The transport of cosmic rays in self-excited magnetic turbulence

Reville, Brian; O’Sullivan, Stephen; Duffy, P.; Kirk, J. G.

doi:10.1111/j.1365-2966.2008.13059.x

Cited by 95 publications

(106 citation statements)

References 20 publications

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“…Here we have developed a systematic derivation of charged particle diffusion in the presence of an isotropic turbulent magnetic field and tested its validity using Monte-Carlo simulation of particles in a synthetically generated turbulent magnetic field. In fact, we would like to point out that incorporating the several factors mentioned above will probably require MHD, hybrid or PIC simulations that provide a self-consistent picture of the development of the cosmic ray transport phenomenon (e.g., Reville et al 2008;Caprioli & Spitkovsky 2014).…”

Section: Discussionmentioning

confidence: 99%

Charged Particle Diffusion in Isotropic Random Magnetic Fields

Subedi

Sonsrettee²,

Blasi

et al. 2017

ApJ

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The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence of a mean magnetic field. Here we consider diffusion of charged particles in fully three-dimensional isotropic turbulent magnetic fields with no mean field, which may be pertinent to many astrophysical situations. We identify different ranges of particle energy depending upon the ratio of the Larmor radius of the charged particle to the characteristic outer length scale of the turbulence. Two different theoretical models are proposed to calculate the diffusion coefficient, each applicable to a distinct range of particle energies. The theoretical results are compared with those from computer simulations, showing good agreement.

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Section: Discussionmentioning

confidence: 99%

Charged Particle Diffusion in Isotropic Random Magnetic Fields

Subedi

Sonsrettee²,

Blasi

et al. 2017

ApJ

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“…Nevertheless, they differ in a strong turbulence regime. Reville et al (2008) discussed some solutions by clearly displaying diffusion coefficient with sub-Bohm values. This issue is beyond the scope of the calculations performed here and its consideration is postponed to a future work (see also a recent work by Shalchi 2009).…”

Section: Upstream Diffusion Regimesmentioning

confidence: 99%

“…The non-resonant waves are produced, at least in the linear growth phase of the instability, on scales much smaller than r L . However, the ability of the instability to both enter deeply into the non-linear regime and saturate at a magnetic field level δB B ∞ remains debated (Reville et al 2008;Niemiec et al 2008;Riquelme & Spitkovsky 2009). In the next paragraph, we summarise the main properties of the wave modes generated by the non-resonant streaming instability (Sect.…”

Section: Equation Parametersmentioning

confidence: 99%

“…The authors identified the maximum CR energy, between the two confinement limits, expected for a standard ISM medium or a completely amplified magnetic field. One should keep in mind that several effects can alterate these conclusions such as the propagation into a partially ionised medium (Bykov & Toptyghin 2005;Reville et al 2007), thermal effects in the dispersion relation of the non-resonant instability (Reville et al 2008), or a back reaction on the CR current (Riquelme & Spitkovsky 2009). …”

Section: Introductionmentioning

confidence: 99%

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Postshock turbulence and diffusive shock acceleration in young supernova remnants

Marcowith¹,

Casse²

2010

A&A

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Context. Thin X-ray filaments are observed in the vicinity of young supernova remnants (SNR) blast waves. Identifying the process that creates these filaments would provide direct insight into the particle acceleration occurring within SNR and in particular the cosmic ray yield. Aims. We investigate magnetic amplification in the upstream medium of a SNR blast wave through both resonant and non-resonant regimes of the streaming instability. We attempt to understand more clearly of the diffusive shock acceleration (DSA) efficiency by considering various relaxation processes of the magnetic fluctuations in the downstream medium. Multiwavelength radiative signatures originating in the SNR shock wave are used to test various downstream turbulence relaxation models. Methods. Analytical and numerical calculations that couple stochastic differential equation schemes with 1D spherical magnetohydrodynamics simulations are used to investigate, in the context of test particles, turbulence evolution in both the forshock and post-shock regions. Stochastic second-order Fermi acceleration induced by resonant modes, magnetic field relaxation and amplification, and turbulence compression at the shock front are considered to model the multiwavelength filaments produced in SNRs. The γ-ray emission is also considered in terms of inverse Compton mechanism. Results. We confirm the result of Parizot and collaborators that the maximum CR energies should not go well beyond PeV energies in young SNRs where X-ray filaments are observed. To reproduce observational data, we derive an upper limit to the magnetic field amplitude and so ensure that stochastic particle reacceleration remains inefficient. Considering various magnetic relaxation processes, we then infer two necessary conditions to achieve efficient acceleration and X-ray filaments in SNRs: (1) the turbulence must fulfil the inequality 2 − β − δ d ≥ 0; where β is the turbulence spectral index and δ d is the relaxation length energy power-law index; (2) the typical relaxation length must be of the order the X-ray rim size. We find that Alvénic/fast magnetosonic mode damping fulfils all conditions; while non-linear Kolmogorov damping does not. By confronting previous relaxation processes with observational data, we deducte that among our SNR sample, data for the older ones (SN1006 and G347.3-0.5) does not comply with all conditions, which means that their X-ray filaments are probably controlled by radiative losses. The younger SNRs, Cassiopeia A, Tycho, and Kepler pass all tests and we infer that the downstream magnetic field amplitude is in the range of 200−300 μGauss.

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“…It is important to determine the propagation parameters, because their value can be compared to theoretical predictions for the transport in turbulent magnetic fields (e.g., Casse et al 2002;Ptuskin et al 2006;Minnie et al 2007;Tautz et al 2008;Yan & Lazarian 2008, and references therein), or related to the source spectra predicted in acceleration models (e.g., Marcowith et al 2006;Uchiyama et al 2007;Plaga 2008;Reville et al 2008;Reynolds 2008, and references therein). The transport and source parameters are also related to Galactic astrophysics (e.g., nuclear abundances and stellar nucleosynthesis - Silberberg & Tsao 1990;Webber 1997), and to dark matter indirect detection (e.g., Donato et al 2004;Delahaye et al 2008).…”

Section: Introductionmentioning

confidence: 99%

A Markov Chain Monte Carlo technique to sample transport and source parameters of Galactic cosmic rays

Putze

Derome

Maurin

2010

A&A

150

191

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Context. Ongoing measurements of the cosmic radiation (nuclear, electronic, and γ-ray) are providing additional insight into cosmicray physics. A comprehensive picture of these data relies on an accurate determination of the transport and source parameters of propagation models. Aims. A Markov Chain Monte Carlo method is used to obtain these parameters in a diffusion model. By measuring the B/C ratio and radioactive cosmic-ray clocks, we calculate their probability density functions, placing special emphasis on the halo size L of the Galaxy and the local underdense bubble of size r h . We also derive the mean, best-fit model parameters and 68% confidence level for the various parameters, and the envelopes of other quantities. Methods. The analysis relies on the USINE code for propagation and on a Markov Chain Monte Carlo technique previously developed by ourselves for the parameter determination. Results. The B/C analysis leads to a most probable diffusion slope δ = 0.86 +0.04 −0.04 for diffusion, convection, and reacceleration, or δ = 0.234 +0.006 −0.005 for diffusion and reacceleration. As found in previous studies, the B/C best-fit model favours the first configuration, hence pointing to a high value for δ. These results do not depend on L, and we provide simple functions to rescale the value of the transport parameters to any L. A combined fit on B/C and the isotopic ratios ( 10 Be/ 9 Be, 26 Al/ 27 Al, 36 Cl/Cl) leads to L = 8 +8 −7 kpc and r h = 120 +20 −20 pc for the best-fit model. This value for r h is consistent with direct measurements of the local interstallar medium. For the model with diffusion and reacceleration, L = 4 +1 −1 kpc and r h = 3 +70 −3 pc (consistent with zero). We vary δ, because its value is still disputed. For the model with Galactic winds, we find that between δ = 0.2 and 0.9, L varies from O(0) to O(2) if r h is forced to be 0, but it otherwise varies from O(0) to O(1) (with r h ∼ 100 pc for all δ > ∼ 0.3). The results from the elemental ratios Be/B, Al/Mg, and Cl/Ar do not allow independent checks of this picture because these data are not precise enough. Conclusions. We showed the potential and usefulness of the Markov Chain Monte Carlo technique in the analysis of cosmic-ray measurements in diffusion models. The size of the diffusive halo depends crucially on the value of the diffusion slope δ, and also on the presence/absence of the local underdensity damping effect on radioactive nuclei. More precise data from ongoing experiments are expected to clarify this issue.

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The transport of cosmic rays in self-excited magnetic turbulence

Cited by 95 publications

References 20 publications

Charged Particle Diffusion in Isotropic Random Magnetic Fields

Charged Particle Diffusion in Isotropic Random Magnetic Fields

Postshock turbulence and diffusive shock acceleration in young supernova remnants

A Markov Chain Monte Carlo technique to sample transport and source parameters of Galactic cosmic rays

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