Measurement of temperature and density using non-collective X-ray Thomson scattering in pulsed power produced warm dense plasmas

Valenzuela, Jorge; Krauland, C.; Mariscal, D.; Krasheninnikov, I. S.; Niemann, C.; Ma, T.; Mabey, P.; Gregori, G.; Wiewiór, P.; Covington, A. M.; Beg, F. N.

doi:10.1038/s41598-018-26608-w

Cited by 13 publications

(8 citation statements)

References 25 publications

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“…Although local equilibrium cannot be verified by ρ S , its existence can still be revealed by examining the detailed balance relation via the system's dynamical variables [127][128][129][130]. In practice, this idea has been adopted in some highenergy physics experiments to measure the temperature of a plasma by using x-ray Thomson scattering [131,132], and it may be potentially useful for nanosystems of our primary interest as well.…”

Section: Local Equilibrium Conditionsmentioning

confidence: 99%

Local temperatures out of equilibrium

2019

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The temperature of a physical system is operationally defined in physics as "that quantity which is measured by a thermometer" weakly coupled to, and at equilibrium with the system. This definition is unique only at global equilibrium in view of the zeroth law of thermodynamics: when the system and the thermometer have reached equilibrium, the "thermometer degrees of freedom" can be traced out and the temperature read by the thermometer can be uniquely assigned to the system. Unfortunately, such a procedure cannot be straightforwardly extended to a system out of equilibrium, where local excitations may be spatially inhomogeneous and the zeroth law of thermodynamics does not hold. With the advent of several experimental techniques that attempt to extract a single parameter characterizing the degree of local excitations of a (mesoscopic or nanoscale) system out of equilibrium, this issue is making a strong comeback to the forefront of research. In this paper, we will review the difficulties to define a unique temperature out of equilibrium, the majority of definitions that have been proposed so far, and discuss both their advantages and limitations. We will then examine a variety of experimental techniques developed for measuring the non-equilibrium local temperatures under various conditions. Finally we will discuss the physical implications of the notion of local temperature, and present the practical applications of such a concept in a variety of nanosystems out of equilibrium. Figure 4: (a) The product of the density of states η(E) times the global distribution function ϕ|ρ|ϕ forms a strongly pronounced peak at the expectation value of the global system energyĒ. (b) The logarithm of the local distribution function a|ρ|a (solid line) and the logarithm of a canonical distribution (dashed line) with the same local temperature for a harmonic chain. (a) and (b) are reprinted with permission from [74].

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Section: Local Equilibrium Conditionsmentioning

confidence: 99%

Local temperatures out of equilibrium

2019

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“…In spite of these significant advances, one crucial piece of the bigger puzzle that is the theory of the warm dense electron gas is yet missing: the response of an electron gas to an external perturbation. In particular, the experimental observation and subsequent theoretical description of the time-dependent density response is of paramount importance as a method of diagnostics in modern WDM applications [56][57][58]. In this context, the central quantity is given by the dynamic densitydensity response function χ(q, ω), with q and ω being the wave vector and frequency, or, equivalently, the dynamic structure factor S(q, ω), that is directly measured in X-ray Thomson scattering experiments, see Ref.…”

Section: Introductionmentioning

confidence: 99%

Ab initio path integral Monte Carlo approach to the static and dynamic density response of the uniform electron gas

2019

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In a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 121, 255001 (2018)] we have presented the first ab initio results for the dynamic structure factor S(q, ω) of the uniform electron gas for conditions ranging from the warm dense matter regime to the strongly correlated electron liquid. This was achieved on the basis of exact path integral Monte Carlo data by stochastically sampling the dynamic local field correction G(q, ω). In this paper, we introduce in detail this new reconstruction method and provide several practical demonstrations. Moreover, we thoroughly investigate the associated imaginary-time density-density correlation function F (q, τ ). The latter also gives us access to the static density-response function χ(q) and static local field correction G(q), which are compared to standard dielectric theories like the widespread random phase approximation. In addition, we study the high-frequency limit of G(q, ω) and provide extensive new results for the dynamic structure factor for different densities and temperatures. Finally, we discuss the implications of our findings for warm dense matter research and the interpretation of experiments.

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“…WDM is nowadays routinely realized at large research facilities like NIF [18,19], LCLS [20,21], and the European X-FEL [22]. Here Xray Thomson scattering (XRTS) [23][24][25] has emerged as an important method of diagnostics, with the electronic dynamic structure factor S(q, ω) being the central quantity. However, to make XRTS a reliable tool, an accurate theoretical description of the dynamic density response of warm dense electrons is indispensable [26].…”

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confidence: 99%

Ab initio Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter

et al. 2018

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The accurate description of electrons at extreme density and temperature is of paramount importance for, e.g., the understanding of astrophysical objects and inertial confinement fusion. In this context, the dynamic structure factor S(q, ω) constitutes a key quantity as it is directly measured in X-ray Thomson (XRTS) scattering experiments and governs transport properties like the dynamic conductivity. In this work, we present the first ab initio results for S(q, ω) by carrying out extensive path integral Monte Carlo simulations and developing a new method for the required analytic continuation, which is based on the stochastic sampling of the dynamic local field correction G(q, ω). In addition, we find that the so-called static approximation constitutes a promising opportunity to obtain high-quality data for S(q, ω) over substantial parts of the warm dense matter regime.Over the recent years, there has been a remarkable spark of interest in so-called warm dense matter (WDM), an extreme state with high densities (r s = a/a B ∼ 1, a is the mean interparticle distance and a B the Bohr radius) and temperatures (θ = k B T /E F ∼ 1, with E F = 2 q 2 F /2m and q F = (9π/4) 1/3 a B /r s being the Fermi energy and wave number). These conditions occur, for example, in astrophysical objects such as white and brown dwarfs [1-5] and giant planet interiors [6-10], hot-electron chemistry [11,12], laser-excited solids [13], and along the compression path in inertial confinement fusion experiments [14][15][16][17]. WDM is nowadays routinely realized at large research facilities like NIF [18,19], LCLS [20,21], and the European X-FEL [22]. Here Xray Thomson scattering (XRTS) [23-25] has emerged as an important method of diagnostics, with the electronic dynamic structure factor S(q, ω) being the central quantity. However, to make XRTS a reliable tool, an accurate theoretical description of the dynamic density response of warm dense electrons is indispensable [26].In this Letter, we focus on the uniform electron gas (UEG), one of the most fundamental model systems in physics and quantum chemistry [27,28]. While the static properties of the UEG in the ground state have mostly been known for over three decades [29][30][31][32], the intricate interplay of Coulomb coupling and quantum degeneracy effects with thermal excitations has rendered a thermodynamic description in the warm dense regime a challenging problem that has only been solved recently [33][34][35], see Ref.[36] for an extensive review. Naturally, dynamic simulations of electrons that are required for frequencyresolved properties (dynamic conductivity, optical absorption, collective excitations etc.) and rigorously take into account all aforementioned effects are even more difficult. Therefore, results for S(q, ω) at WDM conditions that go beyond the random phase approximation (RPA) [37] are sparse and have been obtained using uncontrolled approximations, such as diagram-summationbased Green function techniques [38][39][40][41]. On the other hand, ab initio path integral Mo...

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Measurement of temperature and density using non-collective X-ray Thomson scattering in pulsed power produced warm dense plasmas

Cited by 13 publications

References 25 publications

Local temperatures out of equilibrium

Local temperatures out of equilibrium

Ab initio path integral Monte Carlo approach to the static and dynamic density response of the uniform electron gas

Ab initio Path Integral Monte Carlo Results for the Dynamic Structure Factor of Correlated Electrons: From the Electron Liquid to Warm Dense Matter

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