Gradient expansion, curvature perturbations and magnetized plasmas

The properties of magnetized plasmas are always investigated under the hypothesis that the relativistic inhomogeneities stemming from the fluid sources and from the geometry itself are sufficiently small to allow for a perturbative description prior to photon decoupling. The latter assumption is hereby relaxed and pre-decoupling plasmas are described within a suitable expansion where the inhomogeneities are treated to a given order in the spatial gradients. It is argued that the (general relativistic) gradient expansion shares the same features of the drift approximation, customarily employed in the description of cold plasmas, so that the two schemes are physically complementary in the large-scale limit and for the low-frequency branch of the spectrum of plasma modes. The two-fluid description, as well as the magnetohydrodynamical reduction, are derived and studied in the presence of the spatial gradients of the geometry. Various solutions of the coupled system of evolution equations in the anti-Newtonian regime and in the quasi-isotropic approximation are presented. The relation of this analysis to the so-called separate Universe paradigm is outlined. The evolution of the magnetized curvature perturbations in the nonlinear regime is addressed for the magnetized adiabatic mode in the plasma frame.Comment: 40 pages, no figure

An Analysis of the Shapes of Interstellar Extinction Curves. VI. The Near-IR Extinction Law

We combine new HST/ACS observations and existing data to investigate the wavelength dependence of NIR extinction. Previous studies suggest a power-law form, with a "universal" value of the exponent, although some recent observations indicate that significant sight line-to-sight line variability may exist. We show that a power-law model provides an excellent fit to most NIR extinction curves, but that the value of the power, beta, varies significantly from sight line-to-sight line. Therefore, it seems that a "universal NIR extinction law" is not possible. Instead, we find that as beta decreases, R(V) [=A(V)/E(B-V)] tends to increase, suggesting that NIR extinction curves which have been considered "peculiar" may, in fact, be typical for different R(V) values. We show that the power law parameters can depend on the wavelength interval used to derive them, with the beta increasing as longer wavelengths are included. This result implies that extrapolating power law fits to determine R(V) is unreliable. To avoid this problem, we adopt a different functional form for NIR extinction. This new form mimics a power law whose exponent increases with wavelength, has only 2 free parameters, can fit all of our curves over a longer wavelength baseline and to higher precision, and produces R(V) values which are consistent with independent estimates and commonly used methods for estimating R(V). Furthermore, unlike the power law model, it gives R(V)'s that are independent of the wavelength interval used to derive them. It also suggests that the relation R(V) = -1.36 E(K-V)/E(B-V) - 0.79 can estimate R(V) to +/-0.12. Finally, we use model extinction curves to show that our extinction curves are in accord with theoretical expectations.Comment: To appear in the Astrophysical Journa

Temperature Relaxation in Hot Dense Hydrogen

Temperature equilibration of hydrogen is studied for conditions relevant to inertial confinement fusion. New molecular-dynamics simulations and results from quantum many-body theory are compared with Landau-Spitzer (LS) predictions for temperatures T from 50 eV to 5000 eV, and densities with Wigner-Seitz radii r_s = 1.0 and 0.5. The relaxation is slower than the LS result, even for temperatures in the keV range, but converges to agreement in the high-T limit.Comment: 4 pages PRL style, two figure

The energy partitioning of non-thermal particles in a plasma: or the Coulomb logarithm revisited

The charged particle stopping power in a highly ionized and weakly to moderately coupled plasma has been calculated to leading and next-to-leading order by Brown, Preston, and Singleton (BPS). After reviewing the main ideas behind this calculation, we use a Fokker-Planck equation derived by BPS to compute the electron-ion energy partitioning of a charged particle traversing a plasma. The motivation for this application is ignition for inertial confinement fusion -- more energy delivered to the ions means a better chance of ignition, and conversely. It is therefore important to calculate the fractional energy loss to electrons and ions as accurately as possible, as this could have implications for the Laser Megajoule (LMJ) facility in France and the National Ignition Facility (NIF) in the United States. The traditional method by which one calculates the electron-ion energy splitting of a charged particle traversing a plasma involves integrating the stopping power dE/dx. However, as the charged particle slows down and becomes thermalized into the background plasma, this method of calculating the electron-ion energy splitting breaks down. As a result, the method suffers a systematic error of order T/E0, where T is the plasma temperature and E0 is the initial energy of the charged particle. In the case of DT fusion, for example, this can lead to uncertainties as high as 10% or so. The formalism presented here is designed to account for the thermalization process, and in contrast, it provides results that are near-exact.Comment: 10 pages, 3 figures, invited talk at the 35th European Physical Society meeting on plasma physic

Collisional cross sections and momentum distributions in astrophysical plasmas: dynamics and statistical mechanics link

We show that, in stellar core plasmas, the one-body momentum distribution function is strongly dependent, at least in the high velocity regime, on the microscopic dynamics of ion elastic collisions and therefore on the effective collisional cross sections, if a random force field is present. We take into account two cross sections describing ion-dipole and ion-ion screened interactions. Furthermore we introduce a third unusual cross section, to link statistical distributions and a quantum effect originated by the energy-momentum uncertainty owing to many-body collisions, and propose a possible physical interpretation in terms of a tidal-like force. We show that each collisional cross section gives rise to a slight peculiar correction on the Maxwellian momentum distribution function in a well defined velocity interval. We also find a possible link between microscopical dynamics of ions and statistical mechanics interpreting our results in the framework of non-extensive statistical mechanics.Comment: 8 page

Locally Perturbed Random Walks with Unbounded Jumps

In \cite{SzT}, D. Sz\'asz and A. Telcs have shown that for the diffusively scaled, simple symmetric random walk, weak convergence to the Brownian motion holds even in the case of local impurities if $d \ge 2$. The extension of their result to finite range random walks is straightforward. Here, however, we are interested in the situation when the random walk has unbounded range. Concretely we generalize the statement of \cite{SzT} to unbounded random walks whose jump distribution belongs to the domain of attraction of the normal law. We do this first: for diffusively scaled random walks on $\mathbf Z^d$ $(d \ge 2)$ having finite variance; and second: for random walks with distribution belonging to the non-normal domain of attraction of the normal law. This result can be applied to random walks with tail behavior analogous to that of the infinite horizon Lorentz-process; these, in particular, have infinite variance, and convergence to Brownian motion holds with the superdiffusive $\sqrt{n \log n}$ scaling.Comment: 16 page

High-Precision Entropy Values for Spanning Trees in Lattices

Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the accuracy. In particular, the new values resolve one of their questions.Comment: 7 pages. Revision mentions alternative approach. Title changed slightly. 2nd revision corrects first displayed equatio

Population analysis of open clusters: radii and mass segregation

Aims: Based on our well-determined sample of open clusters in the all-sky catalogue ASCC-2.5 we derive new linear sizes of some 600 clusters, and investigate the effect of mass segregation of stars in open clusters. Methods: Using statistical methods, we study the distribution of linear sizes as a function of spatial position and cluster age. We also examine statistically the distribution of stars of different masses within clusters as a function of the cluster age. Results: No significant dependence of the cluster size on location in the Galaxy is detected for younger clusters (< 200 Myr), whereas older clusters inside the solar orbit turned out to be, on average, smaller than outside. Also, small old clusters are preferentially found close to the Galactic plane, whereas larger ones more frequently live farther away from the plane and at larger Galactocentric distances. For clusters with (V - M_V) < 10.5, a clear dependence of the apparent radius on age has been detected: the cluster radii decrease by a factor of about 2 from an age of 10 Myr to an age of 1 Gyr. A detailed analysis shows that this observed effect can be explained by mass segregation and does not necessarily reflect a real decrease of cluster radii. We found evidence for the latter for the majority of clusters older than 30 Myr. Among the youngest clusters (between 5 and 30 Myr), there are some clusters with a significant grade of mass segregation, whereas some others show no segregation at all. At a cluster age between 50 and 100 Myrs, the distribution of stars of different masses becomes more regular over cluster area. In older clusters the evolution of the massive stars is the most prominent effect we observe.Comment: 14 pages, 12 figures, accepted for publication in Astronomy & Astrophysic