Diffusive shock acceleration: non-classical model of cosmic ray transport
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909828198170624 |
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| author | Lagutin, A. A. |
| author_facet | Lagutin, A. A. |
| contents | In this work the theory of diffusive shock acceleration is extended to the case of non-classical particle transport with Lévy flights and Lévy traps, when the mean square displacement grows nonlinearly with time. In this approach the Green function is not a Gaussian but it exhibits power-law tails. By using the propagator appropriate for non-classical diffusion, it is found for the first time that energy spectral index of particles accelerated at shock front is $γ= [α(\mathrm{r} + 5) - 6 β]/[α(\mathrm{r}-1)]$, where $0 < α< 2$ and $0 <β< 1$ are the exponents of power-law behavior of Lévy flights and Lévy traps, respectively.
We note that this result coincides with standard slope at $α=2, β=1$ (normal diffusion), and also includes those obtained earlier for the subdiffusion ($α=2, β<1$) and superdiffusion ($α<2, β=1$) regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diffusive shock acceleration: non-classical model of cosmic ray transport Lagutin, A. A. High Energy Astrophysical Phenomena In this work the theory of diffusive shock acceleration is extended to the case of non-classical particle transport with Lévy flights and Lévy traps, when the mean square displacement grows nonlinearly with time. In this approach the Green function is not a Gaussian but it exhibits power-law tails. By using the propagator appropriate for non-classical diffusion, it is found for the first time that energy spectral index of particles accelerated at shock front is $γ= [α(\mathrm{r} + 5) - 6 β]/[α(\mathrm{r}-1)]$, where $0 < α< 2$ and $0 <β< 1$ are the exponents of power-law behavior of Lévy flights and Lévy traps, respectively. We note that this result coincides with standard slope at $α=2, β=1$ (normal diffusion), and also includes those obtained earlier for the subdiffusion ($α=2, β<1$) and superdiffusion ($α<2, β=1$) regimes. |
| title | Diffusive shock acceleration: non-classical model of cosmic ray transport |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2509.03091 |