Theoretical foundations of quantum hydrodynamics for plasmas

Beginning from the semiclassical Hamiltonian, the Fermi pressure and Bohm potential for the quantum hydrodynamics application (QHD) at finite temperature are consistently derived in the framework of the local density approximation with the first order density gradient correction. Previously known results are revised and improved with a clear description of the underlying approximations. A fully non-local Bohm potential, which goes beyond of all previous results and is linked to the electron polarization function in the random phase approximation, for the QHD model is presented. The dynamic QHD exchange correlation potential is introduced in the framework of local field corrections, and considered for the case of the relaxation time approximation. Finally, the range of applicability of the QHD is discussed

Dynamical screening of charge potential in classical, quantum and ultrarelativistic plasmas

Dense plasmas have recently gained growing interest due to their relevance for the interior of giant planets as well as for laser interaction with matter and inertial confinement fusion scenarios. Examples of recent experimental studies include the ultrafast thermalization of laser plasmas or free electron laser excited plasmas, inertial confinement fusion experiments at the National Ignition Facility, and magnetized Z-pinch experiments at Sandia. Questions of fundamental theoretical importance are the conductivity and heat conduction, the free energy loss of energetic particles (stopping power) in such a plasma, or the temperature equilibration of the electronic and ionic components..

Ab initio simulation of warm dense matter

Warm dense matter (WDM) -- an exotic state of highly compressed matter -- has attracted high interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applications. The situation has changed with the availability of the first \textit{ab initio} data for the exchange-correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations, for recent reviews, see Dornheim \textit{et al.}, Phys. Plasmas \textbf{24}, 056303 (2017) and Phys. Rep. \textbf{744}, 1-86 (2018). In the present article we review recent further progress in QMC simulations of the warm dense UEG: namely, \textit{ab initio} results for the static local field correction $G(q)$ and for the dynamic structure factor $S(q,\omega)$. These data are of key relevance for the comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models. In the second part of this paper we discuss simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, time-dependent DFT and hydrodynamics. Here we analyze strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method

Dynamical screening of charge potential in classical, quantum and ultrarelativistic plasmas

Dense plasmas have recently gained growing interest due to their relevance for the interior of giant planets as well as for laser interaction with matter and inertial confinement fusion scenarios. Examples of recent experimental studies include the ultrafast thermalization of laser plasmas or free electron laser excited plasmas, inertial confinement fusion experiments at the National Ignition Facility, and magnetized Z-pinch experiments at Sandia. Questions of fundamental theoretical importance are the conductivity and heat conduction, the free energy loss of energetic particles (stopping power) in such a plasma, or the temperature equilibration of the electronic and ionic components..