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...
Several sum rules and other exact relations are employed to determine both the static and the dynamic properties of strongly coupled, partially and completely degenerate one-component plasmas. Emphasis is placed on the electron gas, both at zero and finite temperatures. The procedure is based on the self-consistent method of moments, recently developed in Phys. Rev. Lett., 2017, 119, 045001, that provides a neat expression for the loss function valid at strong couplings. An input value of the method in its classical version is the static structure factor, whose accuracy is shown to insignificantly affect the resulting numerical data. Starting from the Cauchy-Bunyakovsky-Schwarz inequality, a criterion is proposed to verify the quality of various approaches to the evaluation of the static characteristics of one-component, strongly coupled plasmas. KEYWORDSmethod of moments, static and dynamic structure factors, sum rules INTRODUCTIONOne of the great challenges of modern plasma physics is the analytical and numerical description of the transition from collision-less to collision-dominated regimes in different Coulomb systems as well as of the crossover from classical to Fermi liquid behaviour of dense plasmas. [1,2] This is especially true for warm and hot dense matter or strongly coupled plasmas characterized by a wide range of variation of temperature T ∈ (10 4 -10 7 ) K and the mass density ∈ (10 −2 to 10 4 ) g/cm 3 , thereby spanning a few orders of magnitude variation. Within such a broad range of physical conditions, various effects compete with one another at different scales and impede the construction of bridging gap theories capable of predicting static and dynamic properties of systems under investigation. The above-stated domain of plasma parameters is, of course, of high relevance to inertial fusion devices, [3] but it is, nowadays, over-reached by other advanced laboratory studies as evidenced, for instance, in research on ultracold plasmas. [4] The focus of the present consideration is a one-component plasma that consists of a single particle species, say electrons, with the electric charge e, the mass m, and the number density n. The standard procedure is to introduce the following coupling and degeneracy parameters, respectively, as: Γ = e 2 /a and D = −1 = E F , where = (k B T) −1 denotes the inverse temperature in energy units, a = (4 n/3) −1/3 stands for the Wigner-Seitz radius, and E F = ℏ 2 (3 2 n) 2/3 /2m designates the Fermi energy. Another dimensionless quantity appropriate for the description of one-component plasma is the Brueckner parameter, defined as follows:
We report on a development of an alternative method of HED plasma diagnostics using the ideas of the method of moments [I.M. Tkachenko, J. Ortner, and J. Alcober, J. de Physique IV 10, 195 (2000)]. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The dense plasma dynamic collision frequency is modeled by the first two terms of its asymptotic expansion at high frequencies and its values at a few interpolation points on the real axis. This makes the dynamic collision frequency a non-rational function whose extension onto the upper half-plane of the complex frequency is holomorphic with a non-negative imaginary part and with a continuous extension to the real axis. The validity of the suggested analytic form of the latter is tested against the simulation data, where the Kelbg effective potential was used.1 The problem set-up Dynamic collision frequencyOne of the problems of modern plasma physics is to obtain an analytic expression for the dielectric function determining the screening effects, the dispersion relations and other dynamic characteristics, as the conductivity, collision frequency, etc. In the present we discuss the long-wavelength generalized Drude-Lorentz model introduced in [1], see also corresponding references therein and the discussion in [2]. Precisely, the following model expression for the two-component plasma IDF was suggested:Notice that the polynomials D n (z) can be easily found by the Gram-Schmidt procedure from the canonical set 1, z, z 2 , z 3 , . . . using the weight function f (t):D 0 (z) = 1, D 1 (z) = z, D 2 (z) = z − c 2 /c 0 , . . .
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