OCP Dynamical Structure Factor and the Plasma Dispersion: Method of Moments

Adamjan, S. V.; Meyer, Th.; Ткаченко, И. М.

doi:10.1002/ctpp.2150290407

Cited by 13 publications

(13 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here we demonstrate that the method of moments theoretical approach [8] is able to predict the form and structure of the DSF of the OCP, based on static data only, i.e., the PDF or the static structure factor (SSF). As both the PDF and the SSF can be obtained theoretically as well [e.g., within the hypernetted chain (HNC) approximation and its modifications including the bridge function] the present approach provides a purely theoretical access to the full DSF and a full quantitative description of the collective modes, including their decay and other characteristics, without the necessity to use simulation data as input, as it was done in [9,10].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Direct Determination of Dynamic Properties of Coulomb and Yukawa Classical One-Component Plasmas

et al. 2017

View full text Add to dashboard Cite

Dynamic characteristics of strongly coupled classical one-component Coulomb and Yukawa plasmas are obtained within the nonperturbative model-free moment approach without any data input from simulations so that the dynamic structure factor (DSF) satisfies the first three nonvanishing sum rules automatically. The DSF, dispersion, decay, sound speed, and other characteristics of the collective modes are determined using exclusively the static structure factor calculated from various theoretical approaches including the hypernetted chain approximation. A good quantitative agreement with molecular dynamics simulation data is achieved. . SCPs and warm dense matter are highly relevant model systems for inertial fusion devices [6]. The common property of SCPs is that the interparticle potential energy dominates over the thermal energy. Many of the above-mentioned systems have been analyzed and their characteristic effects became understood within the framework of a seminal model system, the one-component plasma (OCP) model that considers explicitly only one type of charged species, while the presence and the effects of other charged species are expressed by the interaction potential φðrÞ.SCPs, as many-body dynamical systems, exhibit various collective excitations, of which the properties have been investigated both via theoretical approaches and numerical simulations. Numerical approaches provide direct access to the central quantity of collective effects, the dynamic structure factor (DSF). The most successful theoretical approach capable of describing strongly coupled plasmas, the quasilocalized charge approximation [7], is able to predict [from the static pair distribution function (PDF)] the dispersion relations of the collective modes; however, it cannot predict the lifetime (decay) of the modes and the form of the DSF itself. Here we demonstrate that the method of moments theoretical approach [8] is able to predict the form and structure of the DSF of the OCP, based on static data only, i.e., the PDF or the static structure factor (SSF). As both the PDF and the SSF can be obtained theoretically as well [e.g., within the hypernetted chain (HNC) approximation and its modifications including the bridge function] the present approach provides a purely theoretical access to the full DSF and a full quantitative description of the collective modes, including their decay and other characteristics, without the necessity to use simulation data as input, as it was done in [9,10].The moment approach is nonperturbative, nonparametric, and model free. Thus it is perfectly applicable to a broad class of fluids characterized by response functions like semidegenerate multicomponent Coulomb systems or even simple liquids. Because of the rigorous mathematical background, the method is based on automatic satisfaction of sum rules and other exact relations. An empirical guidance is plugged directly into the intermediate step of theoretical computations, thus closing the approach and permitting us, in addition, to determine the dynamic...

show abstract

mentioning

confidence: 99%

“…In the present work, we do not reconstruct the NPF from the very data we wish to describe like it was done in [22], but model it by its static value [9,10]: Qðq; ω; κÞ ¼ Qðq; 0; κÞ ¼ ihðq; κÞ, hðq; κÞ > 0. The latter positive parameter function was related in [10] to the static value of the DSF directly via (3).…”

mentioning

confidence: 99%

Direct Determination of Dynamic Properties of Coulomb and Yukawa Classical One-Component Plasmas

et al. 2017

View full text Add to dashboard Cite

show abstract

“…Adamjan et al developed another sum-rule approach, based on the Nevanlinna formula of the classical theory of moments method, to construct the OCP DSF [19], and this approach has been explored for hydrogen-like twocomponent plasmas [20][21][22]. Recently, Arkhipov et al (A) expanded this sum-rule approach to Yukawa OCPs (YOCPs) [23], finding…”

Section: Models and Methodsmentioning

confidence: 99%

“…Increasingly accurate DSF models improve our understanding of dynamical correlations and provide an additional rationale for the use of XRTS as an experimental diagnostic, as well. A survey of extant DSF models reveals a wide diversity of approaches, including early work on memory functions by Hansen and co-workers [15,16], the dynamic local field correction (DLFC) models of Tanaka and Ichimaru [17] and Hong and Kim [18], the sum-rule approaches of Adamjan et al and others [19][20][21][22][23], Mermin's relaxationtime approximation [24] and Murillo's modified Navier-Stokes equation (NS) [6], to name only a few.…”

Section: Introductionmentioning

confidence: 99%

High-frequency response of classical strongly coupled plasmas

2019

View full text Add to dashboard Cite

The dynamic structure factor (DSF) of the Yukawa system is here obtained with highly converged molecular dynamics (MD) over the entire liquid phase. The data provide a rigorous test of theoretical models of ion-acoustic wave-dispersion relations, the intermediate scattering function and the high-frequency response. We compare our MD results with seven diverse models, finding good agreement among those that enforce the three basic sum rules for dispersion properties, although one of the models has previously unreported spurious peaks. The MD simulations reveal that the high-frequency response ∼ ω p of the DSF at intermediate frequencies ω, and p shows non-trivial dependencies on the wavevector q and the plasma parameters κ and Γ. In contrast, among the seven comparison models, the predicted high-frequency response is found to be independent of {q, κ, Γ}. This high-frequency power suggests a useful fitting form. In addition, these results expose limitations of several models and, moreover, suggest that some approaches are difficult or impossible to extend because of the lack of finite moments. We also find the double plasmon resonance peak in our MD simulations that none of the theoretical model predicts.

show abstract

“…The approach we use here to construct the dynamic longitudinal conductivity was initiated in the papers [3,4], see also [5] and [1] for a recent review 3 . It was later applied to the investigation of dynamic properties and modes in real one-and two-component plasmas [9,10], binary ionic mixtures [11], binary electronic layers [12], model Coulomb systems [13][14][15][16][17], magnetized plasmas [18][19][20], and the plasma stopping power [21][22][23][24]. In all these applications the Nevanlinna formula (10) (for r = 1) was employed with the parameter function q (k,z) substituted by its static value q (k,0) = ih (k), with the positive parameter h (k) found from an asymptotic value of the distribution density under investigation (the static conductivity, the zero-frequency value of the dynamic structure factor, etc.)…”

Section: The Drude-lorentz Model From the Point Of View Of The Theorymentioning

confidence: 99%

Two‐moment modelling of the dynamic longitudinal conductivity of strongly coupled Coulomb systems

Ballester

Ткаченко

2005

Contrib. Plasma Phys.

Self Cite

View full text Add to dashboard Cite

A dynamic longitudinal internal conductivity model, derived from the classical method of moments, is applied to the analysis of recent simulation data and reflectivity measurements of shock-compressed dense xenon plasmas. This model satisfies both the non-zero f −sum rule and the second non-zero sum rule, and reproduces the non-monotonicity of the conductivity of dense plasmas beyond the domain of applicability of the Drude-Lorentz model. The Drude-Lorentz model from the point of view of the theory of momentsThe classical model for the (internal) conductivity of dense plasmas and metals,is characterized by two static parameters, the static conductivity σ 0 = σ (ω = 0) = n e e 2 τm −1 = (4π) −1 ω 2 p τ and the relaxation time τ . Here n e is the number density of electrons in the system, −e and m are the electronic charge and mass, and ω p is the plasma frequency.In addition to direct measurements, the static conductivity value can be obtained as [1]Here σ ext (ω) is the external dynamic conductivity of the Coulomb system related to the internal conductivity through the well-known formula 1 [2]:Mathematically, the DL function, σ DL (z), is a simple Nevanlinna (response) function 2 with a single simple pole in the lower half-plane. In addition, the real part of σ DL (z) possesses a single finite frequency moment, which is known also as the f -sum rule:

show abstract

OCP Dynamical Structure Factor and the Plasma Dispersion: Method of Moments

Abstract: The expression for the second moment C2 stems from the f-sum rule: C , = wp2/4; and

Cited by 13 publications

References 3 publications

Direct Determination of Dynamic Properties of Coulomb and Yukawa Classical One-Component Plasmas

Direct Determination of Dynamic Properties of Coulomb and Yukawa Classical One-Component Plasmas

High-frequency response of classical strongly coupled plasmas

Two‐moment modelling of the dynamic longitudinal conductivity of strongly coupled Coulomb systems

Contact Info

Product

Resources

About