Table of contents

This special issue contains papers presented at the International Conference on Strongly Coupled Coulomb Systems (SCCS) which was held during the week of 20–24 June 2005 in Moscow, Russia. The Moscow conference was the tenth in a series of conferences. The previous conferences were organized as follows.

• 1977: Orleans-la-Source, France, as a NATO Advanced Study Institute on Strongly Coupled Plasmas (organized by Marc Feix and Gabor J Kalman)

• 1982: Les Houches, France (organized by Marc Baus and Jean-Pierre Hansen)

• 1986: Santa Cruz, California, USA (hosted by Forrest J Rogers and Hugh E DeWitt)

• 1989: Tokyo, Japan (hosted by Setsuo Ichimaru)

• 1992: Rochester, NY, USA (hosted by Hugh M Van Horn and Setsuo Ichimaru)

• 1995: Binz, Germany (hosted by Wolf Dietrich Kraeft and Manfred Schlanges)

• 1997: Boston, Massachusetts, USA (hosted by Gabor J Kalman)

• 1999: St Malo, France (hosted by Claude Deutsch and Bernard Jancovici)

• 2002: Santa Fe, New Mexico, USA (hosted by John F Benage and Michael S Murillo)

After 1995 the name of the series was changed from `Strongly Coupled Plasmas' to the present name in order to extend the topics of the conferences.

The planned frequency for the future is once every three years. The purpose of these conferences is to provide an international forum for the presentation and discussion of research accomplishments and ideas relating to a variety of plasma liquid and condensed matter systems, dominated by strong Coulomb interactions between their constituents.

Strongly coupled Coulomb systems encompass diverse many-body systems and physical conditions. Each meeting has seen an evolution of topics and emphasis as new discoveries and new methods appear. This year, sessions were organized for invited presentations and posters on dense plasmas and warm matter, astrophysics and dense hydrogen, non-neutral and ultracold plasmas, dusty plasmas, condensed matter 2D and layered charged-particle systems, Coulomb liquids, and statistical theory of SCCS. Within each area new results from theory, simulations and experiments were presented. In addition, a special symposium was held one evening to explore the questions on high-energy-density matter generated by intense heavy ion beams and to discuss the outlook for applications to industry.

As this special issue illustrates, the field remains vibrant and challenging, being driven to a great extent by new experimental tools and access to new strongly coupled conditions. This is illustrated by the inclusion of developments in the areas of warm matter, dusty plasmas, condensed matter and ultra-cold plasmas.

In total, 200 participants from 17 countries attended the conference, including 42 invited speakers. The individuals giving presentations at the conference, including invited plenary and topical talks and posters, were asked to contribute to this special issue and most have done so. We trust that this special issue will accurately record the contents of the conference, and provide a valuable resource for researchers in this rapidly evolving field.

We would like to thank the members of the International Advisory Board and all members of the Programme Committee for their contributions to the conference. Of course, nothing would have been possible without the dedicated efforts of the Local Organizing Committee, in particular Igor Morozov and Valery Sultanov. We wish to thank the Russian Academy of Sciences, the Institute for High Energy Densities, the Institute of Problems of Chemical Physics, the Moscow Institute of Physics and Technology, the Ministry of Education and Science of the Russian Federation, the Russian Foundation for Basic Research, the Moscow Committee of Science and Technologies, the Russian Joint Stock Company `Unified Energy System of Russia', and The International Association for the Promotion of Co-operation with Scientists from the New Independent States (NIS) of the Former Soviet Union for sponsoring this conference.

This special issue is dedicated to the memory of Marc Feix (1928–2005), one of the two co-organizers of the First International Meeting on Strongly Coupled Plasmas, held in Orleans-la-Source, France, in the summer of 1977.

We provide a survey of the concept and several successful applications of effective potentials. After introducing Kelbg's expression we discuss several useful approximations and additional generalizations including non-diagonal expressions. Finally, we present the recent results concerning non-diagonal contributions and the relation to effective interactions arising from the dynamics of Gaussian wave packets.

A review is presented of the novel experimental results of investigation of physical properties of the coupled dense plasmas generated as a result of shock compression up to megabar pressure range. High-energy plasma states were generated by single and multiple shock compression. The highly time-resolved diagnostics permit us to measure thermodynamical, electrophysical and optical properties of high pressure condensed plasmas in the broad phase diagram region—from the compressed condensed solid state up to the low density gas range, including strongly coupled plasma and metal–insulator transition regions.

New results on optical reflectance measurements of shock-compressed dense xenon plasma at wavelengths λ = 532 nm and λ = 694 nm are reported. The investigations have been performed for nonideal plasma (Γ = 0.87–2.0) at densities ρ = 0.27–3.84 g cm⁻³ and pressures P = 1.6–17 GPa. The obtained high optical reflectance values are characteristic of a metallic fluid and are evidence for a conducting state in the shocked xenon. Reflectance measurements at different wavelengths provide information about the density profile of the shock wave front.

Phase shifts, cross sections and transport coefficients of dense semiclassical plasma are investigated. It is shown that consideration of screening effects at large distances and quantum effects at short distances leads to a decrease in scattering probability, i.e., to an increase of the corresponding transport coefficients. The Calogero equation was solved in order to determine phase shifts. Fully and partially ionized hydrogen plasmas were studied, and electrical conductivity and diffusion coefficients of plasma were obtained.

New experimental setup for generation of a non-ideal plasma, placed in a magnetic field of up to 25 T, is presented. The plasma generation technique is based on gas compression and heating behind the front of a shock wave with the use of an explosively driven linear generator. The magnetic field is produced by a discharge of a capacitor through a solenoid reeled on the generator channel. DC electrical conductivity of the plasma is determined by two and four contact techniques. Possibilities of magnetized dense plasma generation are discussed.

We present the most recent results from an experiment aimed at obtaining the temperature equilibration rate between ions and electrons in a strongly coupled plasma by directly measuring the temperature of each component. The plasma is formed by heating a sonic gas jet with a 10 ps laser pulse. The electrons are preferentially heated by the short pulse laser (we are aiming for T_e ∼ 100 eV), while the ions, after undergoing very rapid (sub-ps timescale) disorder-induced heating, should only reach a temperature of 10–15 eV. This results in a strongly coupled ion plasma with a Γ_ii ∼ 3–5. We plan to measure the electron and ion temperatures of the resulting plasma independently during and after heating, using collective Thomson scattering for electrons and a high-resolution x-ray spectrometer for the ions (measuring Doppler-broadened absorption lines). Theory indicates that the equilibration rate could be significantly lower than that given by the usual weakly coupled model (Landau–Spitzer) due to coupled collective modes present in the dense plasma.

X-ray spectral lines of multicharged ions in a solid target interacting with picosecond laser pulses of moderate intensity (∼3 × 10¹⁷ W cm⁻²) were measured on the 'Neodim' laser facility. Strong modulations in x-ray Ly_α line profiles of hydrogen-like fluorine ions were observed, evidencing the presence of intense plasma oscillations with an amplitude of the electric field larger than 10⁸ V cm⁻¹ and a frequency of about 10¹⁵ s⁻¹.

Using wave packet molecular dynamics simulations we calculate the dynamic structure factor S(k, ω) of a two-component plasma (TCP). The results are compared with corresponding classical molecular dynamics simulations of a model TCP with effective interactions. Both approaches agree well in the low frequency part of S(k, ω) but increasingly deviate for high frequencies. This clearly demonstrates a restriction of the method of effective potentials to static properties and low frequency phenomena.

In order to describe dielectric properties in dense plasmas, a consistent calculation of the collision frequency is required. We present new calculations for an electron gas at parameters which are relevant for warm dense matter. In particular, we focus on the influence of the different approximations for the collision frequency in the Gould–DeWitt scheme. We use the dynamic collision frequency in the Born, Lenard–Balescu and ladder approximation. The inclusion of collisions in a consistent manner modifies, e.g., the dielectric function significantly in the warm dense matter regime.

The effective polarization interaction potential between charged and neutral particles is considered for a partially ionized plasma. This pseudopotential is deduced taking into account quantum-mechanical effects at short distances as well as screening effects at large distances. Furthermore, a cutoff radius is obtained using a modified effective-range theory. Explicit results for parameters describing the interaction of the atom with charged particles are given.

We create and operate with a random interelectrode media of high power density using the low energy nanosecond vacuum discharges. The subjects of our study are hard x-ray emission efficiency, generation of energetic ions (∼1 MeV) and neutrons and the trapping and release of fast ions and/or x-rays from interelectrode complex ensembles of cold micro grains with some micro plasmas. The value of the neutron yield from DD microfusion in the interelectrode space is variable and amounts to ∼10⁵–10⁷/4π per shot under ≈1 J of total energy stored to create all discharge processes. In a limiting case of total trapping of fast deuterium ions by the dense 'dusty cloud' of clusters under partial hard x-ray diffusion and multiple fusion events inside, the pulsating neutron yield has maximum values (table-top complex plasma 'microreactor'). The role of virtual cathode formation and electrostatic mechanism of ions acceleration at the regime of unstable current carrying are discussed briefly.

The equation of state and optical properties of shocked compressed silica and LiF are investigated using quantum molecular dynamics in a wide range of pressures and temperatures along the principal Hugoniot. For silica, the increase in reflectivity occurs at about 100 Gpa and saturates around 40%. For LiF, a pressure of 600 GPa is needed to observe a significant reflectivity, but no saturation is observed. Our results are in close agreement with the experimental measurements (Hicks D G, Celliers P M, Collins G W, Eggert J H and Moon S J 2003 Phys. Rev. Lett.91 035502) and a simple fit of the optical index of LiF versus compression is provided.

New results for the reflection coefficient of shock-compressed dense xenon plasmas at pressures of 1.6–20 GPa and temperatures around 30 000 K are interpreted. Reflectivities typical of metallic systems are found at high densities. A consistent description of the measured reflectivities is achieved if a finite width of the shock wave front is considered. Several mechanisms to give a microscopic explanation for a finite extension of the shock front are discussed.

On the basis of numerically calculated values for the dense plasma dynamic conductivity in an external HF electric field, we determine the electrical permeability and the coefficients of refractivity and reflectivity of dense non-ideal plasmas. We consider electronic number density and temperature in the ranges of 10²¹ ⩽ N_e ⩽ 10²³ cm⁻³ and 20 kK ⩽ T ⩽ 1 MK, respectively. The parametrized form of representation of the results is suitable for experimental verification and further usage. The examined range of frequencies covers the IR, visible and near UV regions.

A recently developed method for calculation of electronic transport coefficients of liquid metals was applied to a region of transition from the liquid to the plasma state for non-alkali metals. This technique is based on Ziman theory and a two-component model of the medium with variable ion charge. The results of calculation were compared with calculations and measurements of other authors.

We briefly examine the properties of the dense plasmas characteristic of the interior of giant planets and of the atmospheres of neutron stars. Special attention is devoted to the equation of state of hydrogen and helium at high density and to the effect of magnetic fields on the properties of dense matter.

Thermodynamic properties of the equilibrium strongly coupled quantum plasmas investigated by direct path integral Monte Carlo (DPIMC) simulations within a wide region of density, temperature and positive to negative particle mass ratio. Pair distribution functions (PDF), equation of state (EOS), internal energy and Hugoniot are compared with available theoretical and experimental results. Possibilities of the phase transition in hydrogen and electron–hole plasma from neutral particle system to metallic-like state and crystal-like structures, including antiferromagnetic hole structure in semiconductors at low temperatures, are discussed.

Derivation of weakly nonideal hydrogen plasma EOS and detailed results on partial contributions to plasma pressure for the Sun's interior are presented. The impetus for this work was the demand for high accuracy of the EOS of the solar plasma in relation to the problems of modern helioseismology, accuracy sufficient for reproducing the velocity of sound on the Sun from optical measurements with errors not exceeding 10⁻⁴. In our computations the relativistic corrections, degeneracy of electrons, radiation pressure in plasma, the Coulomb interaction in the Debye–Hückel approximation together with diffraction and exchange corrections and the contribution of bound and scattering states are taken into account. The analysis of the electrical neutrality condition in terms of activities and concentrations is presented. It is shown how to modify the relation between activities and concentrations for removing divergences of the Hartree contribution, representing the first order correction due to the Coulomb interaction in plasma. For the conditions of the Sun trajectory it is shown that the widely used practice of ignoring the neutrality condition in terms of activities, taking the Hartree contribution into account, gives a maximal error for plasma pressure of the order of 10⁻⁵.

Helioseismology has become a very successful diagnosis of the equation of state. Although the gas in the solar interior is only weakly coupled and weakly degenerate, the great observational accuracy of the helioseismological measurements puts strong constraints on the nonideal part of the equation of state. For solar and stellar modelling, a high-quality equation of state is crucial. But the inverse is also true: the astrophysical data (helioseismic today, asteroseismic tomorrow) can put constraints on the physical formalisms, thus making the Sun and the stars laboratories for plasma physics.

In this work, we calculate the thermodynamic properties of hydrogen–helium plasmas with different mass fractions of helium by the direct path integral Monte Carlo method. To avoid unphysical approximations, we use the path integral representation of the density matrix. We pay special attention to the region of weak coupling and degeneracy and compare the results of simulation with a model based on the chemical picture. Further with the help of calculated deuterium isochors, we compute the shock Hugoniot of deuterium. We analyse our results in comparison with recent experimental and calculated data on the deuterium Hugoniot.

We study the equation of state, polarization and radiation properties for nonideal, strongly magnetized plasmas which compose outer envelopes of magnetic neutron stars. Detailed calculations are performed for partially ionized hydrogen atmospheres and for condensed hydrogen or iron surfaces of these stars.

Calculations of thermodynamic properties for the solar plasma are presented. Effects of Coulomb interaction, exchange and diffraction effects, free electron degeneracy, relativistic corrections and radiation pressure contributions are taken into account. Calculations of the equation of state of the solar plasma with different element compositions are carried out. The contribution of various plasma effects and chemical element abundance to thermodynamic functions and in particular Γ₁ is discussed.

In the present work, we use the recently developed cluster multi-range interpolation (CMRI) (Valuev 2005 Comput. Phys. Commun.169 60) of interaction potentials to simulate hydrogen plasma using molecular dynamics (MD). The interpolation is based on variational mixing of cluster connectivity within a given system of electrons and ions described by coordinates of the particles. The use of potential interpolation based on connectivity allows us to treat the collisions of small numbers of particles (up to two ions and three electrons together) by more accurate empirical models and treat such processes as ionization or molecule formation by means of MD simulation on single-valued smooth approximate N-particle potential energy surfaces. The construction of the scheme and the results of equilibrium MD simulations are discussed. Energy spectra and particle pair correlation functions are compared between the current CMRI model and two classical models with pair pseudopotentials.

Microscopic and thermodynamic properties of dense semiclassical partially ionized hydrogen plasma were investigated on the basis of pseudopotential models. Radial distribution functions (RDF) of particles were obtained using a system of the Ornstein–Zernike integral equations. The corrections to internal energy and the equation of state were calculated using RDF.

Real-time thermal field theory is used to reveal the structure of plasma corrections to nuclear reactions. Previous results are recovered in a fashion that clarifies their nature and new extensions are made. Brown and Yaffe have introduced the methods of effective quantum field theory into plasma physics. They are used here to treat the interesting limiting case of dilute but very highly charged particles reacting in a dilute, one-component plasma. The highly charged particles are very strongly coupled to this background plasma. The effective field theory proves that the mean field solution plus the one-loop term dominates; higher loop corrections are negligible even though the problem involves strong coupling. Such analytic results for very strong coupling are rarely available, and they can serve as benchmarks for testing computer models.

We present theoretical results for the equation of state of hydrogen and helium applying the chemical picture which treats the elementary charged particles (electrons, ions) and neutral bound states (atoms, molecules) on an equal footing. The chemical equilibrium for dissociation and ionization processes is solved accounting for nonideality corrections. We compare our results with experiments and other theoretical models and calculate pressures and temperatures in jupiter's interior.

The paper reports molecular dynamics (MD) simulations on two-dimensional, strongly-coulped Yukawa liquids. An effective coupling coefficient Γ* for the liquid phase is identified; thermodynamic properties such as internal energy, pressure and compressibility, as well as longitudinal and transverse mode dispersions are analysed.

Strongly coupled two-dimensional systems of dust particles are often observed in dusty plasma experiments. We analyse thermodynamic quantities of two-dimensional Yukawa plasmas and apply the results to structure formations in two-dimensional finite systems. We include the nonlocal effect which has been neglected in the previous analysis and give a relatively simple method to estimate important parameters in dusty plasmas.

The major properties of complex (dusty) plasmas as a new state of matter are shown to be determined by the collective interaction of two coupled fields, the electrostatic field and the flux field. Both fields determine the grain collective nonlinear screening and grain attraction. Collective interactions together with nonlinear screening are used in the formulation of a new paradigm for plasma crystal formation.

The problem of normal and anomalous diffusion is formulated on the basis of integral master-type equations with various probability transition functions for diffusion in coordinate space (PTD functions). Grain diffusion in dusty plasmas has a normal character. The dependence of the diffusion coefficient as a function of the grain–grain interaction strength is investigated.

We present the generalization to the binary Yukawa mixture of equilibrium molecular dynamic computations of the transport coefficients of the Yukawa one-component plasma (Salin and Caillol 2002 Phys. Rev. Lett.88 065002, Salin and Caillol 2000 J. Chem. Phys.113 10459–63). The simulations were performed within periodic boundary conditions, and Ewald sums were implemented for the potentials, the forces and for all the currents which enter the Kubo formulae. Results include shear and bulk viscosities, ionic thermal conductivity, as in the one-component case, but also diffusion and interdiffusion coefficients. We will present the different coefficients and examples of simulations. We shall also compare our simulation results for large screening parameters with Chapman–Enskog theory (Chapman and Cowling 1970 The Mathematical Theory of Non-Uniform Gases 3rd edn (Cambridge: Cambridge University Press)).

Computer simulation of dusty plasma properties is performed. The radial distribution functions, the diffusion coefficient are calculated on the basis of the Langevin dynamics. A comparison with the experimental data is made.

Classical molecular dynamics and Monte Carlo simulations are used to investigate three-dimensional spherical charged particle clusters which were experimentally observed in dusty plasmas (Arp et al 2004 Phys. Rev. Lett.93 165005). The shell configuration and geometry of the ground state is found to change with the screening parameter. The melting temperature of small clusters exhibits a non-monotonic dependence on the total number of particles.

In this work we present the first observations of dust crystal generated in plasma by the slowing-down proton beam. The crystal observed has a simple cubical lattice with the mean distances between particles for different gases (He, Ne, Ar, Kr, Xe) from 90 µm to 140 µm. For calculation of plasma parameters the model of kinetic processes was developed. Results of our simulation showed that anisotropic dust particles interaction can be the main physical reason for the appearance of the crystal-like structure.

Formation of large-scale dust vortices in the striation of dc glow discharges was experimentally investigated. Dust clouds were formed by monodisperse MF particles with diameters ≈2 µm in the regions of stable striation. Vortices obtained were about 1 cm in size and contained ∼10⁴ particles. Structural (vortex configuration, dust particle flow filaments) and dynamic (rotation frequencies and velocity spectrum) characteristics of large-scale dust vortices were measured.

Structure of clusters of Yukawa particles is analysed by simulations and theoretical approaches in an isotropic environment which can be realized under microgravity or by active cancellation of the effect of gravity. Yukawa particles model dust particles in dusty plasmas and such an environment is suitable to observe their inherent properties. At low temperatures, clusters are composed of spherical shells and, when scaled by the mean distance, the structure seems to depend almost only on the system size or the number of particles. The positions and populations of shells are given by simple interpolation formulae. It is shown that shells have an approximately equal spacing close to that of triangular lattice planes in the bulk close-packed structures. When the cohesive energy in each shell is properly taken into account, the shell model reproduces these structures of spherical Yukawa clusters to a good accuracy.

Various interactions can play a role between the mesoscopic dust grains of a complex plasma. We study a system composed of dust grains that have both an electric charge and a permanent magnetic dipole moment. It is assumed that the grains occupy lattice sites, as dictated by their Coulomb interaction. In addition, they possess a spin degree of freedom (orientation of magnetic dipole moment) that is not constrained by the Coulomb interaction, thus allowing for the possibility of equilibrium orientational ordering and 'wobbling' about the equilibrium orientations. As a result, collective modes develop. We identify in-plane and out-of-plane wobbling modes and discuss their dispersion characteristics both in the ferromagnetic and in the anti-ferromagnetic ground state.

Of interest in modern plasma physics are investigations of dusty plasmas encountered in a variety of experiments, applications and natural phenomena as well. Dust grains are known to form a crystalline structure that poses a question of how attractive forces are generated in a particular dusty plasma. In this paper, a new model of intergrain interaction is proposed. In most works on dusty plasmas, the plasma medium itself is considered to be in an ideal state of matter when the interaction between particles, i.e., electrons and ions, is negligible. Herein this assumption is not implied and, thus, the density–response formalism with the local-field correction is used to account for the plasma screening in the longitudinal dielectric function. Then, a new model of intergrain interaction is defined and it is shown that a molecule-like potential with an energy well appears. Such a model might be appropriate for cryogenic dusty plasma experiments recently reported.

Approximate expressions for the electron and ion fluxes to a dust grain under conditions a ≪ l ≪ λ (a is the grain radius, l is the mean free path of electrons or ions and λ is the screening length) are presented. Such conditions can be realized, for example, in a plasma at atmospheric pressure and temperature T ∼ 0.1 eV for grains of (sub)micron size. In two limit cases l ≪ a, λ and l ≫ a, λ, the expressions for the fluxes are well known. In the intermediate case, the motion of an electron or ion in the spherical layer a < r < a + l is considered as collisionless in the Coulomb potential, while for r > a + l the drift-diffusion approximation is used. The obtained expression for the electron flux is applied for setting the boundary condition near the dust grain in the case of a thermionic plasma.

The Helmholtz free energy of dusty plasmas is analysed as a one-component Yukawa system embedded in an ambient background plasma, and thermodynamic quantities are given in the form of simple interpolation formulae applicable in the domain of intermediate and strong coupling. By calculating the spectrum of the long wavelength fluctuations of the ambient plasma density, it is shown that there is a possibility of observing the divergence in the isothermal compressibility of the Yukawa OCP (a thermodynamic instability of a homogeneous phase) as an enhancement of fluctuation amplitudes and the critical condition is given as a combination of parameters for dusty plasmas.

We discuss the dynamics of recombination of an expanding ultracold plasma into highly excited Rydberg states, with emphasis on the influence of possible strong coupling between the charges and the nonequilibrium character of the electronic component. While the former does not significantly affect recombination in current experimental scenarios, the latter is shown to have a considerable influence on the system dynamics. We derive correction factors quantifying the deviation of collision rates from their respective equilibrium values. The experimentally observed unexpectedly high recombination rate at long evolution times can be reproduced by a proper inclusion of these effects without the need to invoke alternative, previously suggested mechanisms, such as an 'adiabatic motional recombination' or the development of very strong electron correlations by collisional cooling.

The results of recent experiments and simulation for ultracold plasmas are related to the criterion of the thermodynamic stability. Different approaches for the equation of state of strongly coupled plasmas are used: second virial coefficient, electrolyte-like and van der Waals-like approximations. Three areas of ultracold plasma parameters are distinguished: thermodynamically stable, labile and metastable.

Rydberg atoms can be considered as mesoscopic systems at the interface between quantum and classical behaviour. The interaction with the surroundings (bath) becomes essential and leads to dephasing of the wavefunction. An important process in Rydberg plasmas is the collision with free charge carriers. Transition rates due to Coulomb interaction are considered in the Born approximation and are shown to coincide with the dephasing time according to linear response theory for mesoscopic devices. We point out that this description of the dephasing process relies on weak coupling between the Rydberg states and the bath and becomes invalid, if strong scattering is of importance.

Extensive molecular dynamics calculations have been performed on classical, symmetric electronic bilayers at various values of the coupling strength Γ and interlayer separation d to delineate its phase diagram in the Γ–d plane. We studied the diffusion, the amplitude of the main peak of the intralayer static structure factor and the peak positions of the intralayer pair correlation function with the aim of defining equivalent signatures of freezing and constructing the resulting phase diagram. It is found that for Γ greater than 75, crystalline structures exist for a certain range of interlayer separations, while liquid phases are favoured at smaller and larger d. It is seen that there is good agreement between our phase diagram and previously published ones.

We have analysed the dispersion of longitudinal collective modes in classical asymmetric charged-particle bilayer liquids in the strong coupling regime. The theoretical analysis is based on a dielectric matrix calculated in the quasi-localized charge approximation (QLCA). The matrix elements are expressed as integrals over inter-layer and intra-layer pair correlation function data that we have generated by molecular dynamics (MD) simulations. At the same time, MD simulations of density and current fluctuation spectra were analysed to infer the collective mode dispersion. The long-wavelength finite frequency (energy) gap, brought about by strong inter-layer correlations, is a monotonically increasing function of the density ratio, n₂/n₁, and, for the smallest value of the inter-layer spacing considered, the gap reaches its maximum value when the two layer densities are equal. It appears that it stays at that value for n₂/n₁ > 1.

The understanding of the theoretical structure of phonon dispersion in Yukawa lattices and the relationship between these perfect lattice phonons on the one hand, and the excitations in the disordered and liquid states on the other, is an important issue in analysing experimental and simulation results on plasma crystals. As the first step in this programme, we have numerically calculated the full phonon spectrum for 2D triangular Yukawa lattices, for a wide range of (screening parameter) values and along different propagation angles. Earlier calculations of the excitation spectra of the 2D and 3D Yukawa liquids were based on the quasilocalized charge approximation (QLCA), whose implicit premise is that the spectrum of an average distribution (governed by the isotropic liquid pair correlation function) is a good representation of the actual spectrum. To see the implications of this model more clearly, we compare the high Γ (near crystallization) QLCA phonon spectra with the angle-averaged phonon spectra of the lattice phonons.

The well-known problem of beam–plasma instability acquires new aspects when one or both of the two components (the beam and the plasma) are strongly interacting. We have now theoretically considered the case when the plasma is in the solid phase and forms a lattice. In this situation, the inherent anisotropy of the lattice leads to a coupling between the longitudinal and transverse polarizations. One of the novel features of the beam–plasma instability in this scenario is the possible excitation of transverse modes, which should be an experimentally observable signature of the instability. We have initially concentrated on a 2D toy model with the beam lying in the lattice plane. At the same time, we have initiated a molecular dynamics simulation program for studying various aspects of the penetration of a beam into a plasma lattice. The beam parameters can be adjusted in order to see the effects of increasing coupling strength within the beam and to distinguish between collective phenomena and scattering on individual particles. When both components are strongly interacting, a number of remarkable phenomena—trapping of beam particles, creation of dislocations, local melting of the lattice—may be observed.

The photoinduced re-entrant metal-to-insulator transition is considered. Using the concept of coherence length, an equation for the critical concentration, similar to the Mott criterion, is obtained. Experimental results are discussed concerning the metal–insulator transitions in SmS and VO₂.

The isothermal compressibility plays a central role in determining the characteristics of the static response in plasma systems. In a charged particle bilayer this role is assumed by L_ij, the matrix of inverse compressibilities. For weak coupling, the inverse compressibilities of a bilayer of charged particles can be calculated analytically in the Debye limit from the equation of state through the chemical potential. There are two different charging procedures to obtain the latter. We present the results of a rather lengthy analytical calculation, exploring both approaches. The limits of the validity of the Debye description are discussed, and we compare the weak coupling results with L_ij values inferred from S(k → 0) through the compressibility sum rule, where the structure function S(k) is generated for strong coupling both through molecular dynamics simulations and by HNC calculations.

It is shown that the nature of the non-electrostatic part of the pair interaction potential in classical Coulomb fluids can have a profound influence on the screening behaviour. Two cases are compared: (i) when the non-electrostatic part equals an arbitrary finite-ranged interaction and (ii) when a dispersion r⁻⁶ interaction potential is included. A formal analysis is done in exact statistical mechanics, including an investigation of the bridge function. It is found that the Coulombic r⁻¹ and the dispersion r⁻⁶ potentials are coupled in a very intricate manner as regards the screening behaviour. The classical one-component plasma (OCP) is a particularly clear example due to its simplicity and is investigated in detail. When the dispersion r⁻⁶ potential is turned on, the screened electrostatic potential from a particle goes from a monotonic exponential decay, exp(−κr)/r, to a power-law decay, r⁻⁸, for large r. The pair distribution function acquire, at the same time, an r⁻¹⁰ decay for large r instead of the exponential one. There still remains exponentially decaying contributions to both functions, but these contributions turn oscillatory when the r⁻⁶ interaction is switched on. When the Coulomb interaction is turned off but the dispersion r⁻⁶ pair potential is kept, the decay of the pair distribution function for large r goes over from the r⁻¹⁰ to an r⁻⁶ behaviour, which is the normal one for fluids of electroneutral particles with dispersion interactions. Differences and similarities compared to binary electrolytes are pointed out.

The problem of accurately accounting for long ranged Coulomb forces within periodic boundaries in Monte Carlo and molecular dynamics computer simulation of strongly coupled Coulomb systems is considered. Periodicity artefacts characteristic of the conventional Ewald summation procedure are eliminated by angular averaging of Ewald sums over all orientations of the main cell. This approach provides an effective analytical electrostatic interaction potential and allows fast and accurate simulations of strongly coupled Coulomb fluids even on a modern PC. The effectiveness and accuracy of the method is illustrated on simple non-ideal plasma models.

Kubo proposed a physical approach to proving the validity of Boltzmann's ergodic hypothesis. It is to perform the time averages on dynamical functions, thereby avoiding the difficulties of measure theory inherent in the classical approach. To perform time averaging properly, one must have a general solution for the Heisenberg equation of motion such as by the recurrence relations method. A time averaging carried over with a recurrence relations solution is found to yield an ergodic condition in the form of an infinite product. It is linked to the energy transfer mechanisms, hence to the ergodicity itself. The electron gas models are fertile ground for testing ergodicity by this approach. For several static domains, we have evaluated the infinite product and drawn from them a general physical picture that underlies the ergodic hypothesis.

The knowledge of plasma equation of state and photoabsorption requires suitable and realistic models for the description of ions. The number of relevant electronic configurations of ions in hot dense plasmas can be immense (increasing with atomic number Z). In such cases, calculations relying on the superconfiguration approximation appear to be among the best statistical approaches to photoabsorption in plasmas. The superconfiguration approximation enables one to perform rapid calculation of averages over all possible configurations representing excited states of bound electrons. We present a thermodynamically consistent model involving detailed screened ions (described by superconfigurations) in plasmas. The density effects are introduced via the ion-sphere model. In the usual approaches, bound electrons are treated quantum mechanically while free electrons are described within the framework of semi-classical Thomas–Fermi theory. Such a hybrid treatment can lead to discontinuities in the thermodynamic quantities when pressure ionization occurs. We propose a model in which all electrons (bound and free) are treated quantum mechanically. Furthermore, resonances are carefully taken into account in the self-consistent calculation of the electronic structure of each superconfiguration. The model provides the contribution of electrons to the main thermodynamic quantities, together with a treatment of pressure ionization, and gives a better insight into the electronic properties of hot dense plasmas.

Dimensional continuation is employed to compute the energy loss rate for a non-relativistic particle moving through a highly ionized plasma. No restriction is made on the charge, mass, or speed of this particle, but it is assumed that the plasma is not strongly coupled in that the dimensionless plasma coupling parameter g = e²κ_D/4πT is small, where κ_D is the Debye wave number. To leading order in this coupling, dE/dx is of the generic form g² ln[g²C]. The prefactor of the logarithm is well known. We compute the constant C under the logarithm exactly. Our result differs from approximations given in the literature, with differences in the range of about 20% for cases relevant to inertial confinement fusion experiments.

A semi-classical model is built to study the dynamical behaviour of many-electron wavefunctions interacting with strong fields for applications such as the interaction of a laser beam with a high-Z gas at high intensity or the collision between two heavy ions in the intermediate velocity regime. Within the semi-classical model, quantum dynamics of the electrons is described from generalized coordinates, which, as a result of a variational principle, obey classical Lagrange equations. The formalism is first applied to hydrogen ions and then extended to many-electron systems.

The electric microfield distributions (MFD) at charged and neutral particles in classical electron–ion two-component plasmas are described by a theoretical model based on the exponential and the potential-of-mean-force approximations. The MFDs provided by this theoretical treatment are in good agreement with results from molecular dynamics simulations.

The problem of stopping power (SP) for projectile ions is analysed in terms of the dielectric function and effective collision frequency for moderately dense and strongly coupled plasmas (SCP). We consider several issues regarding the calculation of stopping power for correlated ensembles of particles and oscillators. In particular, effects of group (few particle) modes, transition from positive to negative dispersion and excitation of collective modes up to suprathermal level at plasma targets are addressed. Linear SP of dense suprathermal (nonlinear) plasma targets at different levels of target plasma turbulence is estimated. The force of suprathermal plasma oscillations on the projectile ions is mostly in the nature of increased frictional drag. The results obtained show the possibility of increasing low velocity stopping (up to 'turbulent' values) in comparison with losses in equilibrium dense plasma targets. Experimental conditions to create specific turbulent targets as well as some connection between stopping phenomena and SCP transport properties are discussed briefly.

In this work, the previously developed method for calculation of HF electroconductivity of non-ideal plasma is applied to the area of high electron densities: 10²¹ ⩽ N_e ⩽ 10²³ cm⁻³ and in the temperature range 20 000 K ⩽ T ⩽ 1000 000 K. This is enabled by the improvement of the numerical procedure. The real and imaginary parts of the HF conductivity are parametrized in the Drude–Lorentz form. One of the parameters is the static conductivity σ₀. The computations are carried out in the frequency range [0, 0.05ω_p], ω_p being the plasma frequency.

The description of energy absorption in a fully ionized plasma in an electric field is generalized to arbitrary frequencies and field strengths. The limiting cases of weak and of high fields as well as the frequency dependence of the energy absorption rate are discussed.

Collisional absorption of dense fully ionized plasmas in strong laser fields is investigated using quantum kinetic theory as well as molecular dynamics simulations. Quantum statistical calculations are presented for the important case of a two-temperature plasma. Comparision is given to molecular dynamics simulations. Special attention is devoted to the question of how to treat properly the attractive electron–ion interaction for short ranges in classical molecular dynamics simulations.

We present results on the equation of state (EOS) of high density hydrogen plasmas. We use a hybrid first principles method capable of describing fully ionized plasmas. Electrons as well as the electron–ion interactions are described with Green's functions technique which includes dynamic screening and degeneracy effects. The properties of the proton subsystem are calculated using classical integral equations (HNC) which take strong correlations into account. We compare our results to a variety of analytic approaches and simulation techniques.

Three items related to path integrals in quantum statistics are discussed: (1) entropic sampling within Wang–Landau algorithm; (2) calculating partition function for a fermion system using expanded ensemble technique; (3) applying classical density functional theory to expressions in path integral form.

When electrons in a solid are excited to a higher energy band they leave behind a vacancy (hole) in the original band which behaves like a positively charged particle. Here we predict that holes can spontaneously order into a regular lattice in semiconductors with sufficiently flat valence bands. The critical hole to electron effective mass ratio required for this phase transition is found to be of the order of 80.

A model for the Hall coefficient is developed within the framework of the Zubarev formalism and linear response theory. Comparison is made with the relaxation time approximation. Further results are given including electron–electron interactions within linear response theory.

We investigate the coupled relaxation of plasma composition and species temperatures in dense two-temperature plasmas. Nonideality effects are included in the rate coefficients of impact ionization and by quasi-particle shifts that modify the charge carrier energies. Results are presented for laser-produced and for shock-produced plasmas which have very different initial conditions for the species temperatures.

Brilliance spectra of a carbon plasma generated by subpicosecond high intensity laser pulses are analysed (Wilhein et al 1998 J. Opt. Soc. Am.15 1235). The plasma parameters such as electron density and temperature are determined using a plasma slab model. Synthetic carbon He-α and He-β line profiles are calculated for the inferred plasma parameters by using thermodynamic Green's function, based on a microscopic quantum statistical approach assuming local thermal equilibrium. Self-absorption is taken into account considering one-dimensional radiation transport equation. The comparison between the measured spectrum and our calculated synthetic profile is good for He-α line (C V 1s²–1s2p), while discrepancies are found in the case of He-β line (C V 1s²–1s3p).

We investigate the relaxation of nonideal plasmas and demonstrate the connection between the energy transfer rate and potential energy contributions. A quantum-statistical approach is used to determine how the energies of the electron and ion subsystems can be defined. In particular, it is shown that the electron–ion potential energy term must be split equally between both subsystems. We finally demonstrate that this treatment is consistent with the transfer of total energy between the subsystems as it is for instance considered within the coupled mode approach.

The high intensity heavy ion beams provided by the accelerator facilities of the Gesellschaft für Schwerionenforschung (GSI) Darmstadt are an excellent tool to produce large volumes of high energy density (HED) matter. Thermophysical and transport properties of HED matter states are of interest for fundamental as well as for applied research. In this paper we present the most recent results on electrical resistivity of HED matter obtained at the High Temperature Laboratory of the Plasma Physics Department of GSI. The targets under investigation consisted of 5 mm long and 0.25 mm diameter aluminium wires. Uranium beam pulses with durations of approximately 200 ns, intensities of about 2 × 10⁹ ions/bunch and an initial ion energy of 350 A MeV have been used as a driver. An energy density deposition of about 1 kJ g⁻¹ has been achieved by focussing the ion beam to less than 1 mm FWHM. Under these conditions, resistivities of up to 1.5 × 10⁻⁶ Ω m have been observed within 1 µs after irradiation.

Plasma targets for measuring energy loss and charge-state distribution of heavy ions in non-ideal plasmas have been developed. Ar plasmas with Γ-parameters 0.55–1.5 could be realized and the interaction with several ion species studied. Here, the results for 5.9 MeV/u C ions are presented. The energy loss in plasma was reproduced in different experiments.

Detailed theoretical studies have shown that intense heavy-ion beams that will be generated at the future Facility for Antiprotons and Ion Research (FAIR) (Henning 2004 Nucl. Instrum. Methods B 214 211) at Darmstadt will be a very efficient tool to create high-energy-density (HED) states in matter including strongly coupled plasmas. In this paper we show, with the help of two-dimensional numerical simulations, the interesting physical states that can be achieved considering different beam intensities using zinc as a test material. Another very interesting experiment that can be performed using the intense heavy-ion beam at FAIR will be generation of low-entropy compression of a test material such as hydrogen that is enclosed in a cylindrical shell of a high-Z material such as lead or gold. In such an experiment, one can study the problem of hydrogen metallization and the interiors of giant planets. Moreover, we discuss an interesting method to diagnose the HED matter that is at the centre of the Sun. We have also carried out simulations to study the damage caused by the full impact of the Large Hadron Collider (LHC) beam on a superconducting magnet. An interesting outcome of this study is that the LHC beam can induce HED states in matter.

In this paper, we present experimental results on the excitation of solid-state matter by single, energetic heavy ions. The method of x-ray spectroscopy with spatial resolution along the projectile stopping path inside solids was applied to investigate the state of the medium inside the area of heavy-ion tracks. Spectral data of quartz and aluminium media excited by Ni, Ca and Mg ions from the GSI UNILAC accelerator are presented. The ions' initial energies of 11.4 and 5.9 MeV/u and the beam current on the target in the order of 1 µA were chosen. The observation was focused on relative intensities of K_α satellite lines radiated by Si and Al multicharged ions with different charges. The aerogel medium with extremely low bulk density (0.04 g cc⁻¹) was used to investigate the evolution of target media radiation properties during the projectile ions' stopping and, respectively, the change of the ion's energy deposition into the solids. Due to very short lifetimes of the excited levels for the observed multicharged ions, the data for heavy-ion track area were obtained on tens of femtoseconds time scale after excitation. For further analysis and obtaining quantitative description of heavy-ion track parameters, the methods of numerical simulation are suggested.

Collision of fast plasma streams in vacuum is investigated. Plasma streams were produced by irradiation of thin foils with a powerful pulsed electron beam. Interaction of the plasma flows was studied by using frame and streak cameras. One-dimensional numerical simulation was carried out. Application of this method for porous ICF targets and high-energy physics is discussed.

The present paper gives an experimental and theoretical study of the transmission process of protons within the 100 keV to 300 keV energy range through a quartz tube, 100 mm in length and 1.6 mm in diameter. It has been established that protons pass through the tube without energy losses. The proton beam goes through the tube even when the tube axis is tilted from the beam axis. The angular width of the protons' transmission curve versus the angle of incidence makes about 3°. As the authors suggest, this effect is due to self-organization of a beam–wall charge system. Computer simulation has shown that distribution of the charge on the wall is axially symmetric and oscillates along the tube. It is known that when a charge moves inside the oscillating field which has a gradient, it is subjected to the action of a unidirectional force. This force provides protons movement through the channel without collisions with the wall.

Using the SPECTR numerical model based on the (super)configuration approach, Rosseland mean opacities of the Cu-doped Be plasmas were calculated in broad temperature and density ranges in application to the modelling of promising indirect-driven targets proposed for future ICF experiments. Comparisons of mid-ionized plasma opacities to experimental and other theoretical data are also presented.