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The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {\em explicitly} from their Markovian dynamics. The method is shown on an example of a natural sand pile model with a gradient threshold., Comment: 4 pages (REVTeX), incl. 2 figures (PostScript)

It is quite well established that shocks accelerate particles via the Fermi mechanism. We discuss common features of various extragalactic sources, ranging from Gamma-Ray Bursts and jets of Active Galactic Nuclei to Large-Scale Structure shocks and address how they affect particle acceleration. In particular, we address constraints on the maximum energy of ultra-high-energy cosmic rays. Interestingly, some recent studies indicate that Fermi acceleration in relativistic shocks (and GRBs, in particular) faces severe difficulties. We will address this issue and demonstrate that the ‘observed’ shock acceleration of electrons may have nothing to do with Fermi acceleration, but may rather be associated with micro-physics of collisionless shocks.

We have investigated the generation of magnetic fields associated with velocity shear between an unmagnetized relativistic (core) jet and an unmagnetized sheath plasma by the kinetic Kelvin-Helmholtz instability for different mass ratios (m i /m e = 1, 20, and 1836) and different jet Lorentz factors. We found that electron-positron cases have alternating magnetic fields instead of the DC magnetic fields found in electron-ion cases. We have also investigated particle acceleration and shock structure associated with an unmagnetized relativistic jet propagating into an unmagnetized plasma for electron-positron and electron-ion plasmas. Strong magnetic fields generated in the trailing shock lead to transverse deflection and acceleration of the electrons. We have self-consistently calculated the radiation from the electrons accelerated in the turbulent magnetic fields for different jet Lorentz factors. We find that the synthetic spectra depend on the bulk Lorentz factor of the jet, the jet temperature, and the strength of the magnetic fields generated in the shock.

The nonlinear dynamics of collisionless Alfven trains, including resonant particle effects is studied using the kinetic nonlinear Schroedinger (KNLS) equation model. Numerical solutions of the KNLS reveal the dynamics of Alfven waves to be sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. The combined effects of both wave nonlinearity and Landau damping result in the evolutionary formation of stationaryOA S- and arc-polarized directional and rotational discontinuities. These waveforms are freqently observed in the interplanetary plasma., Comment: REVTeX, 6 pages (including 5 figures). This and other papers may be found at http://sdphpd.ucsd.edu/~medvedev/papers.html

Bubbles in the interstellar medium are produced by astrophysical sources, which continuously or explosively deposit large amount of energy into the ambient medium. These expanding bubbles can drive shocks in front of them, which dynamics is markedly different from the widely used Sedov-von Neumann-Taylor blast wave solution. Here we present the theory of a bubble-driven shock and show how its properties and evolution are determined by the temporal history of the source energy output, generally referred to as the source luminosity law, $L(t)$. In particular, we find the analytical solutions for a driven shock in two cases: the self-similar scaling $L\propto (t/t_s)^p$ law (with $p$ and $t_s$ being constants) and the finite activity time case, $L\propto (1-t/t_s)^{-p}$. The latter with $p>0$ describes a finite-time-singular behavior, which is relevant to a wide variety of systems with explosive-type energy release. For both luminosity laws, we derived the conditions needed for the driven shock to exist and predict the shock observational signatures. Our results can be relevant to stellar systems with strong winds, merging neutron star/magnetar/black hole systems, and massive stars evolving to supernovae explosions., 19 pages, 3 figures

The influence of various kinetic effects (e.g. Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvenic wave trains in a finite-beta environment is systematically investigated using a novel, kinetic nonlinear Schrodinger (KNLS) equation. The dynamics of Alfven waves is sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. Numerical solution for the case with Landau damping reveals the formation of dissipative structures, which are quasi-stationary, S-polarized directional (and rotational) discontinuities which self-organize from parallel propagating, linearly polarized waves. Parallel propagating circularly polarized packets evolve to a few circularly polarized Alfven harmonics on large scales. Stationary arc-polarized rotational discontinuities form from obliquely propagating waves. Collisional dissipation, even if weak, introduces enhanced wave damping when beta is very close to unity. Cyclotron motion effects on resonant particle interactions introduce cyclotron resonance into the nonlinear Alfven wave dynamics., 38 pages (including 23 figures and 1 table)

Collisionless regime kinetic models for coherent nonlinear Alfven wave dynamics are studied using fluid moment equations with an approximate closure anzatz. Resonant particle effects are modelled by incorporating an additional term representing dissipation akin to parallel heat conduction. Unlike collisional dissipation, parallel heat conduction is presented by an integral operator. The modified derivative nonlinear Schrodinger equation thus has a spatially nonlocal nonlinear term describing the long-time evolution of the envelope of parallel-propagating Alfven waves, as well. Coefficients in the nonlinear terms are free of the 1/(1-beta) singularity usually encountered in previous analyses, and have very a simple form which clarifies the physical processes governing the large amplitude Alfvenic nonlinear dynamics. The nonlinearity appears via coupling of an Alfvenic mode to a kinetic ion-acoustic mode. Damping of the nonlinear Alfven wave appears via strong Landau damping of the ion-acoustic wave when the electron-to-ion temperature ratio is close to unity. For a (slightly) obliquely propagating wave, there are finite Larmor radius corrections in the dynamical equation. This effect depends on the angle of wave propagation relative to B_0 and vanishes for the limit of strictly parallel propagation. Explicit magnetic perturbation envelope equations amenable to further analysis and numerical solution are obtained. Implications of these models for collisionless shock dynamics are discussed., 34 pages (including 6 figures)

A simple model collisionless, dissipative, compressible MHD (Alfvenic) turbulence in a magnetized system is investigated. In contrast to more familiar paradigms of turbulence, dissipation arises from Landau damping, enters via nonlinearity, and is distributed over all scales. The theory predicts that two different regimes or phases of turbulence are possible, depending on the ratio of steepening to damping coefficient (m_1/m_2). For strong damping (|m_1/m_2|1, steady state turbulence does not exist in the hydrodynamic limit. Rather, spikey, small scale structure is predicted., 6 pages, one figure, REVTeX; this version to be published in PRE. For related papers, see http://sdphpd.ucsd.edu/~medvedev/papers.html

A new class of identical particles which may exhibit both Bose and Fermi statistics with respective probabilities $p_b$ and $p_f$ is introduced. Such an uncertainity may be either an intrinsic property of a particle or can be viewed as an ``experimental uncertainity''. Statistical equivalence of such particles and particles obeying parastatistics of infinite order is shown. Generalized statistical distributions are derived and statistical and thermodynamical properties of an ideal gas of the particles are investigated. The physical nature of such particles and the implications of this investigation for the statistics of extremal black holes are discussed., Comment: 4 pages, REVTeX, 22k, final version, last Eq. corrected. This and other papers may be found at http://sdphpd.ucsd.edu/~medvedev/papers.html

We have investigated particle acceleration and shock structure associated with an unmagnetized relativistic jet propagating into an unmagnetized plasma for electron-positron and electron-ion plasmas. Strong magnetic fields generated in the trailing jet shock lead to transverse deflection and acceleration of the electrons. We have self-consistently calculated the radiation from the electrons accelerated in the turbulent magnetic fields for different jet Lorentz factors. We find that the synthetic spectra depend on the bulk Lorentz factor of the jet, the jet temperature, and the strength of the magnetic fields generated in the shock. We have investigated the generation of magnetic fields associated with velocity shear between an unmagnetized relativistic (core) jet and an unmagnetized sheath plasma. We discuss particle acceleration in collimation shocks for AGN jets formed by relativistic MHD simulations. Our calculated spectra should lead to a better understanding of the complex time evolution and/or spectral structure from gamma-ray bursts, relativistic jets, and supernova remnants.

Spontaneous rapid growth of strong magnetic fields is rather ubiquitous in high-energy density environments ranging from astrophysical sources (e.g., gamma-ray bursts and relativistic shocks), to reconnection, to laser-plasma interaction laboratory experiments, where they are produced by kinetic streaming instabilities of the Weibel type. Relativistic electrons propagating through these sub-Larmor-scale magnetic fields radiate in the jitter regime, in which the anisotropy of the magnetic fields and the particle distribution have a strong effect on the produced radiation. Here we develop the general theory of jitter radiation, which (1) includes anisotropic magnetic fields and electron velocity distributions, (2) accounts for the effects of trapped electrons, and (3) extends the description to large deflection angles of radiating particles thus establishing a cross-over between the classical jitter and synchrotron regimes. Our results are in remarkable agreement with the radiation spectra obtained from particle-in-cell simulations of the classical Weibel instability. Particularly interesting is the onset of the field growth, when the transient hard synchrotron-violating spectra are common as a result of the dominant role of the trapped population. This effect can serve as a distinct observational signature of the violent field growth in astrophysical sources and lab experiments. It is also interesting that a system with small-scale fields tends to evolve toward the small-angle jitter regime, which can, under certain conditions, dominate the overall emission of a source.

The secondary instability of large scale flows, such as zonal flows and streamers, in toroidal ion temperature gradient turbulence is investigated. It is shown that diamagnetic effects (finite pressure fluctuations), such as those for toroidal ion temperature gradient modes, significantly increase the total Reynolds force. In general, pressure fluctuations have a finite phase shift relative to the electrostatic potential. It is shown that both parts (in-phase and out-of-phase) contribute to the diamagnetic Reynolds stress tensor. Also, the out-of-phase component of the pressure fluctuations is responsible for anomalous energy flux. It is shown here, that a specific contribution of the out-of-phase component to the Reynolds stress tensor allows us to decouple zonal flow dynamics from slow evolution of the ion pressure profile. General equations for the zonal flow and streamer instabilities in toroidal ion temperature gradient turbulence are derived and the growth rates are determined.

Recent PIC simulations of relativistic electron-positron (electron-ion) jets injected into a stationary medium show that particle acceleration occurs in the shocked regions. Simulations show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields and for particle acceleration. These magnetic fields contribute to the electron's transverse deflection behind the shock. The “jitter” radiation from deflected electrons in turbulent magnetic fields has different properties from synchrotron radiation calculated in a uniform magnetic field. This jitter radiation may be important for understanding the complex time evolution and/or spectral structure of gamma-ray bursts, relativistic jets in general, and supernova remnants. In order to calculate radiation from first principles and go beyond the standard synchrotron model, we have used PIC simulations. We will present detailed spectra for conditions relevant to various astrophysical sites of collisionless shock formation. In particular we will discuss application to GRBs and SNRs.