Possible acceleration of cosmic rays in a rotating system: Uehling-Uhlenbeck model
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UCLEI, PARTICLES, FIELDS, GRAVITATION, AND ASTROPHYSICS
Possible Acceleration of Cosmic Rays in a Rotating System: Uehling-Uhlenbeck Model1 Chu Rainer Kwang-Hua* Transfer Centre, 2/F, No. 24, Lane 260, Section 1, Muzha Road, Taipei, Taiwan 116, China Distribution Centre, Golmud Mansion, 33, Road Yingbin, Golmud 816000, China *e-mail: [email protected] Received June 6, 2016
Abstract—We illustrate the possible acceleration of cosmic rays passing through a kind of amplification channel (via diffusion modes of propagating plane-wave fronts) induced by a rotating system. Our analysis is mainly based on the quantum discrete kinetic model (considering a discrete Uehling-Uhlenbeck collision term), which has been used to study the propagation of plane (e.g., acoustic) waves in a system of rotating gases. DOI: 10.1134/S1063776116130136
1. INTRODUCTION Radiation that enhances with altitude in the atmosphere were discovered by V. F. Hess in 1912, and it was clear by the early 1930s that this radiation comes from outer space. The all-particle energy spectrum of primary cosmic rays extends from 1 GeV (1012 eV) to above 1020 eV (100 EeV), the highest energies of known individual particles in the Universe [1–3]. The highest-energy particles are so rare that they are detectable only by means of the giant cascades or extensive air showers they create in the atmosphere. Details of how these extensive air showers are observed and the parameters of importance are measured can be found in [1]. In spite of many efforts, we still have only a limited understanding of where these particles are coming from, how they are accelerated to such extremely high energies, and how they propagate through interstellar space [2]. The astrophysical environments that are able to accelerate particles to such high energies, including active galactic nuclei, large-scale galactic wind termination shocks, relativistic jets and hot-spots of Fanaroff-Riley radio galaxies, pulsars, magnetars, quasar remnants, starbursts, colliding galaxies, and gammaray burst fireballs were discussed in [3]. Many researchers believe that cosmic rays are accelerated in a process called diffusive shock acceleration. Suitable astrophysical shocks occur in supernova explosions, and ionized nuclei gain energy as they are repeatedly overtaken by the expanding shock wave. Such mechanisms lead in fact to a power-law spectrum with a maximum energy of about Z × 1015 eV (Z is the atomic 1 The article is published in the original.
number), which roughly agrees with the observed steepening (although the theoretically predicted spectrum proves to be steeper than actually observed) [2]. In this short paper, the highly nonlinear discrete Uehling-Uhlenbeck equations [4] together with the model of free orientations (θ is the relative direction of particle scattering with respect to the normal of the propagating plane-wave front) are solved to study the diverse dispersion relations of plane waves in a system of rotating gases (or disk-like gases). Anomalous amplification channels can occur for di
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