot of liquid deuterium in Nova laser-driven shock experiments.19,20 However, the traverse radiography method has raised doubts in the measurements of particle velocities, which might have been affected by the quality of the aluminum-pusher/deuterium interface Recently, Falk et al performed EOS experiments for deuterium using the Omega laser.12,15 Indeed, they obtained the shock pressure and density of liquid deuterium with the help of theoretical models through comparisons with experimental observables of shock velocity measured by a velocity interferometer system for any reflector (VISAR) and temperature measured by an independent streaked-opticalpyrometry (SOP) system Nevertheless, accurate measurements of EOSs for deuterium and helium are still challenging In particular, the EOS of their mixtures has not been experimentally determined so far Multi-shock compression proves possible to implement much higher compression of plasmas in relation to what we have in a single shot There has been some creative multi-shock experiments were performed for hydrogen,21 helium,21,22 and hydrogen-helium mixtures.23 In general, the multi-shock (more than twice) states are much more difficult to measure directly Therefore, the multi-shock EOSs were usually obtained with the help of hydrodynamic simulations.21–23 In this paper, we present results of the measurements of the Hugoniots of dense gaseous deuterium–helium (D2 ☞He) mixtures A comprehensive diagnostic technique that combines multiple diagnostics enables us to implement (1) an accurate measurement of the single shock state of D2 ☞He mixtures, and (2) the direct measurements of multi-shock states (3) It also provides an experimental paradigm for combining multiple diagnostics that increases the experimental throughput and allows for a more complete set of experimental observables Thus, we get improved information and expanded understanding of dense high pressure shock situations Below we describe this technique and explain the above three aspects (1), (2), and (3) in detail II EXPERIMENTAL DESIGN For the implementation of the comprehensive diagnostic technique, we designed a specific target scheme, which mainly consisted of a steel sample cell with a front baseplate made of stainless steel 304 and a rear composite window The schematic of this target is shown in the left panel of Fig The steel baseplate, with a thickness of 5.0 mm, serves as the shock pusher, which was also used as the pressure standard for IM measurements The initial thickness of the steel sample cell is ∼5.0☞7.0 mm, which was measured from baseplate/sample interface to sample/LiF interface The steel sample cell was filled with the gaseous equimolar-mixed D2 ☞He sample Before shock compression, the D2 ☞He gas was precompressed to a dense state with a pressure of around 20 or 40 MPa from ambient conditions by pressurization devices to gain high initial density The initial density ρ0 of dense D2 ☞He sample was measured with a draining method and a special pressure vessel.24 The uncertainty in ρ0 is around 0.2%, which mainly comes from the random errors in measuring the density and volume of the vessel The composite window is the most important part of the target, which consists of one layer of 4.0 mm thick lithium fluoride (LiF) and one layer of 2.0 mm thick sapphire (Al2 O3 ) behind the LiF to prevent 105309-3 Li et al AIP Advances 6, 105309 (2016) FIG Sketch of the precompressed D2 ☞He mixture target (left) and arrangement of diagnostic probes (right) used in the experiments precompression fracturing A 0.003 mm thick aluminum (Al) film is plated on the front surface (the side towards the flyer) of LiF, which serves as a reflecting interface for velocity interferometry to measure the velocity of the sample/LiF interface Moreover, a 0.13 mm thick Al foil is attached to the aluminum film to maintain the integrity of the aluminum film in multi-shock processes Aluminum was selected because its shock impedance matches approximately that of LiF Apertures, one with a diameter of 4.0 mm and two with a diameter of 1.25 mm, were incorporated on the Al foil and film The aperture of 4.0 mm in diameter was designed to allow the light emitted from the shocked D2 ☞He samples to be measured And the apertures of 1.25 mm in diameter were designed to allow the probe lasers of the velocity interferometer devices to pass through for measuring the velocity of the baseplate/sample interface or shock wave front In our experiments, strong planar shock waves were generated from the impact of high velocity tantalum (Ta) flyers into precompressed D2 ☞He mixture targets The waves then reverberated between the steel baseplate and the composite window to compress the D2 ☞He mixtures The Ta flyer, with a thickness of about 3.3 mm, was accelerated to velocities 4.97☞5.99 km/s using a two-stage light gas gun with a bore diameter of 30.0 mm The sizes of the flyer, baseplate, sample cell, and windows were optimized to ensure that the rarefaction and catch-up waves would not compromise the one-dimension character of compression in the optically observed region The comprehensive diagnostic system consists of two sets of velocity interferometer devices☞Doppler pins system (DPS), two sets of multi-channel optical pyrometers (MCOPs),25 and a streak optical pyrometer (SOP) system with a spectrometer coupled to an optical streak camera The arrangement of these diagnostic devices is shown in the right panel of Fig A 13-fiber bundle positioned at the central area (corresponding to the mm diameter aperture) of the rear sapphire window was used to collect the light emitted from the shocked samples and to direct the light to two sets of six-channel pyrometers with different precisions and the SOP system The six channels of MCOP were centered at six wavelengths between 400 and 700 nm The relatively large sample in these experiments enabled fibers with diameter of 62.5 µm to be used The numerical aperture (N.A.) of the fibers is 0.275 Before each shot, the MCOPs and SOP were carefully calibrated using a standard tungsten light source for shock temperature measurements This calibration is similar to that described in the work of Gu et al.26 and Ni et al.27 The twelve pins connected to the DPS via fibers were distributed symmetrically in four rings of diameters 5.4, 8.0, 10.0, and 12.4 mm, and used to launch the probe laser beams from DPS operating at a wavelength of 1550 nm and to collect the light returning to the DPS The probe laser beams from DPS-I were directed onto the baseplate/sample interface or shock wave front through the 1.25 mm diameter apertures to measure its velocity; the probe laser beams from DPS-II were directly reflected by the Al reflecting film to measure the velocity of sample/LiF interface The velocities of the baseplate/sample and sample/LiF interfaces were determined, with an accuracy of 0.5% via the Doppler shift interference fringes of the reflected light These measurements enable us to obtain all the required variables of shock velocity, particle velocity, pressure, density, and temperature 105309-4 Li et al AIP Advances 6, 105309 (2016) III RESULTS AND DISCUSSION The experimental records for different shots are similar, here, we present a typical experimental record obtained from shot no 140624, as shown in Fig Fig 2(a) is the time-resolved light radiation of shocked D2 ☞He mixtures recorded by MCOP, which provides a clear indication of shock arrival time at baseplate/sample interface (t ) and sample/LiF interface (t ) When the shock produced by the impact between steel baseplate and Ta flyer reached the baseplate/sample interface (t ), a rarefaction wave and a shock wave were generated The rarefaction wave went back into the baseplate and the shock wave entered the sample (the first shock) The signal of MCOP shows a small slope with time during the first shock transit, which can be clearly seen from 430 nm channel This means that the radiation from the first shocked sample has a continuous and small increase with time, which suggests that the first shocked sample is partially transparent In principle, the radiation recorded by MCOP should include the contributions from both the radiation of the first shocked sample and the partial radiation of the release baseplate that penetrates through the compressed layer of sample However, the contribution from the release baseplate is really small because (1) the temperature of release baseplate is obviously small compared with the shock temperature of sample and (2) only a small fraction of the radiation of release baseplate can penetrate through the compressed layer of sample So the radiation of the first shocked sample is predominant in MCOP signals, and the temperature derived from MCOP signals is on the whole the shock temperature of sample When the first shock in the sample arrived at the sample/LiF interface at t , it was reflected back into the first-shocked sample, which was reshocked to a state with higher pressure, density, and temperature FIG Typical signals of MCOP, DPS, and SOP for Shot No 140624: (a) light radiation histories measured by MCOP, providing the times when shock enters the sample (t ) and reaches the LiF (t ), as well as the intensity of light radiation represented by the voltage signal The wavelengths are listed at 430 nm (+25), 480 nm (0), 520 nm (☞25), 570 nm (☞50), 620 nm (☞75), 670 nm (☞100), where the numbers in parentheses are the signal-amplitude shifts; (b) velocity histories of baseplate/sample and sample/LiF interfaces obtained from DPS-I and DPS-II, respectively The signals give the times when shock enters the sample (t ) and reflected by the LiF (t , t ), also the particle velocities of the sample under the first and even shocks (U p,1 , U p,2 , U p,4 ); (c) temporally and spectrally resolved light radiation recorded by SOP, which also offers the times when shock enters the sample (t ) and reaches the LiF (t ), and the intensity of spectral radiance; (d) the time correlation among MCOP, DPS, and SOP signals The signals for MCOP and SOP are at a 430 nm center wavelength The opposite trends between MCOP and SOP signals are due to the different recording modes, while the slope of SOP signal is more evident than that of MCOP signal is due to the amplification factor of SOP is much larger than that of MCOP 105309-5 Li et al AIP Advances 6, 105309 (2016) The increase in temperature leads to an increase in intensity of the light emitted from the sample (the intensity is beyond the recording range of MCOP), which is represented by a jump of the MCOP signal According to the first shock transit time ∆t = t – t and the initial thickness of sample cell, the first shock velocity U s,1 could be obtained It should be noticed that the steel sample cell will be slightly distorted by initial high pressure gases Though this distortion was insufficient to affect the planarity, it should be included in the calculations of the first shock velocity Measurements of the particle velocity are really challenging Fig 2(b) shows the velocity histories of baseplate/sample and sample/LiF interfaces obtained from DPS-I and DPS-II, respectively When the shock broke out into the sample from the baseplate (t ), the baseplate/sample interface accelerated up to a steady speed, i.e., the particle velocity U p,1 behind the first shock In our experiments, the first-shocked sample is modestly dense and is still partially transparent for the 1550 nm probe lasers of DPS-I, so U p,1 can be detected by DPS-I, i.e., the velocity shown in Fig 2(b) corresponding to the first long flat region of the DPS-I signal It should be mentioned that this measurement is only valid for the case that the first-shocked sample is transparent or partially-transparent for probe lasers When the first shock is sufficiently strong, the shock front becomes opaque, and the probe lasers of velocity interferometers will be directly reflected by the shock front, which has been observed in previous experiments driven using a laser or Z-accelerator.9,15,17 The velocity of baseplate/sample interface directly measured by DPS is an apparent velocity The relation between the apparent velocity ua and the actual particle velocity up can be given by,28 ua − up = (n1 − 1)up − D (n1 − n0 ) , (3) where n0 is the refractive index of the uncompressed material, n1 is that of the compressed material, and D is the shock velocity Within the first shock pressure and temperature range, the refractive index for gas can be approximately expressed by a linear relationship to density, n = A + Bρ, (4) with A and B are two parameters related to materials Combining with the conservation of mass, one can obtain ua = A (5) up For gases, the linear relationship will hold as long as the chemical composition does not change In our experiments, the dissociation of deuterium under the first shock is only ∼1%☞3% calculated by the SFVT model.29–31 For D2 +He gas, the refractive index was measured by a special experiment in a pressure range of 0☞100 MPa The parameter A of the obtained linear relationship approaches to 1, and has only variables from the third digit after decimal point Moreover, we also notice the work by Dewaele et al.,32 in which the refractive index for fluid helium and hydrogen measured by the diamond anvil cell are nHe =(1.005±0.001)+0.199ρ [ρ units in g/cm3 , 0.08