Astrophysical dense plasmas are those we find in the interiors, surfaces, and outer envelopes of stellar objects such as neutron stars, white dwarfs, the Sun, and giant planets. Condensed plasmas in the laboratory settings include those in ultrahigh-pressure metal-physics experiments undertaken for realization of metallic hydrogen. We review basic physics issues studied in the past 60 some years on the phase transitions, the interparticle correlations, and the elementary processes in dense plasmas, through survey on scattering of electromagnetic waves, equations of state, phase diagrams, transport processes, stellar and planetary magnetisms, and thermo- and pycnonuclear reactions.

If Norman were alive and attended this symposium, he might have quipped: "Setsuo! What are you talking about! A plasma is, after all, a strongly correlated object, and there is nothing so special about it!""Yes, Norman, you are so correct! A statistical system consisting of mutually non-interacting and thus uncorrelated particles may be an "ideal-gas" system from a physics teacher's pedagogical point of view, but real systems do consist of mutually interacting and thus strongly correlated particles; a plasma is definitely one of them. Here, in the memory of Professor Rostoker's outstanding contributions to strongly correlated plasmas for the past 60 years, we wish to survey on "Scattering of Electromagnetic Waves by a Strongly Correlated Plasma" and "Multi-particle Correlation, Equations of State, and Phase Diagrams" in what follows.

First-principles formulations of the equations of state for hydrogen in metallic and insulator phases are presented, leading to a phase diagram predicting first-order metal-insulator transitions in dense hydrogen. The theory explicitly takes into account the effects of strong electron-ion coupling near the transitions as well as those of lowering or elimination of the atomic and/or molecular levels due to plasma screening. It is shown that the results of recent shock-compression experiments prove consistent with such first-order insulator-to-metal transitions. These observations predict a discontinuous distribution of density and resistivity with a large magnetic Reynolds number near the Jovian surface; the latent heat through the metal-to-insulator transitions is estimated.

Protons being the lightest nuclei, metallic hydrogen may exhibit the features of quantum liquids most relevant to enormous enhancement of nuclear reactions; thermonuclear and pycnonuclear rates and associated enhancement factors of radiative proton captures of high-Z nuclei as well as of deuterons are evaluated. Atomic states of high-Z impurities are determined in a way consistent with the equations of state and screening characteristics of the metallic hydrogen. Rates of pycnonuclear p-d reactions are prodigiously high at densities ⩾20 g/cm3, pressures ⩾1 Gbar, and temperatures ⩾950 K near the conditions of solidification. It is also predicted that proton captures of nuclei such as C, N, O, and F may take place at considerable rates, owing to strong screening by K-shell electrons, if the densities ⩾60–80 g/cm3, the pressures ⩾7–12 Gbar, and the temperatures just above solidification. The possibilities and significance of pycnonuclear p-d fusion experiments are specifically remarked.

Free energies of metallic hydrogen consisting of itinerant electrons and protons in the fluid and the Wigner-crystalline phases are evaluated as functions of density and temperature at various degrees of proton-spin polarization, in a Born–Oppenheimer approximation stemming from substantial mass difference between the two constituents. Those equations of state applicable in quantum and classical regimes are then utilized for the construction of phase diagrams, describing solidification and spin magnetization for proton fluids. Nuclear ferromagnetism due to partial spin-alignment of protons is predicted in an extended parametric domain, including the vicinity of metal-insulator phase boundaries. A contact is made between the magnetic phase diagram so obtained and observed data on the surface magnetic fields and temperatures of magnetic white dwarfs.

Classical and quantum simulation methods based on Monte Carlo and density functional approaches are described; these play vital parts in elucidation of fundamental properties of condensed plasmas. Issues of metallization and magnetization in ultradense hydrogen matter are reviewed in conjunction with experiments In recent ultrahigh-pressure metal physics and with stellar structure and magnetism.

Looked upon as strongly coupled plasmas, specific features of astrophysical and terrestrial matter are summarized. Astronomical objects considered are those in the interiors of the sun, brown dwarfs, giant planets, white-dwarf progenitors of supernovae, and outer crusts of neutron stars. Dense plasma materials in laboratories include conduction electrons in metals, inertial-confinement fusion plasmas, and metallic hydrogen projected under ultrahigh-pressure metal physics.

Rates of pycnonuclear reactions in ultradense fluids and solids and the associated enhancement factors are evaluated by taking account of recent progress in quantum-statistical formulations of the equations of state and phase transitions in dense matter. On the basis of these theoretical developments, we explore outstanding issues on nuclear reactions in dense astrophysical and terrestrial plasmas, and thereby propose a novel scheme of fusion studies in dense liquid-metallic proton-deuteron mixtures, coupled with renovated experiments in ultrahigh-pressure metal physics.

Rates of pycnonuclear reactions in ultradense fluids and solids are evaluated by taking account of recent progress in quantum-statistical formulations of the equations of state and phase transitions in dense matter. New theoretical results are summarized for the reaction rates and the enhancement factors, obtained through systematic studies of the screening effects by relativistic and nonrelativistic electrons, as well as of the thermodynamic properties of dense matter resulting from internuclear cohesion in electron-screened Coulombic fluids and solids; the results prove to be a significant improvement over those in a previous review [S. Ichimaru, Rev. Mod. Phys. 65, 255 (1993)]. On the basis of these theoretical developments, coupled with renovated experiments in ultrahigh-pressure metal physics, outstanding issues of nuclear reactions in stellar and planetary interiors and in terrestrial settings are explored, with inertial-confinement-fusion experiments, and for a novel scheme of fusion studies in dense liquid-metallic proton–deuteron mixtures.

Phase diagrams of hydrogen are constructed through first-principles calculations of the equations of state for metallic and insulator phases. On the bases of these theories of the equations of state and the electric resistivity, it is shown that the results of recent shock-metallization experiments can be consistently interpreted in terms of first-order metal-insulator transitions, involving discontinuous changes in density, entropy and enthalpy. The first-order transitions then predict a discontinuous distribution of density and resistivity near the Jovian surface, with a large magnetic Reynolds number enough to sustain prominent magnetic activities. A phase diagram for freezing and ferromagnetic transitions provides a basic account of strong magnetization observed in magnetic white dwarfs. Feasibility of a novel scheme of fusion studies in ultradense metallic hydrogen is examined in light of these experimental and theoretical developments.

An enhancement in the rates of nuclear reactions in dense matter is approached through calculations of increments between the Coulombic chemical potentials before and after the reactions. The formalism is applied to specific cases of the p-p reactions in the solar interior and of the C-12-C-12 reactions in a white-dwarf progenitor of a supernova; the dependence of the resultant enhancement factors on the relative abundances of the elements in the outgoing channels is thereby illustrated. The effects of plasma screening in the p-p reactions on the solar B-8 neutrinos are examined.

Temporal evolution of enhanced pycnonuclear reactions and resultant thermohydrodynamic expansion in ultrahigh-pressure liquid-metallic hydrogen have been analyzed by taking into account the heating effect of the charged fusion yields and the cooling effect by radiation. It is predicted that the p-d reactions, starting with the initial conditions for the fuel material, (mass density, temperature, pressure) = (10 g/cm(3) 900 K, 130 Mbar), may last for 10(-3) fs, yielding a net gain of thermal energy by a factor of 10(4); the temperature 4 x 10(5) K, attained in the final stage, may not be high enough to re-ignite thermonuclear reactions, however. The d-t reactions, starting with the initial conditions (10(4) g/cm(3), 16, 100 K, 10(7) Mbar), may last for 10(-3) fs and yield a thermal gain by a factor of 24, raising the fuel temperature to approximately 4 x 10(7) K, which is sufficient to re-ignite the thermonuclear reactions, leading to a total gain factor of 90.

Rates of magnetic reconnection are investigated in terms of the spectral functions of magnetic-field turbulence and the density of magnetic helicity. It has been shown that Parker’s scaling of the reconnection rates, sustained through observations in astrophysical and laboratory settings, is a consequence of transverse magnetic fluctuations generated by the influx of fields and plasmas into a reconnection cell, an idea corroborating that of ‘‘forced’’ reconnection. Three-dimensional and helicity-dependent effects in the reconnection processes are also analyzed.