Virial expansion with Feynman diagrams

We present a field theoretic method for the calculation of the second and third virial coefficients b2 and b3 of 2-species fermions interacting via a contact interaction. The method is mostly analytic. We find a closed expression for b3 in terms of the 2 and 3-body T-matrices. We recover numerically, at unitarity, and also in the whole BEC-BCS crossover, previous numerical results for the third virial coefficient b3

Turbulence, magnetic fields and plasma physics in clusters of galaxies

Observations of galaxy clusters show that the intracluster medium (ICM) is likely to be turbulent and is certainly magnetized. The properties of this magnetized turbulence are determined both by fundamental nonlinear magnetohydrodynamic interactions and by the plasma physics of the ICM, which has very low collisionality. Cluster plasma threaded by weak magnetic fields is subject to firehose and mirror instabilities. These saturate and produce fluctuations at the ion gyroscale, which can scatter particles, increasing the effective collision rate and, therefore, the effective Reynolds number of the ICM. A simple way to model this effect is proposed. The model yields a self-accelerating fluctuation dynamo whereby the field grows explosively fast, reaching the observed, dynamically important, field strength in a fraction of the cluster lifetime independent of the exact strength of the seed field. It is suggested that the saturated state of the cluster turbulence is a combination of the conventional isotropic magnetohydrodynamic turbulence, characterized by folded, direction-reversing magnetic fields and an Alfv\'en-wave cascade at collisionless scales. An argument is proposed to constrain the reversal scale of the folded field. The picture that emerges appears to be in qualitative agreement with observations of magnetic fields in clusters.Comment: revtex, 9 pages, 5 figures; invited talk for the 47th APS DPP Meeting, Denver, CO, Oct 2005; minor corrections to match the published versio

Identity of electrons and ionization equilibrium

It is perhaps appropriate that, in a year marking the 90th anniversary of Meghnad Saha seminal paper (1920), new developments should call fresh attention to the problem of ionization equilibrium in gases. Ionization equilibrium is considered in the simplest "physical" model for an electronic subsystem of matter in a rarefied state, consisting of one localized electronic state in each nucleus and delocalized electronic states considered as free ones. It is shown that, despite the qualitative agreement, there is a significant quantitative difference from the results of applying the Saha formula to the degree of ionization. This is caused by the fact that the Saha formula corresponds to the "chemical" model of matter.Comment: 9 pages, 2 figure

Nonlinear growth of firehose and mirror fluctuations in turbulent galaxy-cluster plasmas

In turbulent high-beta astrophysical plasmas (exemplified by the galaxy cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations grow nonlinearly to large amplitudes, dB/B ~ 1, on a timescale comparable to the turnover time of the turbulent motions. The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. The presence of small-scale magnetic fluctuations may dramatically affect the transport properties and, thereby, the large-scale dynamics of the high-beta astrophysical plasmas.Comment: revtex, 4 pages, 1 figure; replaced to match published versio

Equation of state of a strongly magnetized hydrogen plasma

The influence of a constant uniform magnetic field on the thermodynamic properties of a partially ionized hydrogen plasma is studied. Using the method of Green' s function various interaction contributions to the thermodynamic functions are calculated. The equation of state of a quantum magnetized plasma is presented within the framework of a low density expansion up to the order e^4 n^2 and, additionally, including ladder type contributions via the bound states in the case of strong magnetic fields (2.35*10^{5} T << B << 2.35*10^{9} T). We show that for high densities (n=10^{27-30} m^{-3}) and temperatures T=10^5 - 10^6 K typical for the surface of neutron stars nonideality effects as, e.g., Debye screening must be taken into account.Comment: 12 pages, 2 Postscript figures. uses revtex, to appear in Phys. Rev.

Nonlinear theory of mirror instability near threshold

An asymptotic model based on a reductive perturbative expansion of the drift kinetic and the Maxwell equations is used to demonstrate that, near the instability threshold, the nonlinear dynamics of mirror modes in a magnetized plasma with anisotropic ion temperatures involves a subcritical bifurcation,leading to the formation of small-scale structures with amplitudes comparable with the ambient magnetic field

Landau Damping and Coherent Structures in Narrow-Banded 1+1 Deep Water Gravity Waves

We study the nonlinear energy transfer around the peak of the spectrum of surface gravity waves by taking into account nonhomogeneous effects. In the narrow-banded approximation the kinetic equation resulting from a nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at the same time the random version of the Benjamin-Feir instability and the Landau damping phenomenon. We analytically derive the values of the Phillips' constant $\alpha$ and the enhancement factor $\gamma$ for which the narrow-banded approximation of the JONSWAP spectrum is unstable. By performing numerical simulations of the nonlinear Schr\"{o}dinger equation we check the validity of the prediction of the related kinetic equation. We find that the effect of Landau damping is to suppress the formation of coherent structures. The problem of predicting freak waves is briefly discussed.Comment: 4 pages, 3 figure

Fast transport of resonant electrons in phase space due to nonlinear trapping by whistler waves

International audienceWe present an analytical, simplified formulation accounting for the fast transport of relativistic electrons in phase space due to wave-particle resonant interactions in the inhomogeneous magnetic field of Earth's radiation belts. We show that the usual description of the evolution of the particle velocity distribution based on the Fokker-Planck equation can be modified to incorporate nonlinear processes of wave-particle interaction, including particle trapping. Such a modification consists in one additional operator describing fast particle jumps in phase space. The proposed, general approach is used to describe the acceleration of relativistic electrons by oblique whistler waves in the radiation belts. We demonstrate that for a wave power distribution with a hard enough power law tail inline image such that η < 5/2, the efficiency of nonlinear acceleration could be more effective than the conventional quasi-linear acceleration for 100 keV electrons

Fluctuations driven isotropization of the quark-gluon plasma in heavy ion collisions

Averaged over ensemble of initial conditions kinetic transport equations of weakly coupled systems of quarks and gluons are derived. These equations account for the correlators of fluctuations of particles and classical gluon fields. The isotropization of particle momenta by field fluctuations at the early prethermal stage of matter evolution in ultrarelativistic heavy ion collisions is discussed. Our results can be useful for understanding under what conditions isotropization of the quark-gluon plasma in ultrarelativistic heavy ion collisions can be reached within phenomenologically observed time scales.Comment: 16 pages, misprints corrected, to be published in Phys. Rev.