Stochastic Particle Acceleration in Parallel Relativistic Shocks

We present results of test-particle simulations on both the first- and the second-order Fermi acceleration for relativistic parallel shock waves. Our studies suggest that the role of the second-order mechanism in the turbulent downstream of a relativistic shock may have been underestimated in the past, and that the stochastic mechanism may have significant effects on the form of the particle spectra and its time evolution.Comment: Poster at "The XXII Texas Symposium on Relativistic Astrophysics", Stanford, USA, December 2004, (TSRA04), 6 pages, LaTeX, 5 ps/eps figure

Stochastic Acceleration in Relativistic Parallel Shocks

(abridged) We present results of test-particle simulations on both the first and the second order Fermi acceleration at relativistic parallel shock waves. We consider two scenarios for particle injection: (i) particles injected at the shock front, then accelerated at the shock by the first order mechanism and subsequently by the stochastic process in the downstream region; and (ii) particles injected uniformly throughout the downstream region to the stochastic process. We show that regardless of the injection scenario, depending on the magnetic field strength, plasma composition, and the employed turbulence model, the stochastic mechanism can have considerable effects on the particle spectrum on temporal and spatial scales too short to be resolved in extragalactic jets. Stochastic acceleration is shown to be able to produce spectra that are significantly flatter than the limiting case of particle energy spectral index -1 of the first order mechanism. Our study also reveals a possibility of re-acceleration of the stochastically accelerated spectrum at the shock, as particles at high energies become more and more mobile as their mean free path increases with energy. Our findings suggest that the role of the second order mechanism in the turbulent downstream of a relativistic shock with respect to the first order mechanism at the shock front has been underestimated in the past, and that the second order mechanism may have significant effects on the form of the particle spectra and its evolution.Comment: 14 pages, 11 figures (9 black/white and 2 color postscripts). To be published in the ApJ (accepted 6 Nov 2004

Focus in production : Tonal shape, intensity and word order

Peer reviewe

Dynamical effects of self-generated magnetic fields in cosmic ray modified shocks

Recent observations of greatly amplified magnetic fields ($\delta B/B\sim 100$) around supernova shocks are consistent with the predictions of the non-linear theory of particle acceleration (NLT), if the field is generated upstream of the shock by cosmic ray induced streaming instability. The high acceleration efficiencies and large shock modifications predicted by NLT need however to be mitigated to confront observations, and this is usually assumed to be accomplished by some form of turbulent heating. We show here that magnetic fields with the strength inferred from observations have an important dynamical role on the shock, and imply a shock modification substantially reduced with respect to the naive unmagnetized case. The effect appears as soon as the pressure in the turbulent magnetic field becomes comparable with the pressure of the thermal gas. The relative importance of this unavoidable effect and of the poorly known turbulent heating is assessed. More specifically we conclude that even in the cases in which turbulent heating may be of some importance, the dynamical reaction of the field cannot be neglected, as instead is usually done in most current calculations.Comment: 4 pages, 1 figure, accepted for publication in ApJ Letter

Solar interacting protons versus interplanetary protons in the core plus halo model of diffusive shock acceleration and stochastic re-acceleration

With the first observations of solar γ-rays from the decay of pions, the relationship of protons producing ground level enhancements (GLEs) on the Earth to those of similar energies producing the γ-rays on the Sun has been debated. These two populations may be either independent and simply coincident in large flares, or they may be, in fact, the same population stemming from a single accelerating agent and jointly distributed at the Sun and also in space. Assuming the latter, we model a scenario in which particles are accelerated near the Sun in a shock wave with a fraction transported back to the solar surface to radiate, while the remainder is detected at Earth in the form of a GLE. Interplanetary ions versus ions interacting at the Sun are studied for a spherical shock wave propagating in a radial magnetic field through a highly turbulent radial ray (the acceleration core) and surrounding weakly turbulent sector in which the accelerated particles can propagate toward or away from the Sun. The model presented here accounts for both the first-order Fermi acceleration at the shock front and the second-order, stochastic re-acceleration by the turbulence enhanced behind the shock. We find that the re-acceleration is important in generating the γ-radiation and we also find that up to 10% of the particle population can find its way to the Sun as compared to particles escaping to the interplanetary space

The contribution of supernova remnants to the galactic cosmic ray spectrum

The supernova paradigm for the origin of galactic cosmic rays has been deeply affected by the development of the non-linear theory of particle acceleration at shock waves. Here we discuss the implications of applying such theory to the calculation of the spectrum of cosmic rays at Earth as accelerated in supernova remnants and propagating in the Galaxy. The spectrum is calculated taking into account the dynamical reaction of the accelerated particles on the shock, the generation of magnetic turbulence which enhances the scattering near the shock, and the dynamical reaction of the amplified field on the plasma. Most important, the spectrum of cosmic rays at Earth is calculated taking into account the flux of particles escaping from upstream during the Sedov-Taylor phase and the adiabatically decompressed particles confined in the expanding shell and escaping at later times. We show how the spectrum obtained in this way is well described by a power law in momentum with spectral index close to -4, despite the concave shape of the instantaneous spectra of accelerated particles. On the other hand we also show how the shape of the spectrum is sensible to details of the acceleration process and environment which are and will probably remain very poorly known.Comment: 19 pages, 8 figures, published version (references updated

Particle acceleration in thick parallel shocks with high compression ratio

We report studies on first-order Fermi acceleration in parallel modified shock waves with a large scattering center compression ratio expected from turbulence transmission models. Using a Monte Carlo technique we have modeled particle acceleration in shocks with a velocity ranging from nonrelativistic to ultrarelativistic and a thickness extending from nearly steplike to very wide structures exceeding the particle diffusion length by orders of magnitude. The nonrelativistic diffusion approximation is found to be surprisingly accurate in predicting the spectral index of a thick shock with large compression ratio even in the cases involving relativistic shock speeds.Comment: 4 pages, 2 figures, accepted to A&

Introducing willingness-to-pay for noise changes into transport appraisal: an application of benefit transfer.

Numerous research studies have elicited willingness-to-pay values for transport-related noise, however, in many industrialised countries including the UK, noise costs and benefits are still not incorporated into appraisals for most transport projects and policy changes (Odgaard et al, 2005; Grant-Muller et al, 2001). This paper describes the actions recently taken in the UK to address this issue, comprising: primary research based on the city of Birmingham; an international review of willingness-to-pay evidence; development of values using benefit transfers over time and locations; and integration with appraisal methods. Amongst the main findings are: that the willingness-to-pay estimates derived for the UK are broadly comparable with those used in appraisal elsewhere in Europe; that there is a case for a lower threshold at 1 45dB(A)Leq,18hr1 rather than the more conventional 55dB(A); and that values per dB(A) increase with the noise level above this threshold. There are significant issues over the valuation of rail versus road noise, the neglect of non-residential noise and the valuation of high noise levels in different countries. Conclusions are drawn regarding the feasibility of noise valuation based on benefit transfers in the UK and elsewhere, and future research needs in this field are discussed