2008 # The effect of energy amplification variance on shock acceleration

**Abstract:** Shock‐acceleration theory predicts a power‐law energy spectrum in the test particle approximation, and there are two ways to calculate the power‐law index, namely Peacock's approximation and Vietri's formulation. In Peacock's approximation, it is assumed that particles cross a shock front many times and that the energy gain factors for each step are fully uncorrelated. By contrast, correlation of the distribution of the energy‐gain factors is considered in Vietri's formulation. We examine how Peacock's approxi…

Help me understand this report

View preprint versions

Search citation statements

Paper Sections

Select...

1

1

1

1

Citation Types

0

9

0

Year Published

2008

2022

Publication Types

Select...

7

Relationship

5

2

Authors

Journals

(9 citation statements)

0

9

0

“…Largeangle scattering in strong turbulent fields would allow the index harder as p 1 ∼ 1 (e.g. Stecker 2007;Aoi et al 2008;Summerlin & Baring 2012), although our results indicate η g ∼ 10 4.5 implying weak turbulence.…”

confidence: 60%

“…Largeangle scattering in strong turbulent fields would allow the index harder as p 1 ∼ 1 (e.g. Stecker 2007;Aoi et al 2008;Summerlin & Baring 2012), although our results indicate η g ∼ 10 4.5 implying weak turbulence.…”

confidence: 60%

“…References [77,81] find a main minimum and a second minimum in their fitting. The main minimum requires a hard injection spectral index s = 0.9 (or 1.61 with the EGMF), which is different from typical expectations from the diffusive shock acceleration mechanism (although such a hard spectrum could be reached by the shock acceleration at ultrarelativistic shocks [91,92] or other mechanisms such as the shear acceleration [93]). The second minimum suggests s = 2.0 (or 2.3 with the EGMF) and is similar to the mixed composition scenario shown here, but with a σ(X max ) lighter than the Auger measurements between 10 18.8 eV and 10 19.4 eV.…”

confidence: 88%

“…However, the spectral index can be affected by the deflection angle, the ratio of the scattering mean free path to the particle gyroradius and the orientation of the magnetic field to the shock normal. In the large-angle scattering case, where magnetic fluctuations are sufficiently large, particles can gain significant energy in the single scattering and may lead to a harder spectrum [75][76][77]. Such a possibility has been discussed to explain a hard spectrum of blazars [77,78].…”

confidence: 99%