Stochastic relativistic shock-surfing acceleration

We study relativistic particles undergoing surfing acceleration at perpendicular shocks. We assume that particles undergo diffusion in the component of momentum perpendicular to the shock plane due to moderate fluctuations in the shock electric and magnetic fields. We show that dN/dE, the number of surfing-accelerated particles per unit energy, attains a power-law form, dN/dE \propto E^{-b}. We calculate b analytically in the limit of weak momentum diffusion, and use Monte Carlo test-particle calculations to evaluate b in the weak, moderate, and strong momentum-diffusion limits.Comment: 20 pages, 6 figures, accepted by ApJ; this version corrects a few minor typographical error

The chaotic dynamics of comets and the problems of the Oort cloud

The dynamic properties of comets entering the planetary zone from the Oort cloud are discussed. Even a very slight influence of the large planets can trigger stochastic cometary dynamics. Multiple interactions of comets with the large planets produce diffusion of the parameters of cometary orbits and a mean increase in the semi-major axis of comets. Comets are lifted towards the Oort cloud, where collisions with stars begin to play a substantial role. The transport of comets differs greatly from the customary law of diffusion and noticeably alter cometary distribution

Plus Charge Prevalence in Cosmic Rays: Room for Dark Matter in the Positron Spectrum

The unexpected energy spectrum of the positron/electron ratio is interpreted astrophysically, with a possible exception of the 100-300 GeV range. The data indicate that this ratio, after a decline between $0.5-8$ GeV, rises steadily with a trend towards saturation at 200-400GeV. These observations (except for the trend) appear to be in conflict with the diffusive shock acceleration (DSA) mechanism, operating in a \emph{single} supernova remnant (SNR) shock. We argue that $e^{+}/e^{-}$ ratio can still be explained by the DSA if positrons are accelerated in a \emph{subset} of SNR shocks which: (i) propagate in clumpy gas media, and (ii) are modified by accelerated CR \emph{protons}. The protons penetrate into the dense gas clumps upstream to produce positrons and, \emph{charge the clumps positively}. The induced electric field expels positrons into the upstream plasma where they are shock-accelerated. Since the shock is modified, these positrons develop a harder spectrum than that of the CR electrons accelerated in other SNRs. Mixing these populations explains the increase in the $e^{+}/e^{-}$ ratio at $E>8$ GeV. It decreases at $E<8$ GeV because of a subshock weakening which also results from the shock modification. Contrary to the expelled positrons, most of the antiprotons, electrons, and heavier nuclei, are left unaccelerated inside the clumps. Scenarios for the 100-300 GeV AMS-02 fraction exceeding the model prediction, including, but not limited to, possible dark matter contribution, are also discussed.Comment: 36 pages, 6 figure

Magnetic and density spikes in cosmic ray shock precursors

In shock precursors populated by accelerated cosmic rays (CR), the CR return current instability is believed to significantly enhance the pre-shock perturbations of magnetic field. We have obtained fully-nonlinear exact ideal MHD solutions supported by the CR return current. The solutions occur as localized spikes of circularly polarized Alfven envelopes (solitons, or breathers). As the conventional (undriven) solitons, the obtained magnetic spikes propagate at a speed $C$ proportional to their amplitude, $C=C_{A}B_{{\rm max}}/\sqrt{2}B_{0}$. The sufficiently strong solitons run thus ahead of the main shock and stand in the precursor, being supported by the return current. This property of the nonlinear solutions is strikingly different from the linear theory that predicts non-propagating (that is, convected downstream) circularly polarized waves. The nonlinear solutions may come either in isolated pulses (solitons) or in soliton-trains (cnoidal waves). The morphological similarity of such quasi-periodic soliton chains with recently observed X-ray stripes in Tycho supernova remnant (SNR) is briefly discussed. The magnetic field amplification determined by the suggested saturation process is obtained as a function of decreasing SNR blast wave velocity during its evolution from the ejecta-dominated to the Sedov-Taylor stage.Comment: 21 pages, 4 figure

VC-saturated set systems

The well-known Sauer lemma states that a family $\mathcal{F}\subseteq 2^{[n]}$ of VC-dimension at most $d$ has size at most $\sum_{i=0}^d\binom{n}{i}$. We obtain both random and explicit constructions to prove that the corresponding saturation number, i.e., the size of the smallest maximal family with VC-dimension $d\ge 2$, is at most $4^{d+1}$, and thus is independent of $n$

Pick-up ion dynamics at the structured quasi-perpendicular shock

We study the pickup ion dynamics and mechanism of multiple reflection and acceleration at the structured quasi-perpendicular supercritical shock. The motion of the pickup ions in the shock is studied analytically and numerically using the test particle analysis in the model shock front. The analysis shows that slow pickup ions may be accelerated at the shock ramp to high energies. The maximum ion energy is determined by the fine structure of the electro-magnetic field at the shock ramp and decreases when the angle between magnetic field and shock normal decreases. Evolution of pickup ion distribution across the nearly-perpendicular shock and pickup ion spectrum is also studied by direct numerical analysis.Comment: LaTeX (elsart.cls), packages: times,amsmath,amssymb; 15 pages + 13 figures (GIF). To appear in Planetary and Space Science

Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction

Under the conditions of weak Langmuir turbulence, a self-consistent wave-particle Hamiltonian models the effective nonlinear interaction of a spectrum of M waves with N resonant out-of-equilibrium tail electrons. In order to address its intrinsically nonlinear time-asymptotic behavior, a Monte Carlo code was built to estimate its equilibrium statistical mechanics in both the canonical and microcanonical ensembles. First the single wave model is considered in the cold beam/plasma instability and in the O'Neil setting for nonlinear Landau damping. O'Neil's threshold, that separates nonzero time-asymptotic wave amplitude states from zero ones, is associated to a second order phase transition. These two studies provide both a testbed for the Monte Carlo canonical and microcanonical codes, with the comparison with exact canonical results, and an opportunity to propose quantitative results to longstanding issues in basic nonlinear plasma physics. Then the properly speaking weak turbulence framework is considered through the case of a large spectrum of waves. Focusing on the small coupling limit, as a benchmark for the statistical mechanics of weak Langmuir turbulence, it is shown that Monte Carlo microcanonical results fully agree with an exact microcanonical derivation. The wave spectrum is predicted to collapse towards small wavelengths together with the escape of initially resonant particles towards low bulk plasma thermal speeds. This study reveals the fundamental discrepancy between the long-time dynamics of single waves, that can support finite amplitude steady states, and of wave spectra, that cannot.Comment: 15 pages, 7 figures, to appear in Physics of Plasma

Magnetosonic solitons in a dusty plasma slab

The existence of magnetosonic solitons in dusty plasmas is investigated. The nonlinear magnetohydrodynamic equations for a warm dusty magnetoplasma are thus derived. A solution of the nonlinear equations is presented. It is shown that, due to the presence of dust, static structures are allowed. This is in sharp contrast to the formation of the so called shocklets in usual magnetoplasmas. A comparatively small number of dust particles can thus drastically alter the behavior of the nonlinear structures in magnetized plasmas.Comment: 7 pages, 6 figure