Numerical Descriptions of Cosmic-Ray Transport

The behavior of energetic particles in the solar system is described by a well known Fokker-Planck equation. Although analytic methods yield insight into the nature of its solutions, especially in the diffusion regime, calculations that go beyond diffusion are very complicated. The reliability of these calculations is of concern, because numerical methods are notorious for their errors and artifacts. The well known Milne problem of classical transport theory was analyzed with the aid of three different numerical methods. These are: (1) The method of eigenfunctions in which the distribution function is approximated by a sum of eigenfunctions of the scattering operator, (2) Numerical solutions of a finite difference aquation; and (3) Direct simulation of the scattering and streaming of individual particles with the aid of Monte Carlo methods

The Transition from Singly to Multiply-Charged Anomalous Cosmic Rays: Simulation and Interpretation of SAMPEX Observations

Multiply-charged anomalous cosmic rays (ACRs) can arise when singly-charged ACR ions are stripped of one or more of their electrons during their acceleration via, e.g., the process of diffusive shock-drift acceleration at the solar-wind termination shock. Recent measurements of the charge states of ACR neon, oxygen, and nitrogen by SAMPEX at 1 AU have shown that above ≈ 25 MeV/nucleon these ions are multiply charged. In addition, SAMPEX observations have also established that the transition from mostly singly-charged to mostly multiply-charged ACRs (defined as the 50% point) occurs at a total kinetic energy of ≈ 350 MeV. Preliminary simulations for ACR oxygen based on a theory of multiply-charged ACRs were able to show a transition energy at ≈ 300 MeV. However, the simulated intensity distribution among the various charge states was inconsistent with observations. This paper reexamines the predictions of the theory in light of new SAMPEX ACR observations and recently developed and refined estimates of hydrogen-impact ionization cross sections. Based on simulations for multi-species ACR ions, we find that the transition energy is only weakly dependent on characteristic transport parameters, and that the new ionization rates distribute the intensity among the charge states in a manner consistent with observations. The calculated transition energy is in excellent agreement with the measured value

The intensity recovery of Forbush-type decreases as a function of heliocentric distance and its relationship to the 11-year variation

Recent data indicating that the solar modulation effects are propagated outward in the heliospheric cavity suggest that the 11-year cosmic ray modulation can best be described by a dynamic time dependent model. In this context an understanding of the recovery characteristics of large transient Forbush type decreases is important. This includes the typical recovery time at a fixed energy at 1 AU as well as at large heliocentric radial distances, the energy dependence of the recovery time at 1 Au, and the dependence of the time for the intensity to decrease to the minimum in the transient decreases as a function of distance. These transient decreases are characterized by their asymmetrical decrease and recovery times, generally 1 to 2 days and 3 to 10 days respectively at approx. 1 AU. Near earth these are referred to as Forbush decreases, associated witha shock or blast wave passage. At R equal to or greater than + or - 10 AU, these transient decreases may represent the combined effects of several shock waves that have merged together

Cosmic Rays X. The cosmic ray knee and beyond: Diffusive acceleration at oblique shocks

Our purpose is to evaluate the rate of the maximum energy and the acceleration rate that cosmic rays acquire in the non-relativistic diffusive shock acceleration as it could apply during their lifetime in various astrophysical sites, where highly oblique shocks exist. We examine numerically (using Monte Carlo simulations) the effect of the diffusion coefficients on the energy gain and the acceleration rate, by testing the role between the obliquity of the magnetic field to the shock normal, and the significance of both perpendicular cross-field diffusion and parallel diffusion coefficients to the acceleration rate. We find (and justify previous analytical work - Jokipii 1987) that in highly oblique shocks the smaller the perpendicular diffusion gets compared to the parallel diffusion coefficient values, the greater the energy gain of the cosmic rays to be obtained. An explanation of the cosmic ray spectrum in high energies, between $10^{15}$eV and about $10^{18}$eV is claimed, as we estimate the upper limit of energy that cosmic rays could gain in plausible astrophysical regimes; interpreted by the scenario of cosmic rays which are injected by three different kind of sources, (a) supernovae which explode into the interstellar medium, (b) Red Supergiants, and (c) Wolf-Rayet stars, where the two latter explode into their pre-supernovae winds.Comment: Accepted in Astronomy and Astrophysics, 9 pages, 8 figures (for the 'Cosmic Rays' series papers

Charged-Particle Motion in Electromagnetic Fields Having at Least One Ignorable Spatial Coordinate

We give a rigorous derivation of a theorem showing that charged particles in an arbitrary electromagnetic field with at least one ignorable spatial coordinate remain forever tied to a given magnetic-field line. Such a situation contrasts the significant motions normal to the magnetic field that are expected in most real three-dimensional systems. It is pointed out that, while the significance of the theorem has not been widely appreciated, it has important consequences for a number of problems and is of particular relevance for the acceleration of cosmic rays by shocks.Comment: 7 pages, emulateapj format, including 1 eps figure, to appear in The Astrophysical Journal, Dec. 10 1998 issu

Emergence and prevalence of/Mactamase producing Haemophilus influenzae in Finland and susceptibility of 102 respiratory isolates to eight antibiotics

A survey of 102 consecutive clinical isolates of Haemophilus influenzae mainly from otolaryngological patients revealed 13 ampicillin resistant ones, while 2 years earlier none were found. All the 13 strains which were resistant according to the broth dilution minimal inhibitory concentration (MIC) could be shown to produce /Mactamase using the chromogenic cephalosporin 87/312. Routine disc diffusion susceptibility testing had under-estimated the resistance and five of the /Mactamase producing strains had been reported as ampicillin susceptible. Amoxycillin and azidocillin were equally active and slightly less active than ampicillin against /Mactamase negative strains. The 13 ampicillin resistant strains were also resistant to amoxycillin and azidocillin, and also the MICs of cephalothin and cephalexin were significantly increased by /Mactamase production, while cefuroxime, erythromycin and chloramphenicol were not affected. A marked inoculum effect was demonstrated with the /Mactam antibiotics, and only a narrow (about tenfold) range of inoculum concentrations distinguished reliably between susceptible and resistant strains. The MICs of the penicillins against /Mactamase positive H. influenzae increased markedly with incubation time

Particle acceleration in ultra-relativistic oblique shock waves

We perform Monte Carlo simulations of diffusive shock acceleration at highly relativistic oblique shock waves. High upstream flow Lorentz gamma factors are used, which are relevant to models of ultra relativistic particle shock acceleration in Active Galactic Nuclei (AGN) central engines and relativistic jets and Gamma Ray Burst (GRB) fireballs. We investigate numerically the acceleration properties -in the ultra relativistic flow regime of $\Gamma \sim 10-10^{3}$- such as angular distribution, acceleration time constant, particle energy gain versus number of crossings and spectral shapes. We perform calculations for sub-luminal and super-luminal shocks, using two different approaches respectively. The $\Gamma^{2}$ energization for the first crossing cycle and the significantly large energy gain for subsequent crossings as well as the high 'speed up' factors found, are important in supporting the Vietri and Waxman models on GRB ultra-high energy cosmic ray, neutrino, and gamma-ray output.Comment: 24 pages, 35 figures, accepted for publication in Astroparticle Physic

Toward a descriptive model of galactic cosmic rays in the heliosphere

Researchers review the elements that enter into phenomenological models of the composition, energy spectra, and the spatial and temporal variations of galactic cosmic rays, including the so-called anomalous cosmic ray component. Starting from an existing model, designed to describe the behavior of cosmic rays in the near-Earth environment, researchers suggest possible updates and improvements to this model, and then propose a quantitative approach for extending such a model into other regions of the heliosphere

Turbulence and particle acceleration in collisionless supernovae remnant shocks: II- Cosmic-ray transport

Supernovae remnant shock waves could be at the origin of cosmic rays up to energies in excess of the knee ($E\simeq3\cdot 10^{15}$eV) if the magnetic field is efficiently amplified by the streaming of accelerated particles in the shock precursor. This paper follows up on a previous paper \citep{pell05} which derived the properties of the MHD turbulence so generated, in particular its anisotropic character, its amplitude and its spectrum. In the present paper, we calculate the diffusion coefficients, also accounting for compression through the shock, and show that the predicted three-dimensional turbulence spectrum $k_\perp S_{3\rm d}(k_\parallel,k_\perp)\propto k_\parallel^{-1}k_\perp^{-\alpha}$ (with $k_\parallel$ and $k_\perp$ the wavenumber components along and perpendicular to the shock normal) generally leads to Bohm diffusion in the parallel direction. However, if the anisotropy is constrained by a relation of the form $k_\parallel \propto k_\perp^{2/3}$, which arises when the turbulent energy cascade occurs at a constant rate independent of scale, then the diffusion coefficient loses its Bohm scaling and scales as in isotropic Kolmogorov turbulence. We show that these diffusion coefficients allow to account for X-ray observations of supernova remnants. This paper also calculates the modification of the Fermi cycle due to the energy lost by cosmic rays in generating upstream turbulence and the concomittant steepening of the energy spectrum. Finally we confirm that cosmic rays can produced an amplified turbulence in young SNr during their free expansion phase such that the maximal energy is close to the knee and the spectral index is close to 2.3 in the warm phase of the interstellar mediumComment: 13 pages, 4 figures, accepted for publication in Astronomy & Astrophysics main journa

On the escape of cosmic rays from radio galaxy cocoons

(Abridged) A model for the escape of CR particles from radio galaxy cocoons is presented here. It is assumed that the radio cocoon is poorly magnetically connected to the environment. An extreme case of this kind is an insulating boundary layer of magnetic fields, which can efficiently suppress particle escape. More likely, magnetic field lines are less organised and allow the transport of CR particles from the source interior to the surface region. For such a scenario two transport regimes are analysed: diffusion of particles along inter-phase magnetic flux tubes (leaving the cocoon) and cross field transport of particles in flux tubes touching the cocoon surface. The cross field diffusion is likely the dominate escape path, unless a significant fraction of the surface is magnetically connected to the environment. Major cluster merger should strongly enhance the particle escape by two complementary mechanisms. i) The merger shock waves shred radio cocoons into filamentary structures, allowing the CRs to easily reach the radio cocoon boundary due to the changed morphology. ii) Also efficient particle losses can be expected for radio cocoons not compressed in shock waves. There, for a short period after the sudden injection of large scale turbulence, the (anomalous) cross field diffusion can be enhanced by several orders of magnitude. This lasts until the turbulent energy cascade has reached the microscopic scales, which determine the value of the microscopic diffusion coefficients.Comment: A&A in press, 12 pages, 5 figures, minor language improvement