Table of contents

A brief review is given on recent studies of charged soft matter solutions, as modelled by the 'primitive' approach of strongly coupled Coulomb systems, where the solvent just enters as a dielectric background. These include charged colloids, biological macromolecules such as proteins and DNA, polyelectrolytes and polyelectrolyte stars. Also some original results are presented on colloid–polyelectrolyte complex formation near walls and on the anomalous fluid structure of polyelectrolyte stars as a function of increasing concentration.

We propose an analytical approximation for the dependence of the effective charge on the bare charge for spherical and cylindrical macro-ions as a function of the size of the colloid and salt content, for the situation of a unique colloid immersed in a sea of electrolyte (where the definition of an effective charge is non-ambiguous). Our approach is based on the Poisson–Boltzmann (PB) mean-field theory. Mathematically speaking, our estimate is asymptotically exact in the limit κa ≫ 1, where a is the radius of the colloid and κ is the inverse screening length. In practice, a careful comparison with effective charge parameters, obtained by numerically solving the full nonlinear PB theory, proves that our estimate is good down to κa ∼ 1. This is precisely the limit appropriate to treat colloidal suspensions. A particular emphasis is put on the range of parameters suitable to describe both single and double strand DNA molecules under physiological conditions.

Using numerical simulations we show that a variety of novel colloidal crystalline states and multi-step melting phenomena occur on square and triangular two-dimensional periodic substrates. At half-integer fillings different kinds of frustration effects can be realized. A two-step melting transition can occur in which individual colloidal molecules initially rotate, destroying the overall orientational order, followed by the onset of interwell colloidal hopping, in good agreement with recent experiments.

We present a theoretical model that allows us to study linear and non-linear aspects of the femtosecond electron dynamics in metal clusters. The theoretical approach consists in the classical limit of the time-dependent Kohn–Sham equations. The electrons are described by a phase-space distribution function which satisfies a Vlasov-like equation while the ions are treated classically. This allows simulations for clusters containing several hundreds of atoms and extending up to several hundreds of femtoseconds during which the description conserves the fermionic character of the electron distribution. This semi-quantal approach compares very well with the purely quantal treatment. As an application of this approach, we show the prominent role of the electron dynamics during and after the interaction with an intense femtosecond laser pulse.

Colloidal suspensions and polyelectrolyte solutions containing multivalent counterions can exhibit some very counter-intuitive behaviour usually associated with low-temperature physics. There are two particularly striking phenomena resulting from strong electrostatic correlations. One is the like-charge attraction and the second is the polyion overcharging. In this contribution we will concentrate on the problem of overcharging. In particular, we will explore the kinetic limitation to colloidal charge inversion in suspensions containing multivalent counterions.

A modified Feynman construction with a zero-frequency central peak is used to model the dynamical structure functions for layered charged particle systems. This construction recognizes the affinity between layered and multicomponent systems. It also guarantees the simultaneous satisfaction of all three frequency-moment sum rules. The frequencies and spectral weights of the long-wavelength collective excitations and the strength of the diffusive central peak are calculated for arbitrary degeneracy.

This paper reviews our recent molecular dynamics simulation studies of the static and dynamical behaviour of classical bilayers in their liquid phase. The pair correlation functions obtained in the static calculations make it possible to trace the structural changes of the system as well as to calculate the energy and static structure functions of the bilayer. The dynamical calculations show the existence of two (in-phase and out-of-phase) longitudinal and two (in-phase and out-of-phase) transverse collective modes. We present the full dispersion relations for these modes at different layer separations. At low layer separations the out-of-phase modes are found to possess a finite frequency at wave numbers k → 0, confirming the existence of the long-wavelength energy gap in the bilayer system predicted by the quasi-localized charge approximation. It is only at higher layer separations that the dominant portion of the longitudinal out-of-phase mode is well approximated by the acoustic behaviour, resulting from the random phase approximation theory.

Earlier theoretical and computer studies on the dynamics of strongly coupled charged particle bilayers have revealed the existence of an energy gap (ω(k = 0) ≠ 0, optical behaviour) for the out-of-phase plasmon. This is in contrast to the correlationless RPA prediction of acoustic (ω ∼ k) behaviour. We have studied the question whether a classical perturbation calculation for weak coupling shows the onset of the energy gap, and whether there is a minimal coupling threshold for the formation of the gap. A formally exact lowest order expansion technique due to Zhang and Kalman (1992 Phys. Rev. A 45 5935) has been used.

We present calculations for the valence electron–electron structure factor in liquid Mg near freezing, assuming knowledge of the jellium result. On the basis of this, we predict significant corrections to jellium short-range correlations in liquid s–p metals and in particular an increase in the electron–electron contact probability.

We present a first-principles path integral Monte Carlo study of a finite number of strongly correlated electron–hole pairs in two symmetric vertically coupled quantum dots. In this system, the intra- and interdot correlations depend on the distance d between the dots, the density n (strength of confinement potential) and temperature T. For fixed d and T > 0, increasing n leads to four qualitatively different states: an exciton 'liquid', an exciton 'crystal', orientationally decoupled electron and hole 'crystals' and an electron (hole) liquid.

The quantum dynamics of an ensemble of interacting electrons in an array of random scatterers is treated using a new numerical approach for the calculation of average values of quantum operators and time correlation functions in the Wigner representation. This approach combines both molecular dynamics and Monte Carlo methods and computes numerical traces and spectra of the relevant dynamical quantities such as momentum–momentum correlation functions and spatial dispersions. Considering, as an application, a system with fixed scatterers, the results clearly demonstrate that the many-particle interaction between the electrons can lead to an enhancement of the conductivity at intermediate densities.

The model under consideration is a classical 2D Coulomb gas of pointlike positive and negative unit charges, interacting via a logarithmic potential. In the whole stability range of temperatures, the equilibrium statistical mechanics of this fluid model is exactly solvable via an equivalence with the integrable 2D sine-Gordon field theory. The exact solution includes the bulk thermodynamics, special cases of the surface thermodynamics and the large-distance asymptotic behaviour of the two-body correlation functions.

Strong correlations in quantum Coulomb systems (QCS) are attracting increasing interest in many fields ranging from dense plasmas and semiconductors to metal clusters and ultracold trapped ions. Examples are bound states in dense plasmas (atoms, molecules, clusters) and semiconductors (excitons, trions, biexcitons) or Coulomb crystals. We present first-principle simulation results of these systems including path integral Monte Carlo simulations of the equilibrium behaviour of dense hydrogen and electron–hole plasmas and molecular dynamics and quantum kinetic theory simulations of the nonequilibrium properties of QCS. Finally, we critically assess potential and limitations of the various methods in their application to Coulomb systems.

The formation of bound states and their modifications within a dense medium is an important aspect of strongly coupled Coulomb systems. In particular, within the concept of a partially ionized plasma, the plasma is considered as a mixture of electrons and ions in free and bound states. The account of the interaction with the medium by self-energy shifts for the free and bound states becomes less founded at high densities. Within the framework of a systematic Green's function approach, the spectral function is investigated. It is demonstrated how a band is formed if additional contributions which describe hopping between bound states are taken into account. In this way, the connection to condensed matter approaches can be made directly which has not been shown before.

Starting from quantum kinetic theory, collisional absorption of laser radiation is investigated for dense plasmas. The electrical current and the energy balance equations are formulated within the framework of nonequilibrium Green's function methods. Quantum statistical expressions are derived for plasmas in which the coupling between electrons and ions is weak due to the influence of the strong high-frequency laser field, however, the electron and the ion components may be strongly coupled within their respective subsystems. Consequently, the expressions for, e.g., the electrical current and the cycle-averaged energy absorption rate contain the dynamical structure factors and the dielectric function of the strongly correlated electron and ion subsystems. The expressions are valid for arbitrary field strength assuming the nonrelativistic case.

In this paper, the method of thermodynamic Green's functions is applied to investigate thermodynamic properties of dense weakly coupled plasmas. First, we present results for the equation of state for fully ionized hydrogen and compare our results with path integral Monte Carlo simulation data. Densities and temperatures are considered where correlations as well as Fermi statistics have to be taken into account. Then, the correlation energy and the mean value of the kinetic energy of dense plasmas are considered. Usually one finds that the kinetic energy is larger than that of an ideal system due to the interaction. However, in agreement with results from quantum simulations, we found, for certain densities and temperatures, a lowering of the kinetic energy.

Effective two-body potentials for electron–ion plasmas are analysed. Such potentials which have been previously derived by Kelbg and others capture the basic quantum diffraction effects and are exact in the weak coupling limit. Moreover, using path integral Monte Carlo (PIMC) methods, they can be applied to strongly coupled plasmas which include bound states. We investigate the accuracy of the diagonal Kelbg potential (DKP) as well as the off-diagonal Kelbg potential (ODKP) by comparison with accurate numerical solutions of the off-diagonal two-particle Bloch equation. A significant improvement is achieved by correcting the potential value at zero particle separation.

The conventional Vlasov treatment of beam-plasma instabilities is inappropriate when the plasma is strongly coupled. In the strongly coupled liquid state, the strong correlations between the dust grains fundamentally affect the conditions for instability. In the crystalline state, the inherent anisotropy couples the longitudinal and transverse polarizations, and results in unstable excitations in both polarizations. We summarize analyses of resonant and non-resonant, as well as resistive instabilities. We consider both ion-dust streaming and dust beam-plasma instabilities. Strong coupling, in general, leads to an enhancement of the growth rates. In the crystalline phase, a resonant transverse instability can be excited.

We present simplified expressions for the dynamic structure factor, or form factor S(k, ω), which is the quantity describing the inelastic x-ray scattering cross section from a dense plasma or a simple liquid. Our results, based on the random phase approximation (RPA) for the treatment on the charged particle coupling, are compared with analytical expressions for the free electron dynamic structure factor which include effects of strong coupling in both classical and degenerate plasmas. We will show that these modifications introduce minimal corrections to the RPA for typical conditions found in recent non-collective x-ray Thomson scattering experiment on solid density isochorically heated laser plasmas. On the other hand, strong collective scattering may exhibit significant deviations from the RPA. The results shown in this work can be applied to interpreting future x-ray scattering in warm dense plasmas occurring in inertial confinement fusion experiments or for the modelling of solid density matter found in the interior of planets.

Anomalous broadening of ion-acoustic modes has been observed using collective Thomson scattering from both the electron plasma and ion-acoustic waves in ion-collisional plasmas. Ion-acoustic waves may be broadened by Landau damping, plasma inhomogeneities and instrumental effects. A model was constructed to calculate the contribution of these effects based upon spatially and spectrally resolved measurements of collective Thomson scattering. Collisional broadening effects were then calculated using a modification of the Mermin formalism. The computational model was used to interpret experimental measurements of collisional damping rates in dense, moderately coupled, plasmas. Collisional broadening is weakly dependent of ion-acoustic frequency in nearly isothermal plasmas; and therefore collective Thomson scattering can be used as a measurement technique for collisional damping rates provided all additional broadening mechanisms are taken into account. This paper further demonstrates that modelling of collective Thomson scattering from ion-collisional ion-acoustic modes must account for inhomogeneities, Landau damping, and collisions in order to evaluate plasma parameters, such as temperature and average ionization.

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. In addition to former experiments using laser beams with λ = 1.06 µm, measurements at λ = 0.694 µm have been performed recently. Reflectivities typical for metallic systems are found at high densities. Besides free carriers, the theoretical description also takes into account the influence of the neutral component of the plasma on the reflectivity. A consistent description of the measured reflectivities is achieved only if a finite width of the shock wave front is considered.

An approach is developed for computation of the reflectivity from nonideal plasma for probe laser frequencies ω near the plasma frequency ω_p. Different factors are taken into account which could violate the conventional Drude dependence of the reflectivity on the ω/ω_p ratio. Possible nonequilibrium of experimental nonideal plasma appears to be the main factor.

Relaxation of kinetic energy to the equilibrium state is simulated by the molecular dynamics method for nonideal two-component non-degenerate plasmas. Three limiting examples of initial states of strongly nonequilibrium plasma are considered: zero electron velocities, zero ion velocities and zero velocities of both electrons and ions. The initial non-exponential stage, its duration τ_nB and subsequent exponential stages of the relaxation process are studied for a wide range of the nonideality parameter and the ion mass.

The quantum trajectory method (QTM) will be introduced, and an approximation to the QTM known as Fermi molecular dynamics (FMD) will be described. Results of simulations based on FMD will be mentioned for specific nonequilibrium systems dominated by Coulomb interactions.

To determine the Burnett transport coefficients of non-ideal multi-element charged matter the representations of conservation equations of matter as generalized Langevin equations are used. Mori's algorithm is revised to derive the equation of motion of a dynamical value operator of a system in the form of the generalized nonlinear Langevin equation. After transformation, using necessary variational derivatives, these equations are compared with the Burnett hydrodynamical conservation equations. In consequence, the response function expressions of transport coefficients corresponding to second-order derivatives of thermal disturbances are found in the long-wavelength and low-frequency limits. To establish a link between the results of the executed investigations and hydrodynamical problems the properties of the high derivative coefficients matrix of the set of conservation equations in the linearized Burnett approximation are discussed.

Experiments using the rapid wire evaporation technique provided data for the electrical conductivity of aluminium plasmas in a density range of (0.001–2.3) g cm⁻³ and for temperatures between 10000 and 285000 K.

Within the frame of the linear response theory in the formulation of Zubarev, calulations of the electrical conductivity were made in the same density and temperature area. The composition of the plasma was determined within the partially ionized plasma model; the interaction between particles is considered to be a Debye potential (charged particles) and a screened polarization potential (interaction with atoms). The agreement between experimental and theoretical data is reasonable for arbitrary temperatures and densities ϱ < 0.7 g cm⁻³.

For higher densities, in the warm dense fluid region, strong correlation effects occur. These effects can be taken into account including local field corrections in the dielectric function, using a dynamic ion–ion structure factor, or by replacing the Debye potential of the electron–ion interaction with a weak pseudopotential. The latter can be determined within a density functional theory. The influence of these effects on the electrical conductivity of a warm dense aluminium fluid is shown.

We present theoretical estimations of the electrical conductivity of a warm expanded aluminium plasma (ρ = 0.3 g cm⁻³). Our calculations are carried out in the framework of density functional theory and the local density approximation. Ionic configurations were determined by ab initio molecular dynamics simulations, from which the conductivity was computed using the Kubo–Greenwood formula. Theoretical results were validated in the dense coupled regime (ρ = 2 g cm⁻³) against previously published experimental results. For the low-density regime, the result is compared to experiments obtained in our laboratory in an isochoric closed-vessel designed to confine electrical plasma discharges up to 1.5 GPa. In this regime we show that the usual Drude model is no longer relevant and that the electrical conductivity is driven by the optical properties.

We develop the concept which distinguishes the initial stages of the fast (nanosecond) electric explosion of wires: the superheating of the solid conductor, its spontaneous (spinodal) decay and the successive formation of the non-ideal plasma column. We use the molecular dynamics simulation approach to simulate homogeneous nucleation from a stationary state and at a constant heating rate. We study the parameters of the spinodal, the dependence of the melting temperature on the heating rate and the character of the decay. We consider the subsequent evolution of the fluid column and the axial plasma uniformity. We compare the results with the experimental data on nanosecond wire explosions.

The ion–electron coupling properties for an ion impurity in an electron gas and for a two-component plasma are carried out on the basis of a regularized electron–ion potential removing the short-range Coulomb divergence. This work is largely motivated by the study of radiator dipole relaxation in plasmas which makes a real link between models and experiments. Current radiative property models for plasmas include single electron collisions neglecting charge–charge correlations within the classical quasi-particle approach commonly used in this field. The dipole relaxation simulation based on electron–ion molecular dynamics proposed here will provide a means to benchmark and improve model developments. Benefiting from a detailed study of a single ion embedded in an electron plasma, the challenging two-component ion–electron molecular dynamics simulations are proved accurate. They open new possibilities of obtaining reference lineshape data.

Electric field dynamics at a positive ion imbedded in an electron gas is considered using a semiclassical description. The dependence of the field autocorrelation function on charge number is studied for strong ion–electron coupling via MD simulation. The qualitative features for larger charge numbers are a decreasing correlation time followed by an increasing anticorrelation. Stopping power and related transport coefficients determined by the time integral of this correlation function result from the competing effects of increasing initial correlations and decreasing dynamical correlations. An interpretation of the MD results is obtained from an effective single-particle model showing good agreement with the simulation results.

A simplified approach is presented for the analysis of broadening and shift of emission lines in hot dense plasmas. The basic approximation which allows this simplified approach is the factorization of the wavefunction for the many-body problem into the wavefunction for the plasma particles, and the wavefunction which describes the internal degrees of freedom.

Plasma phase transitions in dense hydrogen and electron–hole plasmas are investigated by direct path integral Monte Carlo methods. The phase boundary of the electron–hole liquid in germanium is calculated and is found to agree reasonably well with the known experimental results. Analogous behaviour is found for high-density hydrogen. For a temperature of T = 10 000 K it is shown that the internal energy is lowered due to droplet formation for densities between 10²³ cm⁻³ and 10²⁴ cm⁻³.

Photoionizing laser-cooled atoms produces ultracold neutral plasmas with initial temperatures of 1–1000 K and densities as high as 10¹⁰ cm⁻³. Applied radio frequency fields can excite plasma oscillations that are used to monitor the expansion of the unconfined plasma. Significant three-body recombination of electrons and ions into Rydberg atoms takes place during the plasma expansion. Previous experiments have been done with xenon, but a new experiment is planned with laser-cooled strontium. The strontium ion has an optically allowed transition at a convenient blue wavelength. This will allow direct imaging of the plasma through fluorescence or absorption, and may enable laser cooling and trapping of the plasma.

The relaxation of charged particle systems after sudden changes of the pair interaction strength is investigated. As examples, we show the results for plasmas after ionization and after a rapid change of screening. Comparisons are made between molecular dynamics simulation and a kinetic description based on the Kadanoff–Baym equations. We found the latter very sensitive to the way the scattering cross section is treated. We also predict the new equilibrium state requiring only conservation of energy. In this case, the correlation energy is computed using the hypernetted chain approximation.

It has recently become possible to create ultracold plasmas in the microkelvin temperature regime. Unfortunately, these plasmas are created in a disordered state and the build up of Coulomb correlations leads to rapid electron and ion heating that can be understood in terms of energy conservation. We explore this disorder–induced heating for the ionization of degenerate gases. In particular, we consider the ionization of fermionic gases, which are partially ordered by the Pauli exclusion principle, and the subsequent heating of the bosonic ions. The introduction of fermionic correlations mitigates the heating of the ions. However, we find from energy conservation that the final state for typical experimental situations is a classical plasma where the bosonic character of the particles is negligible.

We report direct observations on the microscopic dynamics of dusty plasma liquid confined in a narrow gap. We measure the horizontal and transverse displacement histograms as well as the transverse particle density distributions from particle trajectories. Under confinement, the liquid forms a layer structure. The dust particle motion at boundaries show anisotropy and three outermost layers is found due to the pinching effect of the boundaries. When the gap width is reduced to below 7d (d = inter-layer width), the dust particle motion in the central region shows a transition from isotropic motion to anisotropic discrete hopping motion, leading to a slower dynamics and layer structure through the whole liquid.

Thermally excited waves in a plasma crystal were numerically simulated using a Box_Tree code. The code is a Barnes_Hut tree code proved effective in modelling systems composed of a large number of particles. Interaction between individual particles was assumed to conform to a Yukawa potential. Particle charge, mass, density, Debye length and output data intervals are all adjustable parameters in the code. Employing a Fourier transform on the output data, dispersion relations for both longitudinal and transverse wave modes were determined. These were compared with the dispersion relations obtained from experiment as well as a theory based on a harmonic approximation to the potential. They were found to agree over a range of 0.9 < κ < 5, where κ is the shielding parameter and is defined as the ratio between interparticle distance a and dust Debye length λ_D. This is an improvement over experimental data as current experiments can only verify the theory up to κ = 1.5.

Penning traps use static magnetic and electric fields to confine charged atomic particles. Static confinement fields enable large numbers of ions to be routinely laser-cooled to low temperatures. We have laser-cooled up to ∼10⁶ ions in spherically shaped plasmas to temperatures less than ∼10 mK. These cold plasmas provide a rigorous realization of a strongly coupled one-component plasma (OCP). After reviewing the ion crystal structures that have been observed in Penning traps and comparing them with theoretical predictions, we summarize two recent experiments. First, we describe careful measurements of the stability of the plasma rotation, which is controlled by a rotating electric field. The application of a shearing force is observed to produce sudden angular jumps or 'slips' of the crystal orientation spaced by intervals where the crystal was 'stuck' relative to the rotating field. We observed power-law distributions of the slip frequency versus slip amplitude. Similar stick–slip dynamics and power-law distributions are also seen with earthquakes, avalanches, and many other stressed systems in nature. We then discuss plasma wakes produced by the radiation pressure of a laser beam directed along the magnetic field but offset from the plasma rotation axis. This pressure excites localized plasma waves which interfere to form a stationary wake that is directly imaged through the dependence of the ion fluorescence on Doppler shifts. Theoretical calculations accurately reproduce these images. The above work has recently been discussed in detail and is not repeated below. For a detailed discussion, see Bollinger et al (2002 Trapped Charged Particles and Fundamental Interactions I. Invited papers from the conference (Wildbad Kreuth, Germany, 25–30 Aug. 2002)), to be published in J. Phys. B: At. Mol. Opt. Phys.36 499–510

Measurements of the spatial distribution of bunched crystalline ion beams in the radio frequency quadrupole storage ring PALLAS are presented for different ratios of the longitudinal and the transverse confinement strengths.

The length of highly elongated crystalline ion bunches and its dependence on the bunching voltage is compared to predictions for a one-dimensional ion string and three-dimensional space-charge-dominated beams. The length is found to be considerably shorter than that predicted by the models. Furthermore, the scaling of the length with the bunching voltage is shown to differ from the expected inverse cube root scaling. These differences can partially be attributed to the formation of a mixed crystalline structure.

Additionally, a concise mapping of the structural transition from a string to a zig-zag configuration as a function of the ratio of the confinement strengths is presented, which in a similar way deviates from the predictions.

Intense heavy ion beams deposit energy very efficiently over extended volumes of solid density targets, thereby creating large samples of strongly coupled plasmas. Intense beams of energetic heavy ions are therefore an ideal tool to research this interesting field. It is also possible to design experiments using special beam–target geometries to achieve low-entropy compression of samples of matter. This type of experiments is of particular interest for studying the problem of hydrogen metallization.

In this paper we present a design study of such a proposed experiment that will be carried out at the future heavy ion synchrotron facility SIS100, at the Gesellschaft für Schwerionenforschung, Darmstadt. This study has been done using a two-dimensional hydrodynamic computer code. The target consists of a solid hydrogen cylinder that is enclosed in a thick shell of lead whose one face is irradiated with an ion beam which has an annular (ring shaped) focal spot. The beam intensity and other parameters are considered to be the same as expected at the future SIS100 facility. The simulations show that due to multiple shock reflection between the cylinder axis and the lead–hydrogen boundary, one can achieve up to 20 times solid density in hydrogen while keeping the temperature as low as a few thousand K. The corresponding pressure is of the order of 10 Mbar. These values of the physical parameters lie within the range of theoretically predicted values for hydrogen metallization.

We have also carried out a parameter study of this problem by varying the target and beam parameters over a wide range. It has been found that the results are very insensitive to such changes in the input parameters.

The physics of dense hydrogen can be developed starting with separate proton and electron (or deuteron and electron) plasmas and formally introducing the coupling between them. If this coupling is treated beyond linear response in the interacting electron gas the dominant pairing features of low-density hydrogen are captured. Progression of effective proton–proton pair interactions, especially with respect to the domain of repulsive behaviour in relation to cell size, and the overall scale of zero-point energy, indicates the possible onset of a near ground-state fluid above a critical density. This fluid will be metallic and unusually different in its properties when compared to more conventional liquid metals. Further assessment of the quantum aspects of such a state suggests the need for a more general analytical approach to the hydrogen problem and one possible route is via scaling relations.

Using intense magnetic pressure, a method was developed to launch flyer plates to velocities in excess of 20 km s⁻¹. This technique was used to perform plate-impact, shock wave experiments on cryogenic liquid deuterium (LD₂) to examine its high-pressure equation of state (EOS). Using an impedance matching method, Hugoniot measurements were obtained in the pressure range of 22–100 GPa. The results of these experiments disagree with the previously reported Hugoniot measurements of LD₂ in the pressure range above ∼40 GPa, but are in good agreement with first principles, ab initio models for hydrogen and its isotopes.

Path integral Monte Carlo simulations have been used to study deuterium at high pressure and temperature. The equation of state has been derived in the temperature and density regions of 10 000 ⩽ T ⩽ 1 000 000 K and 0.6 ⩽ ρ ⩽ 2.5 g cm⁻³. A series of shock Hugoniot curves is computed for different initial compressions in order to compare with current and future shock wave experiments using liquid deuterium samples precompressed in diamond anvil cells.

Recent shock-wave experiments with deuterium [1, 2] in a regime where a plasma phase-transition has been predicted [3] and their theoretical interpretation are the matter of a controversial discussion (see e.g. [4–8]). In this paper, we apply 'wave packet molecular dynamics' (WPMD) simulations to investigate warm dense hydrogen. The WPMD method was originally used by Heller for a description of the scattering of composite particles such as simple atoms and molecules [9]; later it was applied to Coulomb systems by Klakow et al [10, 11]. In the present version of our model the protons are treated as classical point-particles, whereas the electrons are represented by a completely anti-symmetrized Slater sum of periodic Gaussian wave packets. We present recent results for the equation of state of hydrogen at constant temperature T = 300 K and of deuterium at constant Hugoniot E − E₀ + 1/2(1/n − 1/n₀)(p + p₀) = 0, and compare them with the experiments and several theoretical approaches.

We have considered partially ionized hydrogen plasma for the density region n_e = (10¹⁸–10²²) cm⁻³. Charged particles in the system (electrons, protons) interact via an effective potential taking into account three-particle correlations. We use the Buckingham polarization potential to describe electron–atom and proton–atom interactions. The electrical and thermal conductivity is determined using the Chapman–Enskog method. We compare the obtained results with other available data.

Shock experiments have reached the megabar pressure range and temperatures typical in planets such as Jupiter. The equation of state and other material properties such as electrical conductivity are needed for hydrogen and helium in order to model such objects. We develop an equation of state that considers pressure dissociation and ionization. We make use of fluid variational theory and Padé approximations. A chemical picture is applied considering the species electrons, protons, atoms and molecules. Comparison with experimental equation of state data is presented.

We review the derivation of the electrostatic screening effect from first principles. We show that under the conditions prevailing in the Sun the number of particles in the Debye sphere is of the order of unity. Consequently, fluctuations play a dominant role in the screening process and lead to an energy exchange between the scattering particles and the surrounding plasma that depends on the energy of the particles. Extensive molecular dynamics calculations show that low-energy particles gain on the average energy from the plasma while high-energy particles lose energy to the plasma, in contrast with the classical Salpeter picture in which all particles gain during the close approach to each other the mean Coulomb energy.

Next, we adopt the Langevin equation for charged particles with the Rosenbluth potential. We show how the two completely independent methods, the molecular dynamics and Langevin equation, yield the same physical results.

We then review the arguments for a static screening based on a static potential and show its basic assumptions and shortcomings. The particular assumptions leading to the Salpeter formula are discussed along with the approximations involved in its derivation. One of the tacit fundamental assumptions in the Salpeter approximation is that the scattering is fully elastic. The inelastic nature of the collisions which are dominant under the solar conditions is clarified.

We have already shown that binary Coulomb compounds in disordered states are stabilized against phase separation in a minor ion rich region as charge asymmetry is enhanced; a stable phase appears approximately beyond the charge ratio R_Z = 6. In this paper, the mechanical properties of the stable compounds are elucidated through extensive calculations of the Coulomb energy increments due to virtual deformations. The compounds turn out to be much more isotropic than the mixed pure crystals in the linear response regime. And their effective elastic constants obtained by averaging over directions are well expressible in terms of those of the pure crystals. The compounds, however, show fragile behaviour at the degree of deformation where the pure crystal still retains its elasticity.

The dynamics of Saturn's F ring have been a matter of curiosity ever since Voyagers 1 and 2 sent back pictures of the ring's unusual features. Some of these images showed three distinct ringlets with the outer two displaying a kinked and braided appearance. Many models have been proposed to explain the braiding seen in these images; most of these invoke perturbations caused by the shepherding moons or kilometre-sized moonlets embedded in the ring and are purely gravitational in nature. These models also assume that the plasma densities and charges on the grains are small enough that electromagnetic forces can be ignored. However, Saturn's magnetic field exerts a significant perturbative force on even weakly charged micron- and submicron-sized grains causing the grains to travel in epicyclic orbits about a guiding centre. This study examines the effect of Saturn's magnetic field on the dynamics of micron-sized grains along with gravitational interactions between the F ring's shepherding moons, Prometheus and Pandora. Due to the differences in charge-to-mass ratios of the various sized grains, a phase difference between different size populations is observed in the wavy orbits imposed by passage of the shepherding moons.

We present a kinetic model of the stationary solar wind based on the equation for two-particle (electron–proton) velocity distribution. The influence of collisions and the magnetic field is neglected. The approximation of the quasi-neutral plasma is applied to close the model, which results in excluding a Coulomb potential of plasma polarization field from consideration. The kinetic equation is solved using the method of characteristics. Solar wind density and speed are evaluated by integrating the two-particle distribution function over its domain of definition formed by related characteristics. The obtained dependences of the density and velocity on heliocentric distance agree with observational data of the in-ecliptic slow solar wind.

The pair distribution function g(r) ≡ g(x, y, z) and the radial pair distribution function g(r) of ions in body-centred-cubic and face-centred-cubic Coulomb crystals are calculated within the harmonic-lattice (HL) approximation in a wide temperature range, from the high-temperature classical limit (T ≫ w_p, w_p being the ion plasma frequency) to the low-temperature quantum limit (T ≪ w_p). In the classical limit, g(r) is also calculated by the Monte Carlo (MC) method. MC and HL results are demonstrated to be in good agreement. With decreasing T, the correlation peaks of g(r) and g(r) become narrower. At T ≪ w_p they become temperature independent (determined by zero-point ion vibrations).

We investigate recently observed experiments in the strongly correlated 2D systems (r_s ≫ 1) (low-density 2D plasmons, metallic behaviour of 2D systems and frictional drag resistivity between two 2D hole layers). We compare them with our theoretical results calculated within a conventional Fermi liquid theory with RPA screening.

We present an overview of the problem of screening of an impurity in a strongly coupled one-component plasma within the framework of the linear response (LR) theory. We consider 3D, 2D and quasi-2D layered systems. For a strongly coupled plasma the LR can be determined by way of the known S(k) structure functions. In general, an oscillating screening potential with local overscreening and antiscreening regions emerges. In the case of the bilayer, this phenomenon becomes global, as overscreening develops in the layer of the impurity and antiscreening in the adjacent layer. We comment on the limitations of the LR theory in the strong coupling situation.

A Monte Carlo scheme to sample the screening potential H(r) of Yukawa plasmas notably at short distances is presented. This scheme is based on an important sampling technique. Comparisons with earlier results for the Coulombic one-component plasma are given. Our Monte Carlo simulations yield an accurate estimate of H(r) as well for short-range and long-range interparticle distances.

Using molecular dynamics simulations we investigate the dynamic structure factor S(k, ω) of a two-component model plasma where the Coulomb interaction is regularized at short distances. New simulation results are presented and discussed, and they are used to verify different theoretical treatments: the standard random-phase approximation, a dynamic local field correction with input from HNC calculations and a new approach, which includes a dynamic collision frequency via the Mermin ansatz.

Starting from a generalized response theory, the inverse response function can be expressed in terms of equilibrium correlation functions for which a perturbation expansion is carried out. In the long-wavelength limit, this can be exploited to obtain an approximation for the dynamic collision frequency. Utilizing the Mermin ansatz, the dynamical structure factor is determined from the long-wavelength limit. The results are compared with classical simulation data. Different effective potentials which model the electron–ion interaction are discussed. It is shown that the high-frequency behaviour of the dynamic collision frequency is sensitive to the form of the chosen interaction.

The spectrum of ion density fluctuations in a strongly coupled plasma is described both within the static G(k, 0) and high-frequency G(k, ∞) local field approximation. By a direct comparison with molecular dynamics data, we find that for large coupling, G(k, 0) is inadequate. Based on this result, we employ the Zwanzig–Mori memory function approach to model the Thomson scattering cross section, i.e. the electron dynamic form factor S_ee(k, ω) of a dense two-component plasma. We show the sensitivity of S_ee(k, ω) to three approximations for G(k, ω).

The radial distribution function of two-dimensional Yukawa systems has been computed with the hypernetted chain equations and compared with molecular dynamics simulations. A comparison is also made with similar quantities in three-dimensional systems. The importance of the bridge function in two dimensions is illustrated. Collective behaviour is described in terms of the dynamic structure factor S(q, ω); inclusion of the local field correction G(q, ω) incorporates physics beyond the random phase approximation. Simulation results are compared with renormalized mean-field approximations G(q, ω) ≈ G(q, 0) and G(q, ω) ≈ G(q, ∞). These approximations fail to capture details of the spectrum.

This special issue contains papers presented at the International Conference on Strongly Coupled Coulomb Systems (SCCS) which was held during the week of 2–6 September 2002 in Santa Fe, New Mexico. It was the ninth in a series of conferences starting in 1977 in Orléans-la-Source, France as a summer institute. The second in the series was a workshop held in Les Houches in 1982. The conferences were then held in the following order: Santa Cruz, California in 1986, Tokyo, Japan in 1989, Rochester, USA in 1992, Binz, Germany in 1995, Boston, USA in 1997 and St Malo, France in 1999. The planned frequency for the future is 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 plasma, liquid and condensed 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, colloids, condensed matter, two-dimensional systems, astrophysics, dense hydrogen, ultra-cold plasmas, traps and beams, dusty plasmas, clusters, kinetic theory and statistical mechanics. Within each area new results from theory, simulation and experiment were presented. In addition, a special panel discussion was held one evening to explore the questions which continue to be posed by the experiments on and modelling of dense hydrogen. 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 area of beams, traps, plasma crystals and ultra-cold plasmas.

In total, 105 participants from 13 countries attended the conference, including 34 invited speakers. Unfortunately, some international speakers could not attend due to problems with obtaining visas, and we deeply regret the difficulties and lost opportunities. These individuals and all others 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 all members of the International Advisory Board for their contributions to the conference. In particular, we thank Chairman Jean-Pierre Hansen for his diligent work at coordinating the International Advisory Board, the Programme Committee and the Local Organizing Committee. Of course, nothing would have been possible without the dedicated efforts of the Local Organizing Committee. We wish to thank the Los Alamos National Laboratory (Theoretical, Physics, Applied Physics, Materials Science and Technology divisions) and Sandia National Laboratory (Pulsed Power Sciences) for sponsoring this conference. We also gratefully acknowledge the administrative support we received from Marianna Martinez, Marion Hutton and Ellie Vigil of Los Alamos National Laboratory, all of whom were major contributors to the success of the conference.

John F Benage, James W Dufty and Michael S Murillo Guest Editors

Please see PDF for photograph of conference participants.

Local Organizing Committee

J F Benage Los Alamos National Laboratory, USA M Desjarlais Sandia National Laboratory, USA G J Kalman Boston College, USA J Kress Los Alamos National Laboratory, USA M S Murillo Los Alamos National Laboratory, USA G Ortiz Los Alamos National Laboratory, USA J Weisheit Los Alamos National Laboratory, USA

SCCS International Advisory Board

A Alastuey Ecole Normale Supérieure de Lyon, France D Andelman Tel Aviv University, Israel N W Ashcroft Cornell University, USA J Bollinger NIST, Boulder, USA J-M Caillol Université Paris XI, France D M Ceperley University of Illinois, USA G Chabrier Ecole Normale Supérieure de Lyon, France J Clerouin CEA Bruyeres-le-Chatel, France S das Sarma University of Maryland, USA A DeSilva University of Maryland, USA H DeWitt Lawrence Livermore National Laboratory, USA D Dubin University of California, USA J Dufty University of Florida, USA W Ebeling Humboldt University, Germany V Filinov Institute of High Temperature Physics, Russia M Fisher University of Maryland, USA V E Fortov Institute of High Temperature Physics, Russia K Golden University of Vermont, USA J-P Hansen Cambridge University, UK F Hensel Philipps-Universität, Germany G Kalman Boston College, USA W Kohn University of California, USA H Lowen University of Dusseldorf, Germany G Morfill Max Planck Institute of Extraterrestrial Physics, Germany D Neilson University of New South Wales, Australia G Patey University of British Columbia, Canada F Peeters University of Antwerp, Germany D Pines Los Alamos National Laboratory, USA G Roepke University of Rostock, Germany M Rosenberg University of California, USA Y Rosenfeld Negev Nuclear Research Center, Israel M Schlanges University of Greifswald, Germany G Senatore University of Trieste, France H Totsuji Okayama University, Japan J Weisheit Los Alamos National Laboratory, USA

Obituary

Forty years of plasma line broadening—in memory of Professor Charles Hooper Jr

Our friend and colleague, Charles Hooper Jr, died on 5 May 2002 after a long illness and a valiant battle against it. This presentation is a brief look back at the issues in plasma line broadening over the past forty years, and the contributions to them by Chuck and his students.

Chuck graduated from Dartmouth College in 1954. He served in the US Navy for two years before receiving a PhD from Johns Hopkins University in 1963. He then joined the faculty at the University of Florida where his first two papers were written on `Electric microfield distributions in plasmas' and `Relaxation theory of spectral line broadening in plasma'. These two topics were the focus of his research for the next four decades. A personal perspective on the primary problems in this field for each decade is presented here to highlight the many contributions from his research programme. Chuck was particularly proud of the seventeen PhD students who graduated during this time, most of whom are still active in line broadening and related areas.

During the early 1970s he recognized the importance of laser fusion and was a strong protagonist for US investment in this area at the national laboratories. He became a leader in this field through his continuing work on spectroscopy as the primary diagnostic tool for laser-produced plasmas. As such Chuck served on several advisory panels at Lawrence Livermore National Laboratory and Los Alamos National Laboratory. He was also co-organizer of a series of conferences on radiative and atomic processes in dense plasmas for the past twenty years. His most recent research has been in collaboration with the University of Rochester Laser Laboratory where he designed and analysed experiments on laser-produced plasmas. The Department of Energy has continuously supported his research since 1974.

Less well-known to the plasma community are Chuck's successes as Chairman of the Physics Department at the University of Florida from 1979–86. He initiated a new phase of growth in many science departments at both the University of Florida and Florida State University through his statewide cross-disciplinary Microfabritec programme, bringing significant new funds and faculty lines to physics and materials sciences. He was recognized with The Distinguished Service Award from the National High Magnetic Field Laboratory in 2000 as founder and former director of that programme.

The field of plasma line broadening has lost one of its most dedicated and enthusiastic spokesmen. His colleagues will miss a cheerful and personable friend, and will remember well his irrefutable response to disagreement, `I am not convinced...'.

James W Dufty

Department of Physics, University of Florida, Gainesville, FL 32611

Obituary

In Memorium: Dr Yaakov (Yasha) Rosenfeld

In his research life, all too brief, Yasha Rosenfeld notably enriched and significantly advanced an area of physics which is still one of the more challenging fields in the expanding pantheon of the condensed matter sciences: the statistical physics of the liquid state. The ambit of physics associated with this highly correlated state of matter is itself extraordinarily broad, and Yasha's work has had notable impact over an impressively wide front, including charged and neutral liquids, uniform and non-uniform liquids, classical and quantal liquids, single component and multicomponent liquids, liquids close to and far from criticality, liquids both disturbed and in equilibrium. He also greatly elucidated the universal and scaling properties of liquids, and many at this conference will have encountered and admired his remarkable fundamental measures functional, originating in the latter stages of his life.

Yasha was an undergraduate at the Technion, and a graduate student (for both masters and doctoral degrees) at the Weizmann Institute. He was a Weizmann Fellow at Cornell University in 1977–78, and it was both a great pleasure and a considerable stimulation to work with him during this period. Subsequently he held several visiting appointments at distinguished intitutions in the US and in Europe, while holding (since 1973) a permanent position at the Nuclear Research Center of the Negev. His first two papers (in 1974 and 75, and joint with Thieberger) dealt with the square well fluid and solid; at the end of his life he had again taken up the pressure dissociation of dense hydrogen a topic he also worked on in 1976. In the intervening years there are more than 100 papers prolifically covering all the areas mentioned above.

Because of his originality and eclectic interests, and particularly his ability to link to so many areas in the physics of liquids, he was always much in demand as a speaker at conferences (such as ours). We can but speculate on what more he might have contributed, for he was surely one of the most productive of physicists in our field and also surely in full flight with respect to his creative powers. Yasha's passing has therefore robbed us of one who has given `...a purpose in liquidity...' and for many of us we have also lost a deeply admired friend and colleague, one who was unfailingly generous with insights and ideas, and one whose cheerful scepticism was invariably a constant creative and innovative force on the road to the deeper understanding of the liquid state.

Neil Ashcroft