Quantum Hydrodynamics for Plasmas – a Thomas‐Fermi Theory Perspective

Michta, David; Graziani, Frank; Bönitz, M.

doi:10.1002/ctpp.201500024

Cited by 91 publications

(82 citation statements)

References 59 publications

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“…(4), the coefficient α is a monotonically decreasing function of the fugacity, showing that the quantum force becomes less effective in denser systems. The result α → 1 for non-degenerate systems agrees with the quantum hydrodynamic model for semiconductor devices derived in [23], while α → 1/3 agrees with [31,32] in the fully degenerate case. On the other hand, high frequency waves such as quantum Langmuir waves would be correctly described by a value α = 3, in order to reproduce the Bohm-Pines [33] dispersion relation The detailed account of the collisionless damping of quantum ion-acoustic waves has been considered in [19], where the damping rate is shown to be small, as long as the ion temperature is much smaller than the electron temperature of the plasma.…”

Section: B Kinetic Theorysupporting

confidence: 80%

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

Haas

Mahmood

2015

Phys. Rev. E

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Linear and nonlinear ion-acoustic waves are studied in a fluid model for non-relativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and apply equally well both to fully degenerate or classical, non-degenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long wavelength limit the results agree with quantum kinetic theory.Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

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Section: B Kinetic Theorysupporting

confidence: 80%

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

Haas

Mahmood

2015

Phys. Rev. E

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“…To overcome this bottleneck, it will be advantageous to incorporate the T = 0 limit of E xc and, thus, to perform an interpolation across the remaining gap where no ab initio data are available. In addition to finite-T DFT, we expect such a fit to be of key importance as input for quantum hydrodynamics [55,56] and time-dependent DFT. Finally, our FSC procedure is expected to be of value for other simulations of warm dense plasmas [57][58][59], as well as 2D systems, e.g.…”

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confidence: 99%

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

et al. 2016

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We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown et al. [PRL 110, 146405 (2013)]. Extensive new QMC results for up to N = 1000 electrons enable us to compute the potential energy V and the exchange-correlation free energy Fxc of the macroscopic electron gas with an unprecedented accuracy of |∆V |/|V |, |∆Fxc|/|F |xc ∼ 10 −3 . A comparison of our new data to the recent parametrization of Fxc by Karasiev et al. [PRL 112, 076403 (2014)] reveals significant deviations to the latter.The uniform electron gas (UEG), consisting of electrons on a uniform neutralizing background, is one of the most important model systems in physics [1]. Besides being a simple model for metals, the UEG has been central to the development of linear response theory and more sophisticated perturbative treatments of solids, the formulation of the concepts of quasiparticles and elementary excitations, and the remarkable successes of density functional theory.The practical application of ground-state density functional theory in condensed matter physics, chemistry and materials science rests on a reliable parametrization of the exchange-correlation energy of the UEG [2], which in turn is based on accurate quantum Monte Carlo (QMC) simulation data [3]. However, the charged quantum matter in astrophysical systems such as planet cores and white dwarf atmospheres [4,5] is at temperatures way above the ground state, as are inertial confinement fusion targets [6][7][8], laser-excited solids [9], and pressure induced modifications of solids, such as insulator-metal transitions [10,11]. This unusual regime, in which strong ionic correlations coexist with electronic quantum effects and partial ionization, has been termed "warm dense matter" and is one of the most active frontiers in plasma physics and materials science.The warm dense regime is characterized by the existence of two comparable length scales and two comparable energy scales. The length scales are the mean interparticle distance,r, and the Bohr radius, a 0 ; the energy scales are the thermal energy, k B T , and the electronic Fermi energy, E F . The dimensionless parameters [12] r s =r/a 0 and Θ = k B T /E F are of order unity. Because Θ ∼ 1, the use of ground-state density functional theory is inappropriate and extensions to finite T are indispensible; these require accurate exchange-correlation functionals for finite temperatures [13][14][15][16][17]. Because neither r s nor Θ is small, there are no small parameters, and weakcoupling expansions beyond Hartree-Fock such as the Montroll-Ward (MW) and e 4 (e4) approximations [18,19], as well as linear response theory within the random- phase approximation (RPA) break down [20,21]. Finite-T Singwi-Tosi-Land-Sjölander (STLS) [22,23] local-fiel...

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“…[18][19][20][21][22][23] This Bohm force term is responsible for quantum tunnelling effects in a quantum plasma associated with electrons and positrons due to their wave-like nature. In case of a non-degenerate plasma, → 1, while for the fully degenerate electrons/positrons case, = 1/3 for low-frequency waves such as ion-acoustic waves and = 3 for high-frequency waves such as quantum Langmuir waves, which gives the Bohm-Pines dispersion relation.…”

Section: Basic Set Of Equationsmentioning

confidence: 99%

Two‐dimensional magnetosonic shock wave propagation in dense electron–positron–ion plasmas

Hussain

Abdykian

Mahmood

2018

Contributions to Plasma Physics

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Two-dimensional (2D) magnetosonic wave propagation in magnetized quantum dissipative plasmas is studied. The plasma system is comprised of inertial ions, inertia-less electrons, and positrons. The multi-fluid quantum hydrodynamic model is used, in which quantum statistical and quantum tunnelling effects of electrons and positrons are included. Reductive perturbation analysis is performed to derive the Zabolotskaya-Khokhlov equation for the 2D propagation of a magnetosonic shock wave in a magnetized qauntum plasma. The effects of varying the different plasma parameters such as positron density and magnetic field intensity on the propagation characteristics of magnetosonic shock waves are discussed with non-relativistic degenerate plasma parameters in astrophysical plasma situations.

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Quantum Hydrodynamics for Plasmas – a Thomas‐Fermi Theory Perspective

Cited by 91 publications

References 59 publications

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

Ab InitioQuantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit

Two‐dimensional magnetosonic shock wave propagation in dense electron–positron–ion plasmas

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