9

METALLIZATION OF NONIDEAL PLASMAS

The behavior of a hydrogen plasma under conditions of extreme heating and compression – as well as of any other plasma produced from a dielectric substance – is of general interest for physics. The properties of such plasmas are also of substantial importance for various applications, e.g., in astrophysics and power engineering. For astrophysics, the importance follows from the fact that the cosmological abundance of hydrogen is about 90 at.%. Giant planets, like Jupiter and Saturn, consist mostly of hydrogen, heated and compressed at pressures of dozens of Mbar. Knowledge of the equation of state for hydrogen and its mixture with helium allows us to calculate the inner structure of stars and giant planets – e.g., knowing the magnitude of the metallization pressure, one can estimate the size of the metallic core and, therefore, the magnitude of the magnetic field. The equation of state and physical properties of liquid hydrogen (and its isotopes) is very important for inertial fusion. Stimulated by searching for metallic hydrogen (Wigner and Huntington 1935; Abrikosov 1954; Maksimov and Shilov 1999) in connection with its possible high–temperature superconductivity in a metastable atomic state (Ashcroft 1968), a great deal of e ort has been put into the investigation of the dielectric metallization at high pressures. One of the most brilliant ideas about the possibility for hydrogen to form a metastable metallic phase at zero pressure belongs to Brovman, Kagan and Kholas (1971), who showed that strongly anisotropic string–like structures can exist. Although it is rather obvious that the transition to the conductive state should occur in any dielectric, provided the compression is strong enough (see, e.g., the quasiclassical calculations by Kirzhnits et al. 1975), the calculations of the transition pressure and density require the most sophisticated methods of band theory to be applied. Such calculations (in some cases supported by experimental measurements) showed that the metallization of dielectrics can be expected in a fairly broad range of pressures – from tens of kbars up to tens of Mbars, whereas the compression of metals, e.g., Ni (McMahan and Albers 1982), Li, Na (Neaton and Ashcroft 1999, 2001; Fortov et al. 2001), can be accompanied by the formation of quasi–dielectrics. In fact, properties of strongly compressed matter are much more diverse than one can deduce from extremely simplified quasiclassical models, and the investigations of the electronic structure of hot substances at sub-Mbar pressures is currently one of the “hot topics” in the physics of condensed matter.

Note that in nature not only the metallization of dielectrics is possible, but also the transition of metals into a dielectric state can take place. Implementing the isothermal expansion of low–boiling metals at supercritical pressures (Hensel

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and Franck 1968; Alekseev and Vedenov 1971), one can continuously pass from a high–conducting “metallic” state to low–conducting gaseous “dielectric” states. It is established that a metal–dielectric transition occurs in a narrow range of densities that are close to (for Cs, Rb, K), or somewhat greater (for Hg) than the density at the critical point (see Chapter 6 for details). For the majority of other metals, which constitute 80% of the elements of the periodic table, critical temperatures and pressures are extremely high and are inaccessible with static experiments. Recent results obtained with fast electric explosion of metallic conductors at supercritical pressures (DeSilva and Katsouros 1998; Saleem et al. 2001) show that the metallic conductivity probably disappears upon significant expansion (a factor of 5 to 7) of solid metals.

In the previous chapters we mostly discussed properties of plasmas created by strong heating up to the temperatures comparable to the ionization potential of atoms (kT I). However, the plasma can also be formed at low temperatures by strong compression, when the atomic size ra becomes comparable to the interparticle distance n−a 1/3. The latter case is referred to as “cold” ionization or “pressure–induced” ionization. While the processes accompanying the thermal ionization are well studied (Fortov 2000), investigations of pressure–induced ionization are very complicated, since one has to deal with a “cold” (kT I) compression of a plasma up to Mbar pressures and densities that considerably exceed the solid state values. In this regime the electron shells of atoms and molecules overlap and the typical electrical conductivity is comparable to the metallic one. Although Zeldovich and Landau (1944), Mott and Davis (1979), and Hensel and Franck (1968) showed that a metal can be distinguished from a dielectric only by deviations in the electron spectra at T = 0, but not by the magnitude of the conductivity, this regime is nevertheless often called “metallization”. (For instance, relatively rarefied tokomak plasmas, with ne ni 1014 cm−3 and kT 5–10 keV, have conductivity close to that of pure copper.) Estimates of the metallization pressure p obtained for various substances by employing the methods of the band theory of solids at T = 0 yield values in the Mbar range (pH2 0.3 TPa (Wigner and Huntington 1935; Abrikosov 1954; Trubitsyn 1966; Ashcroft 1968; Brovman et al. 1971; Maksimov and Shilov 1999), pXe 0.15 TPa (Ross and McMahan 1980), pHe 11 TPa (Young et al. 1981), pNe 134 TPa (Boettger 1986). Although the static experimental technique of diamond anvils provides pressures as high as 0.5 TPa (Maksimov and Shilov 1999), the metallization with this technique was obtained only recently, in xenon at p = 150 GPa (Goettel et al. 1089), whereas hydrogen seems to remain a dielectric at pressures 340 GPa.

By using the technique of strong shock waves for the compression and irreversible heating of matter, one can obtain very high pressures (currently, the record value is p 400 TPa; Avrorin et al 1993). The pressures are limited only by the intensity of the shock wave generator, whereas for static compression the upper limit is the strength of diamond under static conditions. The viscous dissipation of the flux kinetic energy occurring in the shock wave front along