Stable transport in proton driven Fast Ignition

Proton beam transport in the context of proton driven Fast Ignition is usually assumed to be stable due to protons high inertia, but an analytical analysis of the process is still lacking. The stability of a charge and current neutralized proton beam passing through a plasma is therefore conducted here, for typical proton driven Fast Ignition parameters. In the cold regime, two fast growing Buneman-like modes are found, with an inverse growth-rate much smaller than the beam time-of-flight to the target core. The stability issue is thus not so obvious, and Kinetic effects are investigated. One unstable mode is found stabilized by the background plasma protons and electrons temperatures. The second mode is also damped, providing the proton beam thermal spread is larger than $\sim$ 10 keV. In Fusion conditions, the beam propagation should therefore be stable.Comment: Submitted to Po

Classical Strongly Coupled QGP: VII. Energy Loss

We use linear response analysis and the fluctuation-dissipation theorem to derive the energy loss of a heavy quark in the SU(2) classical Coulomb plasma in terms of the $l=1$ monopole and non-static structure factor. The result is valid for all Coulomb couplings $\Gamma=V/K$, the ratio of the mean potential to kinetic energy. We use the Liouville equation in the collisionless limit to assess the SU(2) non-static structure factor. We find the energy loss to be strongly dependent on $\Gamma$. In the liquid phase with $\Gamma\approx 4$, the energy loss is mostly metallic and soundless with neither a Cerenkov nor a Mach cone. Our analytical results compare favorably with the SU(2) molecular dynamics simulations at large momentum and for heavy quark masses.Comment: 18 pages, 15 figures. v2: added references, changed title, replaced figures for Fig. 7, corrected typo

Classical Strongly Coupled QGP: VII. Shear Viscosity and Self Diffusion

We construct the Liouville operator for the SU(2) classical colored Coulomb plasma (cQGP) for arbitrary values of the Coulomb coupling $\Gamma=V/K$, the ratio of the mean Coulomb to kinetic energy. We show that its resolvent in the classical colored phase space obeys a hierarchy of equations. We use a free streaming approximation to close the hierarchy and derive an integral equation for the time-dependent structure factor. Its reduction by projection yields hydrodynamical equations in the long-wavelength limit. We discuss the character of the hydrodynamical modes at strong coupling. The shear viscosity is shown to exhibit a minimum at $\Gamma\approx 8$ near the liquid point. This minimum follows from the cross-over between the single particle collisional regime which drops as $1/\Gamma^{5/2}$ and the hydrodynamical collisional regime which rises as $\Gamma^{1/2}$. The self-diffusion constant drops as $1/\Gamma^{3/2}$ irrespective of the regime. We compare our results to molecular dynamics simulations of the SU(2) colored Coulomb plasma. We also discuss the relevance of our results for the quantum and strongly coupled quark gluon plasma (sQGP)Comment: 36 pages, 14 figure

The influence of local field corrections on Thomson scattering in non-ideal two-component plasmas

Thomson scattering in non-ideal (collision-dominated) two-component plasmas is calculated accounting for electron-ion collisions as well as electron-electron correlations. This is achieved by using a novel interpolation scheme for the electron-electron response function generalizing the traditional Mermin approach. Also, ions are treated as randomly distributed inert scattering centers. The collision frequency is taken as a dynamic and complex quantity and is calculated from a microscopic quantum-statistical approach. Implications due to different approximations for the electron-electron correlation, i.e. different forms of the OCP local field correction, are discussed

Relaxation of the distribution function tails for systems described by Fokker-Planck equations

We study the formation and the evolution of velocity distribution tails for systems with long-range interactions. In the thermal bath approximation, the evolution of the distribution function of a test particle is governed by a Fokker-Planck equation where the diffusion coefficient depends on the velocity. We extend the theory of Potapenko et al. [Phys. Rev. E, {\bf 56}, 7159 (1997)] developed for power law potentials to the case of an arbitrary potential of interaction. We study how the structure and the progression of the front depend on the behavior of the diffusion coefficient for large velocities. Particular emphasis is given to the case where the velocity dependence of the diffusion coefficient is Gaussian. This situation arises in Fokker-Planck equations associated with one dimensional systems with long-range interactions such as the Hamiltonian Mean Field (HMF) model and in the kinetic theory of two-dimensional point vortices in hydrodynamics. We show that the progression of the front is extremely slow (logarithmic) in that case so that the convergence towards the equilibrium state is peculiar

On the Ground State of Electron Gases at Negative Compressibility

Two- and three-dimensional electron gases with a uniform neutralizing background are studied at negative compressibility. Parametrized expressions for the dielectric function are used to access this strong-coupling regime, where the screened Coulomb potential becomes overall attractive for like charges. Closely examining these expressions reveals that the ground state with a periodic modulation of the charge density, albeit exponentially damped, replaces the homogeneous one at positive compressibility. The wavevector characterizing the new ground state depends on the density and is complex, having a positive imaginary part, as does the homogeneous ground state, and real part, as does the genuine charge density wave.Comment: 6 double-column pages, 2 figures. 2nd version is an extension of the 1st one, giving more detail

Structure Functions and Pair Correlations of the Quark-Gluon Plasma

Recent experiments at RHIC and theoretical considerations indicate that the quark-gluon plasma, present in the fireball of relativistic heavy-ion collisions, might be in a liquid phase. The liquid state can be identified by characteristic correlation and structure functions. Here definitions of the structure functions and pair correlations of the quark-gluon plasma are presented as well as perturbative results. These definitions might be useful for verifying the quark-gluon-plasma liquid in QCD lattice calculations.Comment: 9 pages, 1 figure, revised version (new remark on the coupling parameter on page 2), to be published in Phys. Rev.

Plasma Oscillations and Expansion of an Ultracold Neutral Plasma

We report the observation of plasma oscillations in an ultracold neutral plasma. With this collective mode we probe the electron density distribution and study the expansion of the plasma as a function of time. For classical plasma conditions, i.e. weak Coulomb coupling, the expansion is dominated by the pressure of the electron gas and is described by a hydrodynamic model. Discrepancies between the model and observations at low temperature and high density may be due to strong coupling of the electrons.Comment: 4 pages, 4 figures. Accepted Phys. Rev. Let

Wave spectra of 2D dusty plasma solids and liquids

Brownian dynamics simulations were carried out to study wave spectra of two-dimensional dusty plasma liquids and solids for a wide range of wavelengths. The existence of a longitudinal dust thermal mode was confirmed in simulations, and a cutoff wavenumber in the transverse mode was measured. Dispersion relations, resulting from simulations, were compared with those from analytical theories, such as the random-phase approximation (RPA), quasi-localized charged approximation (QLCA), and harmonic approximation (HA). An overall good agreement between the QLCA and simulations was found for wide ranges of states and wavelengths after taking into account the direct thermal effect in the QLCA, while for the RPA and HA good agreement with simulations were found in the high and low temperature limits, respectively.Comment: 26 pages, 9 figure

Strongly Coupled Quark Gluon Plasma (SCQGP)

We propose that the reason for the non-ideal behavior seen in lattice simulation of quark gluon plasma (QGP) and relativistic heavy ion collisions (URHICs) experiments is that the QGP near T_c and above is strongly coupled plasma (SCP), i.e., strongly coupled quark gluon plasma (SCQGP). It is remarkable that the widely used equation of state (EoS) of SCP in QED (quantum electrodynamics) very nicely fits lattice results on all QGP systems, with proper modifications to include color degrees of freedom and running coupling constant. Results on pressure in pure gauge, 2-flavors and 3-flavors QGP, are all can be explained by treating QGP as SCQGP as demonstated here.Energy density and speed of sound are also presented for all three systems. We further extend the model to systems with finite quark mass and a reasonably good fit to lattice results are obtained for (2+1)-flavors and 4-flavors QGP. Hence it is the first unified model, namely SCQGP, to explain the non-ideal QGP seen in lattice simulations with just two system dependent parameters.Comment: Revised with corrections and new results, Latex file (11 pages), postscript file of 7 figure