66 DYNAMIC METHODS IN THE PHYSICS OF NONIDEAL PLASMA

of studies into nondegenerate plasma of materials which, in their initial state, are gases. A combination of preheated pneumatic, electric discharge and explosion tubes provided information on the thermodynamic, electrophysical, and optical properties of plasma at pressures of up to 30 GPa, electron concentrations of about 1023 cm−3, and densities of up to 4.5 g cm−3(1.5 times higher than the crystallographic density of xenon). Under these conditions, the Coulomb energy is an order of magnitude higher than the kinetic energy of particle motion so that, from the physical viewpoint, such a plasma resembles a liquid while di ering from the latter by a richer and complex spectrum of interparticle interactions. The plasma behavior at ultramegabar pressures is currently of special interest from the standpoint of ascertaining the role of band structure e ects and determining the lower range of application of quasiclassical models of the equation of state. In order to reach this pressure range, nuclear explosions, laser radiation, and rapid electric explosion of metal foils have been used to advantage (see Section 3.5).

Shock and isentropic compression techniques make it possible to attain high pressures and temperatures in a medium of increased density and, because of thermodynamic restrictions, do not allow an investigation of the boiling curve and the near–critical states of metals. The most e ective method, from the standpoint of obtaining plasma with a less–than–solid–state density, is isentropic expansion of metals (see Section 3.5) prestressed in a powerful shock front. This method helps in the investigation of an extremely wide region of the phase diagram of metals from a highly condensed metallic liquid to ideal gas, including the region of nonideal degenerate and Boltzmann plasma and the neighborhood of the critical point.

The results of registration of release isentropes served as a basis for the construction of modern wide-range equations of state and, in addition, helped form a more conclusive opinion on the general qualitative form of the phase diagram of matter at high pressures and temperatures. This problem is not trivial for a highly nonideal plasma, in view of the existence of numerous predictions of exotic phase transitions due to the “metal–dielectric” transformation, as well as to a strong interaction of charged particles with each other and with neutrals. We shall discuss the relevant experimental studies in Sections 3.4 and 5.9.

3.1The principles of dynamic generation and diagnostics of plasma

The classification of plasma states in Chapter 1 shows (cf. Fig. 1.1) that only the plasma states with extremely high pressures and temperatures located at the periphery of the phase diagram of matter, where the interparticle interaction is low, are accessible to consistent theoretical analysis. The range of existence of nonideal plasma appears restricted and is located in Fig. 1.1 within the triangle defined by the γ = 1 and εF e2n1e/3 curves, the upper part of this triangle relating to a degenerate plasma and the lower part to a Boltzmann plasma. The maximum attainable values of the nonideality parameter are finite and do not exceed several units. Figure 1.1 demonstrates that optimum conditions exist for the generation of highly nonideal plasma. These conditions are further

complemented by their optima dictated by the processes of ionization under conditions of the method selected for the realization of those states (cf. Sections 3.2 and 3.3). Given the isochoric heating of a Boltzmann plasma in the initial stages of ionization, the electron concentration grows sharply with temperature, n2e naT 3/2exp(−I/T ), thus leading to a faster growth of the Coulomb energy as compared with kT . A further temperature increase causes full ionization of the given electron shell (ne const.), and a decrease in γ in view of the increase in kinetic energy. While putting o the qualitative assessment of this e ect until Sections 3.2 and 3.3, we note that these optima formed the basis for the designs of most devices for dynamic compression of plasma.

Although it appears restricted in Fig. 1.1, the nondeal plasma takes an exceedingly wide region in the real p − V diagram of the state of matter (Fig. 3.1). It adjoins directly and actually penetrates the region of the condensed state (Ebeling, Kreft, and Kremp 1976; Fortov 1982) where the physical description is extremely di cult because it depends on the specific electron spectra of atoms and molecules. Therefore, priority is given in this case to the experimental, primarily dynamic, methods (Altshuler 1965; Kormer 1968; Minaev and Ivanov 1976; Duvall and Graham 1977; Davison and Graham 1979) which enabled one to perform elegant measurements of the thermodynamic, optical, and electrophysical properties of condensed matter in the megabar pressure range. Modern high–temperature experimental techniques have facilitated the advancement into the region of the boiling curve and the neighborhood of the critical point of low– boiling metals, such as mercury, cesium, and rubidium, and the investigation of the liquid phase region of a number of other elements at p 0.4 GPa, T 5 ·103 K (Shaner and Gathers 1979) (Chapter 2). However, not only have the critical parameters not been found for the great majority of other metals (amounting to about 80% of all elements in the periodic system), but the qualitative form of the phase diagram has also not been clarified. This is because the greater part of the latter is taken by the region of nonideal plasma, which is inaccessible to traditional experimental techniques.

In order to produce a plasma with strong interparticle interaction, a considerable amount of energy release is required in a higher–density medium. The concomitant pressures and temperatures, as a rule, appreciably exceed the thermal– strength limits of the structural materials of the respective facilities. Therefore, such a plasma can only be maintained for a short period of time, which is defined by its inertial expansion. This compels one to conduct the experiment under heavy–duty pulsed conditions at a high power level. The appropriate experimental facilities must provide a fast energy supply to the material under investigation, and should feature geometric dimensions that are su cient for reliable diagnostics. The existing possibilities for plasma generation are listed in Table 3.1, which lists the characteristic (not necessarily maximum) parameters of energy sources used in the compression and heating of the material. Whilst doing so, because of the above restrictions due to plasma degeneracy and superheating, the extreme parameters listed in Table 3.1 do not correspond at all to

68 DYNAMIC METHODS IN THE PHYSICS OF NONIDEAL PLASMA

Schematic illustrating the principles of dynamic generation of plasma. pχ is the boundary of maximum compressions of the material, that is, the “cold” (T = 0 K) compression curve. The shaded areas show two–phase regions of melting and evaporation. C is the critical point. Circles indicate the initial states of the medium. H1 and H2 are the curves of cesium and inert gas compression by incident and reflected (prime) shock waves.

H3 and Hm are shock–wave compression of solid and porous metals. S1 is the curve of adiabatic compression of cesium while S2 is the unload adiabats for shock–compressed metals.

the maximum Coulomb nonideality e ects.

The dynamic methods of plasma generation are based on hydrodynamic methods of heating a material as a result of viscous dissipation of energy in a shock front or adiabatic compression of the medium (Zel’dovich and Raizer 1966). By now, three techniques have come to be most widely used in plasma investigations, namely, isentropic and shock compression, as well as isentropic expansion of pre–shock–compressed material. The use of various energy sources to excite shock and compression waves, such as compressed and electric discharge– heated gas, condensed and nuclear explosives, and powerful laser and neutron fluxes, enabled one to produce a nonideal plasma of di erent elements in a wide and continuously varying range of densities: from solid state to gas at pressures of hundreds of thousands of megapascals and temperatures of tens of kiloelectron volts.

A considerable amount of these data were obtained by propagating shock waves over the material under investigation to cause its irreversible compression, heating, and acceleration. In doing so, the initial states of the material may be

Table 3.1 Sources of energy and experimental facilities employed in the physics of high energy concentrations.

70 DYNAMIC METHODS IN THE PHYSICS OF NONIDEAL PLASMA

either in the solid or gas phase. The latter case is especially convenient to obtain a highly nonideal Boltzmann plasma (Sections 3.2 and 3.3). It is generated as a result of shock compression of high–pressure gases whose initial states are (cf. Fig. 3.1) in the neighborhood of the saturation curve (cesium, argon) or under supercritical conditions (xenon). By recording the state of single or double compression, it is possible to obtain a plasma with supercritical parameters in a wide range of pressures (up to 11 GPa) and temperatures (up to 105 K) and to penetrate, from the “gas” phase side, the condensed state region. The maximum density of xenon plasma amounted to 4.5 g cm−3. This is about 1.5 times greater than the density of solid xenon and the order of the density of aluminum. The compression of liquid xenon using light–gas “guns” in the pressure range of up to 140 GPa yields valuable information on the electron spectrum of superdense plasma in the range of 105 MPa. Adiabatic compression of saturated cesium vapors, S1 (Fig. 3.1), makes it possible (Section 3.2) to attain lower degrees of plasma heating where the charge–neutral interaction prevails. The compression of metals by powerful shock waves (Altshuler 1965; Kormer 1968; Minaev and Ivanov 1976; Duvall and Graham 1977; Davison and Graham 1979), a result of the detonation of condensed explosive, transforms the metal into a state with a pressure of up to 1000 GPa and temperature of tens of thousands degrees when the metal is molten. As a matter of fact, a disordered electron–ion plasma, in which the electron component is degenerate or partly degenerate, is realized.

The use of powerful underground explosions (Altshuler et al. 1968; Trunin et al. 1969, 1972; Vladimirov et al. 1984; Simonenko et al. 1985; Avrorin et al. 1987), neutron radiation resulting from the blasting of nuclear charges (Thom and Schneider 1971), and concentrated laser radiation (Anisimov et al. 1984) increase the pressure up to 100 TPa. It also serves a basis for extrapolation checks of quasiclassical theories (Kirzhnits et al. 1975).

One characteristic feature of the shock–wave technique is that it helps the attainment of high pressures and temperatures in compressed media while the region of lower plasma densities (including the boiling curve and the neighborhood of the critical point) prove inaccessible for such techniques. The intermediate plasma states between solid and gas can be investigated using the isentropic expansion technique (Section 3.5). It is based on plasma generation under conditions of adiabatic expansion of condensed matter (S2, Fig. 3.1) precompressed and irreversibly heated in a powerful shock front. In this way, it was possible to investigate the properties of metals in a wide range of phase diagram, from a highly compressed condensed state to an ideal gas, including the region of degenerate and Boltzmann low–temperature plasma, near–critical and two–phase states, as well as the “metal–dielectric” transition region.

We see that the dynamic methods, in their various combinations, enable one to realize and investigate a wide spectrum of plasma states with variegated and strong interparticle interaction. In doing so, it proves possible to both actually realize states with high energy concentrations and fully diagnose those exotic states.

The dynamic diagnostic methods are based on the utilization of the relationship between the thermodynamic properties of the medium under investigation and the experimentally observed hydrodynamic phenomena occurring upon accumulation of high–energy densities in the matter (Zel’dovich and Raizer 1966). In the general form, this relationship is expressed by a system of nonlinear (three– dimensional) di erential equations of nonstationary gas dynamics. Its complete solution appears to be beyond the capabilities of most powerful modern computers. For this reason, one tends to use in dynamic investigations self–similar solutions of the type of stationary shock wave or centered Riemann expansion wave (Altshuler 1965; Zel’dovich and Raizer 1966), which express the conservation laws in a simple algebraic or integral form. While doing so, the conditions of self–similarity of flow must be observed in the experiment in order to use these simplified relationships.

Upon propagation of a stationary shock–wave discontinuity through the material, the laws of conservation of mass, momentum, and energy are satisfied in the front of the latter (Zel’dovich and Raizer 1966):

which allows the derivation of the hydrodynamic and thermodynamic characteristics of the material from the recording of any two out of five parameters characterizing the shock wave discontinuity (E, p, v, D, u). The shock velocity D is measured most readily and accurately using baseline techniques. The choice of the second parameter to be measured depends on the actual experimental conditions.

An analysis of errors in the relationships included in Eq. (3.1) indicates (Lomakin and Fortov 1973; Kunavin et al. 1974) that in the case of readily compressible (“gas”) media, it is practical to perform the recording of density, ρ = v−1, of shock–compressed material. A procedure has been developed for such measurements based on the registration of absorption by cesium (Section 3.2), argon (Section 3.5), and the air (Section 3.6) plasma of “soft” X–ray radiation. In the case of lower compressibility of the system (condensed media), tolerable accuracies are ensured (Altshuler 1965) by recording the mass velocity of travel u.

In the experiments which involve the recording of the isentropic expansion curves for shock–compressed matter (Section 3.5), the states in a centered release wave are described by the Riemann integrals (Zel’dovich and Raizer 1966):

which are calculated along the measured isentrope pS = pS (u). By recording under di erent initial conditions and shock–wave intensities, one can determine the caloric equation of state E = E(p, v) in the region of the p − v diagram,