Quasiclassical Theory and Molecular Dynamics of Two‐Component Nonideal Plasmas

Abstract

A b s t r a c t I n t r o d u c t i o nIn nearly all cases gaseous plasmas behave classically and the largest part of plasma physics is based on classical theory. However strictly speaking classical theory cannot provide the full truth since the Coulomb singularity does not admit a classical treatment. It was first Planck in the twenthies who reckognized this principal difficulty and made a first approach how to develop a consequent semi-classical theory. Planck's basic idea was to split the pair states into bound states which have to be treated by quantum theory and free states which admit a semi-classical tratment. This idea was developed by Brillouin and treated in recent time with modern quantum statistical methods by Larkin and others [l, 21. Here MD-calculations are performed and compared with theoretical expressions. Our main interest is devoted to the semi-classical theory of the free charges in plasmas consisting of electrons and ions in the range of large nonideality (coupling) parameter r = ez/kTd, where d = ( 3 / 4~n , ) ' /~ is the average distance between the ions. Berlin and Montroll, Unsold, Ecker and Weizel, Kaklyugin and others [3, 4, 5, 61 predicted that in the region of large r the thermodynamic functions, e.g. the mean Coulomb energy U,, should observe a linear scaling with r. Method of effective potentialsThe idea of effective potentials is to incorporate classical as well as quantum-mechanical effects by appropriate potentials. Such a quasi-classical approach has of course several limits which are basically connected with the trajectory concept. We mention for example the principal difficulty to describe microspic quantum effects as tunneling, and macroscopic quantum effects as superfluidity and superconductance. Our aim is only the calculation of standard macroscopic properties which have a well defined classical limit. Since bound states cannot be described classically our method is restricted to the subsystem of free charges. However this is not a very serious restriction since most properties of the plasma are determined by the subsystem of the free charges. In the following we shall use the BPL-convention for the bound states and quasi-classical approximations for the effective potential [l, 2, 7, 81 The most easy way to arrive at potentials including quantum effects is through the so-called Slater sums. The Slater sum is an analogue of the classical Boltzmann factor and allows to define effective potentials [l, 2, 7, 81 62 Contrib. Plapma Phys. 39 (1999) where with 5 = r/&b. The effective potentials derived from perturbation theory (Kelbg-like potentials) do not include bound state effects and give the constant A = 0. They may be used only in the region of high temperaturesIn the region of inter,mediate temperatures 0.1 < T < 0.3 we may use the Kelbg-potential with a temperature-dependent correction A(T) which is adapted in such away that Sob(r = 0) has the exact value corresponding to the two-particle wave functions [l]. At lower temperatures T < 0.1 we may perform the limit li + 0...

Standards for molecular dynamics modelling and simulation of relaxation

“…Let us consider a fully-ionized two-component plasma of N electrons and N singly ionized ions with masses m and M, respectively. The particles exert each other with a quasiclassical interaction potential such as 'corrected Kelbg' pseudopotential [39]. The number of ions in those particular simulations is N ¼ 64-800.…”

“…The number of particle chosen is sufficient to study oscillations at plasma frequencies [11], and this choice does not influence very much the results of all simulations presented below. Interaction between electrons and ions is described by the pair Coulomb potential modified at small separations [8,11,39] to exclude for quantum bound states. Particles of the same type interact via the bare Coulomb potential.…”

Standard of Molecular Dynamics Modeling and Simulation of Relaxation in Dense Media

“…The formation of the bound states should be prohibited in classical MD simulations of the systems of free charges by the appropriate choice of the interaction pseudopotential. We use the so called "corrected Kelbg" pseudopotential [14]. As low bound states are excluded the pseudopotential does not depend on the chemical element.…”

Semiclassical Dynamics and Time Correlations in Two‐Component Plasmas

“…However, at small interparticle distances it shows a deviation from the exact value of −k B T · ln(S ab (r = 0)). In order to describe the right behavior also at small distances it is better to use a corrected Kelbg potential defined by [24] u ab (r) = (e a e b /r) · F (r/λ ab ) − r k B T e a e bà ab (ξ ab ) exp −(r/λ ab ) 2 .…”

“…(7) the coefficient A ab (T ) is adapted in such a way that S ab (r = 0) and his first derivative S ′ ab (r = 0) have the exact value corresponding to the two-particle wave functions of the free states [13,24,23]. The corresponding coefficients for the elctron-electron and for the electron-ion interaction read…”