Jeffrey Wrighton

Theoretical description of Coulomb balls: fluid phase.

A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean-field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correlations is developed here by an extension of the hypernetted chain approximation, developed for bulk fluids, to the confined charges. The results reproduce all of the qualitative features observed in molecular dynamics simulations and experiments. These predictions are then tested quantitatively by comparison with benchmark Monte Carlo simulations. Quantitative accuracy of the theory is obtained by correcting the hypernetted chain approximation with a representation for the associated bridge functions.

Kinetic Theory for Electron Dynamics Near a Positive Ion

A theoretical description of time correlation functions for electron properties in the presence of a positive ion of charge number Z is given. The simplest case of an electron gas distorted by a single ion is considered. A semi-classical representation with a regularized electron–ion potential is used to obtain a linear kinetic theory that is asymptotically exact at short times. This Markovian approximation includes all initial (equilibrium) electron–electron and electron–ion correlations through renormalized pair potentials. The kinetic theory is solved in terms of single-particle trajectories of the electron–ion potential and a dielectric function for the inhomogeneous electron gas. The results are illustrated by a calculation of the autocorrelation function for the electron field at the ion. The dependence on charge number Z is shown to be dominated by the bound states of the effective electron–ion potential. On this basis, a very simple practical representation of the trajectories is proposed and shown to be accurate over a wide range including strong electron–ion coupling. This simple representation is then used for a brief analysis of the dielectric function for the inhomogeneous electron gas.

Charge Correlations in a Harmonic Trap

A system of N classical Coulomb charges trapped in a harmonic potential displays shell structure and orientational ordering. The local density profile is well understood from theory, simulation, and experiment. Here, pair correlations are considered for this highly inhomogeneous system for both the fluid and ordered states. In the former, it is noted that there is a close relationship to pair correlations in the uniform one component plasma. For the ordered state, it is shown that the disordered “tiling” is closely related to the ground state Thomson sites for a single sphere (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Shell Structure of Confined Charges at Strong Coupling

A theoretical description of shell structure for charged particles in a harmonic trap is explored at strong coupling conditions of = 50 and 100. The theory is b ased on an extension of the hypernetted chain approximation to confined systems plus a phenomenological representation of associated bridge functions. Predictions are compared to corresponding Monte Carlo simulations and quantitative agreement for the radial density profile is obtained.

Theoretical description of spherically confined, strongly correlated Yukawa plasmas.

A theoretical description of the radial density profile for charged particles with Yukawa interaction in a harmonic trap is described. At strong Coulomb coupling shell structure is observed in both computer simulations and experiments. Correlations responsible for such shell structure are described here using a recently developed model based in density functional theory. A wide range of particle number, Coulomb coupling, and screening lengths is considered within the fluid phase. A hypernetted chain approximation shows the formation of shell structure, but fails to give quantitative agreement with Monte Carlo simulation results at strong coupling. Significantly better agreement is obtained within the hypernetted chain structure using a renormalized coupling constant, representing bridge function corrections.

On the Kubo-Greenwood model for electron conductivity

Currently, the most common method to calculate transport properties for materials under extreme conditions is based on the phenomenological Kubo-Greenwood method. The results of an inquiry into the justification and context of that model are summarized here. Specifically, the basis for its connection to equilibrium DFT and the assumption of static ions are discussed briefly.

Linear response for confined particles

The dynamics of fluctuations is considered for electrons near a positive ion or for charges in a confining trap. The stationary nonuniform equilibrium densities are discussed and contrasted. The linear response function for small perturbations of this nonuniform state is calculated from a linear Markov kinetic theory whose generator for the dynamics is exact in the short time limit. The kinetic equation is solved in terms of an effective mean field single particle dynamics determined by the local density and dynamical screening by a dielectric function for the nonuniform system. The autocorrelation function for the total force on the charges is discussed.

Electron Dynamics Near a Charged Radiator

Time correlation functions for electron dynamics near a positively charged radiator are described by a mean field kinetic theory that is exact in the short time limit. The important case of the electric field autocorrelation function is examined and the dependence on radiator charge number is shown to be dominated by the bound states of the electron‐ion potential. A very simple practical model is proposed and shown to be accurate over a wide range of electron‐ion coupling conditions. The model is expected to be useful for more complex conditions confronted in recent theories for line shapes.

Charge Correlations in Plasma Line Broadening

The traditional theory of plasma line broadening is re‐examined to correct for phenom‐enological assumptions regarding charge correlations. Conditions for static ions are assumed, and the ion microfield distribution is introduced without neglecting ion‐electron correlations, and with a precise definition for the ion field at the radiator. Radiator and plasma subsystems are defined so as to make a second order calculation of electron broadening valid for the case of high Z radiators. The electron broadening operator is identified in terms of the fluctuation of the electron density at the radiator, averaged over the entire plasma constrained by a given value for the ion microfield.