Experimental Study of the Compressibility of a Helium Plasma at a Pressure up to 20 TPa

A nonideal helium plasma has been compressed to a density of ρ ≈ 14 g/cm³ at a pressure of $P \approx 20{\kern 1pt}$ TPa (200 Mbar) in a spherical two-cascade device. The design of the device has been presented and the thermodynamic parameters of the helium plasma reached in it have been estimated. Data on the dynamics of the external and internal cascades in the device used to choose the calculation method have been obtained in a preliminary experiment with a hemispherical prototype. The experiment has been performed on the X-ray complex at the Russian Federal Nuclear Center All-Russian Research Institute of Experimental Physics, which includes BIM 234.3000 betatrons with a boundary energy of 60 MeV used in the multipulse bremsstrahlung generation regime with a multichannel optoelectronic system of recording X-ray images. A high-current linear accelerator LIU-R-T and an image detector assembly consisting of photochromic ADC screens have been used in addition to betatrons to detect the compressed shell cavity.

1 INTRODUCTION

The quasi-isentropic compression of gases in cylindrical and spherical two-cascade devices using powerful chemical explosives ensured megabar pressures in experimental studies of the properties of a strongly nonideal helium plasma at the Russian Federal Nuclear Center All-Russian Research Institute of Experimental Physics (VNIIEF) [1–10]. A high energy density in such devices induces thermal and/or pressure ionization resulting in a plasma whose theoretically description is strongly complicated because of complex physical processes occurring in it. Data on the behavior of helium at such record pressures are necessary to verify its equation of state in a wide region of the phase diagram. The study of the properties of helium is of great fundamental significance because the helium plasma at megabar pressures corresponds to the states of the internal parts of most giant planets of the solar system and to exoplanets. Even higher thermodynamic parameters of the plasma occur in inertial controlled fusion devices. Interest in the study of the properties of the nonideal helium plasma is significantly due to predictions of the existence of anomalies of extraordinary “plasma” (ionization-driven) phase transitions in a hot dense helium fluid.

The properties of the helium plasma compressed to a density 8 g/cm³ at pressures up to 5000 GPa, were studied in VNIIEF experiments at the equal initial pressure 25 MPa of the gas in both cascades in [1–3]. The properties of quasi-isentropically compressed helium plasma at compression degrees of 600 and 900 were studied experimentally in [4, 5], respectively, using a spherical two-cascade chamber with separated cavities. The shock wave compressibility of helium to P ≈ 83 GPa was also studied in [5]. Using an explosive charge of 85 kg of TNT, the nonideal helium plasma was compressed to a density of ρ ≈ 9 g/cm³ at a pressure of Р ≈ 10 000 GPa in [6] and compressed to a density of ρ ≈ 13 g/cm³ at a pressure of Р ≈ 16 700 GPa in [7]. The quasi-isentropic compression of dense gaseous helium was also studied in [8, 9] at pressures up to 500 and 2000 GPa, respectively. The compressibility of helium in the pressure range of 200–600 GPa at a constant final temperature of T ≈ 21 000 K was studied in recent experiment [10].

In this work, we propose a new design of a spherical two-cascade device with a MT-18F-alloy shell of the internal cascade, carry out the experimental study of the compressibility of helium at a pressure of Р ≈ 20 TPa, perform a one-dimensional gas-dynamic calculation of the proposed device, and estimate the thermodynamic parameters of helium reached in the proposed device.

To detect the compression of helium, we use X-ray facility at the VNIIEF, which consists of BIM234.3000 betatrons [11] operating in the multipulse bremsstrahlung generation mode, multichannel optoelectronic detection system for X-ray images, and a high-current accelerator LIU-R-T [12].

2 EXPERIMENTAL SETUP AND TECHNIQUE

The device was based on a helium-filled spherical chamber (see Fig. 1), which was fabricated by soldering from high-strength steel. To compress helium, we used an HMX explosive charge of 55 kg of TNT (B), which surrounds the outer steel shell (Fe) designed for a gas pressure of Р = 200 MPa. The main element of the entire setup is a combined internal cascade, which consists of a polycaproamide (polyamide-6) spherical shell (K) and a thin-wall shell made of MT-18F alloy (95% W, 3.5% Ni, 1.5% Fe) (W) placed inside the first shell.

Fig. 1.

Geometry of the experimental device for the study of the compression of the nonideal helium plasma at a pressure of 20 TPa: (He-1, He-2) helium; (W) MT-18F alloy shell; (K) polycaproamide (polyamide-6) shell; and (B) explosive.

The aim of the experiment was to record the trajectory R(t) of the shell of the experimental device and to determine its size at the “stop” time when the compression of the studied material is maximal; i.e., the average density of the compressed helium plasma was measured in the experiment. Under the condition that the mass of the compressed material was conserved, its density was calculated by the formula

$$\rho = {{\rho }_{0}}{{({{R}_{0}}{\text{/}}{{R}_{{\min }}})}^{n}},$$

where ρ₀ is the initial density of the gas; R₀ and ${{R}_{{\min }}}$ are the inner radii of the shell in the initial state and at its stop time, respectively; and n = 3 in the case of the spherical geometry.

To choose the X-ray recording regime of the helium compression process, the new device was preliminarily tested at the initial phase of its operation when the effect of the gas can be neglected. Data on the motion dynamics of the outer and inner cascades used to choose the equations of state of the elements of the design were obtained in the experiment with the hemispherical prototype modeling the experimental device. The prototype (see Fig. 2) consisted of a loading device (2) and a hemispherical steel chamber (3) glued to a steel case (4), on which a hemispherical polycaproamide shell (5) with the MT-18F shell (6) and a measuring detector with electric contact gauges (7) were placed.

Fig. 2.

(Color online) General sketch of the hemispherical device: (1) initiation points of the electric match, (2) explosive, (3) steel shell, (4) case, (5) polycaproamide shell, (6) MT-18F shell, and (7) measuring instrument, where black lines are electric contact gauges and the red line is the PDV sensor.

The following parameters were detected in the experiment: (i) the times of arrival t₁ and t₂ of a shock wave at the outer and inner surfaces of the shell (3), respectively, using electric contact gauges (12 gauges on each surface of the shell); (ii) the times of arrival t₃ and t₄ of the shock wave at the outer and inner surfaces of the polycaproamide shell (5), respectively, using electric contact gauges (8 and 12 gauges on the outer and inner surfaces of the shell, respectively); (iii) the time of arrival t₅ of the shock wave at the inner surface of the MT-18F shell using 12 electric contact gauges; (iv) the velocity of the shell (3) using four PDV sensors; and (v) the positions of shells (3, 6) at three time using the pulsed X-ray diffraction method.

Data from electric contact gauges detecting the arrival of the shock wave at the surfaces of shells 3, 5, and 6, which indicate a high symmetry of the motion of the shock wave, are shown in Fig. 3, where the solid lines are averaged values. The time was measured from the arrival of a trigger pulse to the electric match (1).

Fig. 3.

Times of motion of the shock wave through the shells: ($\diamondsuit$) t₁ = (27.44 ± 0.05) μs, ($\circ$) t₂ = (28.19 ± 0.05) μs, ($\Delta$) t₃ = (38.45 ± 0.29) μs, ($\square$) t₄ = (40.69 ± 0.03) μs, and ($\times$) t₅ = (40.95 $\pm$ 0.03) μs.

The velocity of the steel shell (3) was measured using an instrument [13] based on an optical laser interferometer [14]. Velocity diagrams of the shell (3) according to data from four PDV sensors are presented in Fig. 4. All diagrams almost coincide with each other. The maximum velocity of the steel shell was $V$ = (5.0 ± 0.02) km/s. Averaging of signals from the PDV sensors allowed us to determine the start time t₀ = 28.041 μs of the steel shell (r₀₁ = 97.1 mm) and to calculate its trajectory R(t) (see below). The amplitude and time accuracies of detection by the instrument [13] are 20 m/s and 10 ns, respectively.

Fig. 4.

(Color online) Four diagrams of the velocity of the inner surface of the steel shell of the experimental device according to data from the PDV sensors.

As in [7], the positions of steel and tungsten shells were detected at three time using the pulsed X-ray diffraction method. A typical X-ray diffraction pattern of the positions of the steel and tungsten shells at the time of motion t_γ = 41.61 μs is shown in Fig. 5. To record images of the shells, we used assemblies of ten photochromic ADC screens based on europium-doped barium halide. To increase the quantum efficiency of detection, screens were interleaved with lead plates ≈1 mm thick. Figure 5 also presents the results of tracing of shell contours described in [15]. This method is based on the extrapolation of near-surface functions from the left and right sides of the surface in order to determine their intersection point, which is accepted as the surface coordinate. The data obtained on the radii of the surfaces are summarized in Table 1.

Fig. 5.

(Color online) Experimental X-ray diffraction patterns of the (W) MT-18F and (Fe) steel shells (see Fig. 1) and results of functional tracing of the (white line) outer and (black line) inner surfaces of the steel shell and the (red line) outer and (blue line) inner surfaces of the MT-18F shell.

Table 1. Results of tracing the surfaces of the W and Fe shells (see Fig. 1)

3 QUASI-ISENTROPIC COMPRESSIBILITY OF HELIUM

The data obtained in the preliminary experiment with the hemispherical prototype were used to choose times of the detection of shell in the experiment on the measurement of the compressibility of the helium plasma. The layout of the experiment is shown in Fig. 6. The experimental device (1) was placed between two concrete structures (2) with X-ray sources. In the experiment, we used two pulsed BIM234.3000 betatrons (3) [11], which operated in the regime of successive generation of three X-ray pulses, and linear induction accelerator LIU-R-T (7) (see Fig. 6). This accelerator whose technical characteristics in the optimal regime allows transmitting objects with a mass thickness up to 300 g/cm² was used with the expected high density of the compressed helium plasma of ρ ≈ 15 g/cm³. X rays from the accelerator LIU-R-T were detected by the array of ten photochromic screens (8).

Fig. 6.

(Color online) Layout of the experiment: (1) experimental device, (2) protective structures, (3) X-ray sources (betatrons), (4) detectors, (5) Pb collimators, (6) Al cone, (7) high-current linear accelerator LIU-R-T, and (8) set of photochromic screens.

A thermocompressor was used to fill the chamber with helium. The pressure of gases in the process of filling was measured with a pressure gauge with an accuracy class of 0.25. The initial temperature was controlled by a chromel–alumel thermocouple placed in a pipeline used to introduce the gas. The initial density of helium was determined using tabular data [16]. Seven experimental X-ray patterns are presented in Fig. 7 and demonstrate a high symmetry of compressed cavities with the helium plasma.

Fig. 7.

(Color online) Experimental X-ray diffraction patterns at times t = (1) 43.00, (2) 43.38, (3) 43.78, (4) 44.12, (5) 44.44, (6) 44.80, and (7) 44.88 μs.

To trace the surfaces of the spherical shells, we applied a functional method. The results are presented in Fig. 7. The characteristics of the device, experimental conditions, and the resulting data are summarized in Table 2.

Table 2. Characteristics of the device (see Fig. 1) and experimental results. The initial density ρ₀, pressure P₀, and temperature T₀ of helium. The initial pressures of helium in both cavities are the same. The weighted average calculated density ρ_exp, pressure P_calc, and temperature T_calc under the maximum compression of helium at the radius R_min of the stop of the device

Experimental R(t) data on the compressibility of the helium plasma are presented in Fig. 8 together with results obtained from the experiment with the gas-dynamic simulation, and gas-dynamic calculation results.

Fig. 8.

(Color online) Experimental and calculated trajectories R(t) of the surfaces of the elements of the experimental device. Model experiment: ($\square$) data from electric contact gauges, ($\bullet$) data from PDV sensors, and ($\times$, $*$, $\Delta$, $\blacksquare$) X-ray diffraction data ($\times$, $*$) for the outer surfaces of the ($\times$) steel and ($*$) polycaproamide shells and for the ($\Delta$) outer and ($\blacksquare$) inner surfaces of the MT-18F shell. Main experiment data for the ($\circ$) inner and ($\diamondsuit$) outer surfaces of the MT-18F shell and (red solid line) the trajectory of the inner surface of the steel shell according to data from the PDV sensors. The black solid lines are gas-dynamic calculations.

According to Fig. 8, gas-dynamic calculations with the chosen technique well reproduce all reference points ($p1,p2,p3$) of propagation of the shock wave through the steel shell of the first cascade (Fe1), the arrival of the shock wave at the MT-18F shell, as well as the edges of the outer shell of the experimental device measured by the X-ray diffraction method. The calculation also reproduces the dynamics of motion of the inner surface of the steel shell detected by the heterodyne-interferometer method in the reported experiment with the hemispherical prototype and positions of the surfaces of the MT-18F shell.

The trajectories of the shells, as well as the distributions of the density, pressure, and temperature over the radius of the compressed helium cavity were calculated using a one-dimensional gas-dynamic program [17] taking into account the thermodynamic and strength properties of all elements of the experimental device and their equations, which were introduced in the VNIIEF computational complex and were presented [1–10]. The results obtained in this work are presented in the (Р, ρ) coordinates are shown in Fig. 9 together with other VNIIEF data.

Fig. 9.

Quasi-isentropic compressibility of the helium plasma at pressures up to 20 TPa according to the experimental data from ($\blacktriangledown$) this work, ($\Delta$) [1, 3, 6], ($\bullet$) [4], ($\circ$) [9], ($\square$) [7], ($*$) [8], and ($\star$) [10]. The black solid line is the isentrope for S/R = 16.

The minimum radius of the compressed cavity with the helium plasma detected in the experiment at the time t_stop = 44.8 μs was R_min = 0.410 cm, which differs by 1.22% from the calculated radius R_calc = 0.407 cm at the stop time and corresponds to the helium density ρ_exp = 13.9 g/cm³, which differs by 7% from the calculated value ρ_calc = 14.34 g/cm³. The calculated pressure at the time of the maximum compression of the helium plasma is Р_calc = 19 700 GPa at a temperature of T = 146 kK. The satisfactory description of all trajectories R(t) of the shells of the experimental devices, which is reached in this work, can be considered as the main criterion of the accuracy of the calculated pr-essure.

4 CONCLUSIONS

To summarize, the compressibility of helium has been studied using a combined spherical shell with a contrasting layer made of MT-18F alloy. A gas-dynamic simulation of the proposed device has been performed with a prototype in order to obtain data on the motion dynamics of the outer and inner surfaces of the cascades of the device to choose models for the calculation of the design and for further use of such shells in experiments with other gases at megabar pressures. The helium plasma has been compressed to a density of ρ_exp = 13.9 g/cm³ by a pressure of Р ≈ 20 TPa at a temperature T = 146 000 K, which are currently record characteristics.