MULTIPLE SHOCK WAVE COMPRESSION OF DIELECTRICS

335

with the compression leads to significant heating, thus stimulating the thermal ionization of a plasma. Kinetics and thermodynamics of such plasmas have been studied in detail both for the ideal and strongly nonideal case. In comparison to the fully developed thermal ionization, the influence of density e ects on the ionization equilibrium is not very strong and is described by various models of the reduced ionization potential (see Chapter 4). The thermodynamic states obtained so far in static and dynamic experiments (Hawke et al. 1978; Grigor’ev et al. 1978; Pavlovskii et al. 1987; Holmes et al. 1995; Weir et al. 1996a; Da Silva et al. 1997; Nellis et al. 1998; Fortov et al. 1999a; Ternovoi et al. 1999; Mostovych et al. 2000; Mochalov and Kuznetsov 2001; Knudson et al. 2001; Belov et al. 2002) are shown in the phase diagram of molecular hydrogen in Fig. 9.1. Also, theoretical estimates for plasma phase transitions are given along with the corresponding critical points (Robnik and Kundt 1983; Haronska et al. 1987; Saumon and Chabrier 1989, 1992; Beule et al. 1999; Nellis 2000; Mulenko et al. 2001).

In order to separate the density and thermal e ects of ionization, one should naturally try to suppress the e ects of irreversible heating by employing a quasi– isentropic compression. For this purpose, in the work by Fortov et al. (2003) the compression was produced by a sequence of direct and reflected shock waves, due to the reverberation in planar and cylindrical geometry. The explosive devices of the end–face and cylindrical throwing were implemented to generate shock waves (see Chapter 3). By using processes of multiple shock compression, one can reduce the heating by an order of magnitude and increase the plasma compression by a factor of ten, as compared to what direct wave compression gives. Also, in experiments with H2, He, Xe, Kr, and some other substances, the plasma conductivity rose by five orders of magnitude in a narrow density range, which is peculiar to the regime of “cold” ionization.

9.1Multiple shock wave compression of condensed dielectrics

9.1.1Planar geometry

A typical sketch of experiments to implement multiple shock wave compression of condensed hydrogen and inert gases in a planar geometry is shown in Fig. 9.2 (Fortov et al. 1999a, 2003; Ternovoi et al. 1999; Fortov et al. 2003; Mintsev et al. 2000; Ternovoi et al. 2002). Shock waves were generated by the impact of a steel impactor 2 (of 1–3 mm thickness and 30–40 mm diameter). It was accelerated by detonation products of an explosive (hexogen) 1 to velocities of 3–8 km s−1, by employing the “gradient cumulation” e ect (Ternovoi 1980). Explosive throwing devices developed for these experiments provided a diameter 15–30 mm of the flat part of the impactor by the moment when it hit the bottom of the experimental assembly. The absence of melting and evaporation of the impactor material as well as the absence of mechanical fracture of the impactor during acceleration was tested in a series of dedicated experiments. The transition of a shock wave from a metallic screen 3 (of 1–1.5 mm thickness) to the studied substance 4 (of the initial thickness of 1 to 5 mm) generated the

336	METALLIZATION OF NONIDEAL PLASMAS

P,GPa

103

Metal

102 Diamond

anvil

10

Solid state

1

Static

10-1 compression

10-2

Liquid state 1 10-3

CP1

10-4

10-5 Gas

10-6

0.01

	Magnetic			Jupiter	Condensed		Laser shock
	compression Light-gas gun à						waves
					explosives
			curve	å			neλ3	=1
				compression
							CP2
		adiabatic					ΓD=1
Shock			Multiple
			Plasma phase transition			Explosively driven
				12			shock tubes
				13				pinch
				14		Calculation
				15
				16			17	Z-
Experiment							18
							19
1		7		Shock tubes
2		8				Discharge
3		9

4 10

5	11
6

1	10	50
	T, 103K

Fig. 9.1. Phase diagram of hydrogen. Experimental data: 1 and 2, magnetic compression (Hawke et al. 1978; Pavlovskii et al. 1987); 3, Z–pinch (Knudson et al. 2001); 4 and 5, cylindrical compression (Grigor’ev et al. 1978; Mochalov and Kuznetsov 2001); 6, spherical compression (Belov et al. 2002); 7 and 8, single and multiple compression in a light–gas gun (Holmes et al. 1995; Weir et al. 1996a; Nellis et al. 1998); 9, multiple shock compression (Fortov et al. 1999a; Ternovoi et al. 1999); 10 and 11, shock compression by laser (Da Silva et al. 1997; Mostovych et al. 2000). Estimates for the plasma phase transition: 12, Beule et al. (1999); 13, Robnik and Kundt (1983); 14, Saumon and Chabrier (1989, 1992); 15, Haronska et al. (1987), 16, Mulenko et al. (2001). Experimental and simulation data: 17, compression in diamond anvils (DA) (Maksimov and Shilov 1999); 18, Jupiter atmosphere (Nellis 2000); 19, shock adiabat for hydrogen (Da Silva et al. 1997).

first shock wave with pressure p1 = 2–80 GPa. The wave, being reflected from a transparent sapphire window 5 (of 4–5 mm thickness and 20 mm diameter) excited a shock of secondary compression. Further re-reflection of shock waves between screen 3 and window 5 led to multiple shock compression of the sample up to maximum pressures of p 100–200 GPa. This magnitude was determined by the velocity of the impinging impactor, its thickness, and sizes of the studied substance.

The initial states of the substances for a further multiple compression corresponded either to the gaseous region of the phase diagram, at pressures p0 = 5– 35 MPa and temperatures T0 = 77.4–300 K, or to the liquid region at p0 0.1– 1 MPa and T0 20.4–160 K. In the latter case, the liquefaction was performed

MULTIPLE SHOCK WAVE COMPRESSION OF DIELECTRICS

337

	9
	8		5
10	6	7	4
			3

2

1

Fig. 9.2. Experimental setup for multiple shock wave compression of condensed hydrogen and inert gases in planar geometry (Fortov et al. 2003). 1, explosive; 2, steel plate; 3, bottom part of the assembly; 4, studied substance; 5, leucosapphire window; 6, iridium electrodes; 7, shunt resistance; 8, quartz–quartz light guide; 9, coaxial electric cables; 10, gas supply pipes.

from high–purity gases supplied to the setup through pipes 10. A two–contour system of cooling was used: To liquefy hydrogen, the external contour was filled with nitrogen, whereas for xenon the internal contour was filled with ethanol. The temperature in the assembly was monitored by thermocouples and platinum resistance thermometers.

The process of multiple compression was observed by means of fast optoelectronic converters and a five–channel fiber–optic–coupled pyrometer 8 with the time resolution of 2–5 ns. Since the shock compressed sapphire of optic window 5 retained transparency up to 20 GPa and, hence, made it possible to record the moments of the shock wave reflections from its surface at higher pressures, and also, since its insulating properties were at an acceptable level under compression up to 220 GPa (Weir et al. 1996b), five to six reverberations of shock waves could be detected by measuring the conductivity of the compressed layer and the optical radiation. The initial stages of the compression (up to 20 GPa) were recorded in individual experiments by using a VIZAR di erential laser interferometer (Barker et al. 1986).

338	METALLIZATION OF NONIDEAL PLASMAS

In this experimental scheme, the compression and irreversible heating of the substance were performed by a series of shock waves produced upon successive reflections from the sapphire window and the steel screen. A hydrodynamic analysis of the process suggested that, after the propagation of the first two shocks through the compressed layer, the further compression proceeded quasi– isentropically. This made it possible to achieve higher densities (ρ/ρ0 10–100) in comparison to the case of a single wave compression and to reduce the fi- nal temperature, thus increasing the e ects of the interparticle interaction. The shock reverberation is clearly revealed by distinct “steps” seen in oscillograms of radiation and electrical conductivity. The measured moments of the shock arrival at the plasma boundaries allow us to determine independently the thermodynamic parameters of the shock compression, p, ρ, and E, by using mass, momentum, and energy conservation (see Chapter 3). The data obtained up to pressures of 30–60 GPa for the caloric and thermal equations of state of hydrogen and helium – the latter was chosen as a reference substance – are in agreement both with the “chemical” model of nonideal plasma (Ebeling et al. 1991) and with the results given by the semiempirical equation of state of hydrogen (Grigor’ev et al. 1978; Juranek et al. 1999). At pressures above 60 GPa, however, no reliable data on the thermodynamics of hydrogen were obtained. In that case, the thermodynamic parameters of multiple shock compression at the final stage were calculated on the basis of 1D hydrodynamic codes that employ semiempirical equations of state for hydrogen (Grigor’ev et al. 1978; Juranek et al. 1999) and the materials used in the assembly (Bushman et al. 1992).

The obtained set of gas–dynamic and temperature measurements was used to determine the thermodynamic parameters of shock compression at the initial stages. Also, the measurements were used as input data (along with the velocity of the impactor) in testing 1D and 2D gas–dynamic codes, which were employed

– together with semiempirical broad–range equations of state – to determine the values of pressure, density, and temperature after multiple compression. The errors in the p, ρ, and T values obtained with this method were about 5, 10, and 20%, respectively.

The electrical conductivity of the shock–compressed plasma was determined with electrical probes. An electric current through the compressed plasma was supplied via electrodes (6) oriented perpendicular to the shock front. The current flowed along the compressed sample, then arrived at the surface of steel screen (3), and left the compressed region through a grounding electrode. The electric signals were transferred by high–frequency coaxial cables (9) and recorded by multichannel digital oscilloscopes with transmission bandwidth 500 MHz. The two– or three–electrode schemes were implemented to measure the resistance. In the latter case, it was possible to suppress the cophased noises and, thus, to record moments of the shock reflection not only from the optical window but also from the screen. In order to eliminate the breakdown and arc e ects during the transmission of the transport current through a plasma, the current density was maintained below 104 A cm−2. In a dedicated series of measurements,