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Weak quasi-perpendicular high-β shocks accelerate protons inefficiently, while stronger or less-oblique shocks do better.

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2026-07-13 06:21 UTC pith:YYDWUGK7

load-bearing objection Solid 3D hybrid map of proton efficiency at high-β oblique shocks: weak quasi-perp cases stay inefficient, stronger ones reach a few percent with steep spectra, and obliquity matters a lot. the 3 major comments →

arxiv 2607.08835 v1 pith:YYDWUGK7 submitted 2026-07-09 astro-ph.HE

Hybrid Simulations of Proton Acceleration at Oblique High-β Shocks

Yevhen Kylivnyk , Damiano Caprioli , Luca Orusa This is my paper
classification astro-ph.HE
keywords hybrid simulationscollisionless shocksproton accelerationhigh-β plasmagalaxy clustersradio relicscosmic-ray efficiencymagnetic obliquity
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper uses three-dimensional hybrid plasma simulations to test whether the weak, high-β shocks that form in galaxy clusters can accelerate protons into cosmic rays. The simulations show that quasi-perpendicular shocks with sonic Mach numbers below about 5 produce essentially no nonthermal proton population, while stronger shocks develop clear power-law tails and reach a few percent efficiency. Magnetic obliquity is decisive: tilting the field toward 45 degrees markedly raises the efficiency even at low Mach number. The result supplies a microphysical reason why radio relics (electron synchrotron) are common while cluster gamma-ray emission from hadronic interactions has not been detected, and it offers a simple efficiency formula that large-scale cluster models can use.

Core claim

For high-β, quasi-perpendicular (ϑ = 80°) shocks, proton acceleration efficiency stays below 0.1 % when Ms ≲ 5 and only reaches ~3 % once Ms ≳ 10, accompanied by steep energy spectra (q ~ 4). Reducing the obliquity to ~45° restores substantially higher efficiencies even at Ms = 3. Thus magnetic geometry, not merely Mach number or plasma β, controls whether cluster shocks inject protons.

What carries the argument

The hybrid (kinetic ions, fluid electrons) measurement of cosmic-ray acceleration efficiency ε_CR, defined as the downstream energy fraction above Einj ≃ 10 Esh, together with the empirical fit ε_CR(Ms, MA) that maps the simulated parameter space for ϑ = 80°.

Load-bearing premise

The simulations assume a laminar upstream plasma driven by a reflecting wall; real cluster shocks sit in turbulent, possibly resistive plasma at still lower Mach numbers and may therefore inject differently.

What would settle it

A three-dimensional hybrid or full-PIC run of an Ms ≲ 2, ϑ = 80° shock that develops a sustained nonthermal proton tail with ε_CR ≳ 1 % would overturn the claimed threshold.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Typical radio-relic shocks (weak and quasi-perpendicular) contribute negligibly to the cluster cosmic-ray proton budget.
  • The electron-to-proton ratio at such shocks can be far larger than the SNR value of ~10^{-3}, formally diverging if proton injection vanishes.
  • Steep (q ~ 4) proton spectra further suppress hadronic gamma-ray yields relative to standard DSA expectations.
  • Large-scale cluster simulations can insert the provided empirical fit for ϑ = 80° to regulate ion injection.
  • Quasi-parallel or moderately oblique shocks remain viable proton accelerators even at modest Mach numbers.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If pre-existing ICM turbulence or seed cosmic rays are added, the low-Ms quasi-perpendicular channel may reopen, offering a natural test for future hybrid runs.
  • Polarization maps of radio relics that show mixed or quasi-parallel patches should coincide with local gamma-ray or neutrino excesses if the obliquity dependence holds.
  • The same obliquity threshold may govern whether high-β shocks in other environments (e.g., AGN lobes or IGM filaments) produce detectable hadronic signatures.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper presents 3D hybrid (kinetic ions, fluid electrons) simulations of quasi-perpendicular (ϑ = 80°) high-β (β ≳ 15) shocks with sonic Mach numbers Ms ∼ 3–15, conditions representative of the ICM/IGM. Using the dHybridR code, the authors measure proton acceleration efficiency ε_CR (Eq. 1, Einj ≃ 10 Esh) and spectra over a suite of runs (Table 1). They report that weak shocks (Ms ≲ 5) remain essentially thermal (ε_CR ≲ 0.1%), while stronger shocks (Ms ≳ 10) develop power-law tails with energy slope q ∼ 4.0 and reach ε_CR ∼ 3%. An empirical fit for ε_CR(Ms, MA) at ϑ = 80° is provided (Eq. 2). A dedicated 2D/3D obliquity scan at fixed Ms = 3, β = 120 shows that efficiency rises sharply as ϑ decreases toward ∼ 45°. The authors interpret these results as a microphysical explanation for the lack of cluster γ-ray detections and for radio-relic polarization implying electron acceleration at oblique shocks.

Significance. If the reported efficiencies hold, the work supplies a concrete, simulation-calibrated microphysical basis for why high-β quasi-perpendicular ICM shocks should not produce an observable hadronic γ-ray signal, while still allowing electron acceleration at the same shocks. The empirical fit (Eq. 2) is immediately usable in large-scale cluster models. The systematic 3D hybrid coverage of the high-β, moderate-Ms, oblique regime, the explicit comparison of 2D vs 3D at varying obliquity, and the clear documentation of resolution and uncertainty choices are genuine strengths relative to earlier 1D/2D or short-duration studies. The paper also correctly flags its own extrapolation limits (Ms ≲ 2, laminar upstream).

major comments (3)
  1. §3.1 and Table 1: the transverse domain is fixed at Ly = Lz = 20 di for all runs. The paper itself notes that 3D dynamics and cross-field diffusion are essential for ion injection at oblique shocks (Introduction; Orusa et al. 2026). With only ∼ 10 di-scale structures visible in Fig. 1, it is unclear whether the box is large enough to capture the full spectrum of corrugation and porosity that sets ε_CR. A short convergence test (or a clear statement that one was performed) at the highest-Ms, highest-efficiency cases would strengthen the claim that ε_CR ∼ 3% is not box-size limited.
  2. §4 (Discussion): the central astrophysical claim is that typical radio-relic shocks (observationally Ms ∼ 1–1.5 in the shock frame) are inefficient proton accelerators. All simulated Ms are ≥ 2 (downstream frame), corresponding to still higher shock-frame values, and the paper correctly notes that Ms ≲ 2 requires different driving and possibly resistivity/electron physics. The extrapolation from Ms ∼ 3–5 (ε_CR ≲ 0.1%) to Ms ≲ 2 is therefore an assumption, not a measurement. The text should state more explicitly that the inefficiency conclusion for observed merger shocks rests on this monotonic extrapolation rather than on direct simulation of the relevant Mach-number range.
  3. Eq. (2) and Fig. 3: the empirical fit is presented as ready for large-scale models, yet it is calibrated only over 2 ≲ Ms ≲ 13.5, 15 ≲ MA ≲ 70 and is forced to zero below 0.1%. The functional form (involving Ms / √(MA - 2) - 26) has no stated physical motivation and the coefficient 1/21 is purely numerical. The manuscript should either (i) provide a brief justification or residual analysis for this particular form, or (ii) clearly label it as a convenient interpolant valid only inside the simulated rectangle, with no claim of validity outside that rectangle.
minor comments (5)
  1. Fig. 2b: the power-law fits are shown only for the most efficient cases; adding the fitted q values (and the energy range used) to the legend or caption would make the q ∼ 4.0 claim easier to verify.
  2. Table 1: tend varies from 8 to 32 Ωc-1. A short note on how the asymptotic ε_CR was judged to have been reached (especially for the short runs) would help the reader assess saturation.
  3. §2: the conversion between simulation-frame Ms and shock-frame Ms is given, but the table reports only the former. Adding a column (or a sentence) with the corresponding shock-frame values would reduce ambiguity when comparing to X-ray Mach numbers.
  4. Fig. 4 caption: the final times for 2D and 3D runs are listed; stating whether the 45° cases are still rising or have plateaued would clarify how much the quoted efficiencies could still grow.
  5. References: a few arXiv-only or in-preparation citations (Ly et al. 2026; Sharma & Caprioli in prep.; Diesing et al. 2025) are fine for context, but the main claims should not rest on them; the present manuscript is self-contained on that score.

Circularity Check

0 steps flagged

No significant circularity: efficiencies and spectra are direct measurements from new hybrid runs; the empirical formula is an explicit post-hoc fit, not a disguised prediction.

full rationale

The paper's central claims (ε_CR ≲ 0.1% for Ms ≲ 5 at ϑ = 80°, ε_CR ∼ 3% and q ∼ 4 for Ms ≳ 10, strong rise in efficiency as ϑ drops to ∼45°) are obtained by integrating particle spectra from the 3D hybrid runs listed in Table 1 (Eq. 1 with Einj ≃ 10 Esh). These are new numerical measurements under the stated setup (dHybridR, reflecting wall, Ly = Lz = 20 di, high-β parameters). Equation 2 is introduced explicitly as an empirical interpolation fitted to those measured points for use in large-scale models; it is not presented as a first-principles derivation or independent prediction. Self-citations (Orusa & Caprioli 2023; Orusa et al. 2026; Caprioli & Spitkovsky 2014a; Haggerty & Caprioli 2019) supply the code, the porosity-driven interpretation of why low-Ms shocks remain laminar, and prior low-β benchmarks, but the load-bearing numbers and spectral slopes do not algebraically reduce to those earlier results. No uniqueness theorem, ansatz smuggled as theorem, or self-definitional loop is present. The work is therefore self-contained against its own simulation suite; any limitations (laminar upstream, reflecting-wall Ms floor, Einj threshold) are setup caveats, not circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The central claims rest on standard hybrid-plasma assumptions, a conventional energy-threshold definition of nonthermal particles, and an empirical interpolation fitted to the simulation suite. No new physical entities are postulated. The main free parameters are the injection energy cut and the coefficients of the efficiency fit; the domain assumptions are those of the hybrid model and the laminar reflecting-wall setup.

free parameters (3)
  • Einj threshold = ≈ 10 Esh
    Particles above Einj ≈ 10 Esh are counted as nonthermal (Eq. 1); the factor 10 is a conventional choice taken from prior hybrid literature and directly controls the reported ε_CR.
  • Empirical efficiency fit coefficients (Eq. 2) = 1/21, -2, -26, floor 0.1%
    ε_CR ≈ (1/21)(Ms / √(MA - 2) - 26) is an ad-hoc interpolation calibrated only on the simulated (Ms, MA) rectangle; the numerical prefactors and the floor at 0.1% are free.
  • Transverse box size Ly = Lz = 20 di = 20 di
    Fixed by computational cost; may suppress longer-wavelength corrugation modes that could affect injection.
axioms (4)
  • domain assumption Hybrid approximation: ions kinetic, electrons massless charge-neutralizing fluid with adiabatic index γ = 5/3.
    Standard for ion-scale shock studies; invoked throughout §2 and the code description.
  • domain assumption Reflecting-wall setup with laminar upstream plasma produces a shock whose late-time injection physics is representative of ICM merger shocks.
    Stated in §2; limitations for Ms ≲ 2 discussed in §4.
  • domain assumption Nonthermal population is defined by the integral above Einj ≈ 10 Esh of the downstream energy spectrum.
    Eq. 1 and surrounding text; conventional but not unique.
  • standard math Rankine-Hugoniot jump conditions remain a good reference when ε_CR ≲ 3%.
    Used to interpret measured compression ratios in §3.1.

pith-pipeline@v1.1.0-grok45 · 16998 in / 3387 out tokens · 33786 ms · 2026-07-13T06:21:15.332512+00:00 · methodology

0 comments
read the original abstract

Collisionless shocks in the intracluster and intergalactic medium (ICM/IGM) are expected to energize both electrons and ions. While electron acceleration is revealed by prominent radio emission, $\gamma$-ray emission from hadronic interactions remains undetected, suggesting that high-$\beta$ (ratio of thermal to magnetic pressure), low-Mach-number shocks cannot accelerate protons efficiently. We present three-dimensional hybrid simulations, in which ions are treated kinetically and electrons as a fluid, of quasi-perpendicular (magnetic obliquity $\vartheta = 80^\circ$) shocks with sonic Mach numbers $M_s \sim 3{-}15$ and plasma $\beta \gtrsim 15$, representative of cluster environments. We find that weak shocks ($M_s \lesssim 5$) fail to develop significant nonthermal populations, with cosmic ray (CR) acceleration efficiencies $\varepsilon_{\rm CR} \lesssim 0.1\%$. In contrast, stronger shocks ($M_s \gtrsim 10$) develop clear power-law tails with slopes $q \sim 4.0 $ and reach $\varepsilon_{\rm CR} \sim 3\%$. These results suggest that weak, oblique ICM shocks are generally unlikely to accelerate protons efficiently. However, reducing $\vartheta$ to $\sim 45^\circ$ leads to substantially higher acceleration efficiencies, indicating that magnetic obliquity plays a critical role in determining proton acceleration. Our findings provide a microphysical framework for interpreting radio relic observations, whose polarization suggests that electrons are accelerated at oblique shocks, and the absence of cluster $\gamma$-ray detections.

Figures

Figures reproduced from arXiv: 2607.08835 by Damiano Caprioli, Luca Orusa, Yevhen Kylivnyk.

Figure 1
Figure 1. Figure 1: 3D rendering of total magnetic field Btotal and density (top and bottom panel, respectively) for Run 12 in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) CR acceleration efficiency, εCR, as a function of time. (a1) correspond to highly inefficient shocks with εCR, final < 0.1%, (a2) to intermediate efficiencies with εCR, final > 0.1%, and (a3) to very efficient shocks with εCR, final > 1%. (b) Energy spectra at the final timestep for selected runs. For highly efficient cases, Maxwellian and power-law fits of the form f(E) ∝ E −q are shown (black lines),… view at source ↗
Figure 3
Figure 3. Figure 3: shows εCR for a range of plasma β values and sonic Mach numbers. We find that low-Ms per￾pendicular shocks (Ms ≲ 5) are rather inefficient, with εCR ≲ 0.1% at late times. In contrast, higher-Ms shocks (Ms ≳ 10) reach an asymptotic value εCR ∼ 3%, indicating the development of an appreciable nonther￾mal ion component. To facilitate inclusion of these re￾sults into large-scale simulations of galaxy clusters … view at source ↗
Figure 4
Figure 4. Figure 4: Asymptotic acceleration efficiency, εCR, as a function of shock obliquity, ϑ. The final times are tlast = [160.0, 128.0, 128.0, 128.0] Ω−1 c for the 2D runs and [64.0, 36.0, 18.0, 18.0, 18.0] Ω−1 c for the 3D runs, ordered by increasing ϑ. All runs correspond to shocks with β = 120, MA = 30, and Ms = 3. At large obliquities, both configura￾tions are inefficient (especially in 2D) and converge to typical qu… view at source ↗

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Reference graph

Works this paper leans on

300 extracted references · 75 linked inside Pith

  1. [1]

    A Song of Shocks and Dynamo: Numerical Studies of a Galaxy Cluster Merger in the HIMAG Project , journal =

    Dom. A Song of Shocks and Dynamo: Numerical Studies of a Galaxy Cluster Merger in the HIMAG Project , journal =. 2019 , eprint =

    2019

  2. [2]

    and de Gasperin, F

    Jones, A. and de Gasperin, F. and Cuciti, V. and Hoang, D. N. and Botteon, A. and Br. Radio relics in PSZ2 G096.88+24.18: A connection with pre-existing plasma , journal =. 2021 , volume =

    2021

  3. [3]

    and Feretti, L

    Bonafede, A. and Feretti, L. and Murgia, M. and Govoni, F. and Giovannini, G. and Dallacasa, D. and Dolag, K. and Taylor, G. B. , title =. Astronomy & Astrophysics , year =

  4. [4]

    , keywords =

    The ``toothbrush-relic'': evidence for a coherent linear 2-Mpc scale shock wave in a massive merging galaxy cluster?. , keywords =. doi:10.1051/0004-6361/201219000 , archivePrefix =. 1209.2196 , primaryClass =

    Pith/arXiv arXiv doi:10.1051/0004-6361/201219000

  5. [5]

    , keywords =

    Constraining the efficiency of cosmic ray acceleration by cluster shocks. , keywords =. doi:10.1093/mnras/stw584 , archivePrefix =. 1603.02688 , primaryClass =

    Pith/arXiv arXiv doi:10.1093/mnras/stw584

  6. [6]

    arXiv e-prints , keywords =

    Ion Weibel Instability in the hybrid framework: the optimal resolution. arXiv e-prints , keywords =. doi:10.48550/arXiv.2604.05021 , archivePrefix =. 2604.05021 , primaryClass =

    Pith/arXiv arXiv doi:10.48550/arxiv.2604.05021

  7. [7]

    , keywords =

    Simulating the -ray emission from galaxy clusters: a universal cosmic ray spectrum and spatial distribution. , keywords =. doi:10.1111/j.1365-2966.2010.17328.x , archivePrefix =. 1001.5023 , primaryClass =

    doi:10.1111/j.1365-2966.2010.17328.x 2010

  8. [8]

    , keywords =

    On the mediation of a shock front by Fermi-accelerated cosmic rays. , keywords =. doi:10.1086/157998 , adsurl =

    doi:10.1086/157998

  9. [9]

    , keywords =

    Cluster Magnetic Fields from Large-Scale Structure and Galaxy Cluster Shocks. , keywords =. doi:10.1086/504470 , archivePrefix =. astro-ph/0512079 , primaryClass =

    Pith/arXiv arXiv doi:10.1086/504470

  10. [10]

    , keywords =

    Generation of Magnetic Fields in the Relativistic Shock of Gamma-Ray Burst Sources. , keywords =. doi:10.1086/308038 , archivePrefix =. astro-ph/9904363 , primaryClass =

    Pith/arXiv arXiv doi:10.1086/308038

  11. [11]

    , keywords =

    Gamma-Ray Burst Afterglow: Polarization and Analytic Light Curves. , keywords =. doi:10.1086/306720 , archivePrefix =. astro-ph/9807111 , primaryClass =

    Pith/arXiv arXiv doi:10.1086/306720

  12. [12]

    , keywords =

    Particle Transport in Tangled Magnetic Fields and Fermi Acceleration at Relativistic Shocks. , keywords =. doi:10.1086/376353 , archivePrefix =. astro-ph/0304058 , primaryClass =

    Pith/arXiv arXiv doi:10.1086/376353

  13. [13]

    , keywords =

    The acceleration time-scale for first-order Fermi acceleration in relativistic shock waves. , keywords =. doi:10.1093/mnras/283.2.447 , archivePrefix =. astro-ph/9608078 , primaryClass =

    Pith/arXiv arXiv doi:10.1093/mnras/283.2.447

  14. [14]

    , keywords =

    Fermi acceleration by relativistic shock waves. , keywords =. doi:10.1093/mnras/196.2.135 , adsurl =

    doi:10.1093/mnras/196.2.135

  15. [15]

    , keywords =

    Microphysics of Particle Reflection in Weibel-mediated Shocks. , keywords =. doi:10.3847/1538-4357/ad527d , archivePrefix =. 2310.12950 , primaryClass =

    Pith/arXiv arXiv doi:10.3847/1538-4357/ad527d

  16. [16]

    , keywords =

    Electron-Ion Temperature Ratio in Astrophysical Shocks. , keywords =. doi:10.3847/1538-4357/acc528 , archivePrefix =. 2303.08849 , primaryClass =

    Pith/arXiv arXiv doi:10.3847/1538-4357/acc528

  17. [17]

    arXiv , Author =:1511.05343 , Journal =

    doi:10.1051/0004-6361/201527761 , Eid =. arXiv , Author =:1511.05343 , Journal =

    Pith/arXiv arXiv doi:10.1051/0004-6361/201527761

  18. [18]

    Collisionless Shocks in a Partially Ionized Medium. II. Balmer Emission , Volume =. doi:10.1088/0004-637X/760/2/137 , Eid =. arXiv , Author =:1210.4296 , Journal =

    Pith/arXiv arXiv doi:10.1088/0004-637x/760/2/137

  19. [19]

    2019 , Bdsk-Url-1 =

    European Physical Journal Web of Conferences , Doi =. 2019 , Bdsk-Url-1 =. arXiv , Author =:1902.08124 , Keywords =

    Pith/arXiv arXiv 2019

  20. [20]

    and Akaike, Y

    Adriani, O. and Akaike, Y. and Asano, K. and Asaoka, Y. and Bagliesi, M. G. and Berti, E. and Bigongiari, G. and Binns, W. R. and Bonechi, S. and Bongi, M. and Brogi, P. and Bruno, A. and Buckley, J. H. and Cannady, N. and Castellini, G. and Checchia, C. and Cherry, M. L. and Collazuol, G. and Di Felice, V. and Ebisawa, K. and Fuke, H. and Guzik, T. G. an...

    doi:10.1103/physrevlett.122.181102 2019

  21. [21]

    Manconi and M

    S. Manconi and M. Di Mauro and F. Donato , Doi =. Multi-messenger constraints to the local emission of cosmic-ray electrons , Url =. Journal of Cosmology and Astroparticle Physics , Month =

  22. [22]

    doi:10.1088/0004-637X/786/2/124 , Eid =

    2014 , Bdsk-Url-1 =. doi:10.1088/0004-637X/786/2/124 , Eid =. arXiv , Author =:1305.1242 , Journal =

    Pith/arXiv arXiv doi:10.1088/0004-637x/786/2/124 2014

  23. [23]

    2001 , Bdsk-Url-1 =

    Reviews of Modern Physics , Keywords =. 2001 , Bdsk-Url-1 =. doi:10.1103/RevModPhys.73.1031 , Eprint =

    doi:10.1103/revmodphys.73.1031 2001

  24. [24]

    Cowsik and T

    R. Cowsik and T. Madziwa-Nussinov , Doi =. The Astrophysical Journal , Month =

  25. [25]

    doi:10.1017/S0022377816000660 , Eid =

    2016 , Bdsk-Url-1 =. doi:10.1017/S0022377816000660 , Eid =. arXiv , Author =:1601.01570 , Journal =

    Pith/arXiv arXiv doi:10.1017/s0022377816000660 2016

  26. [26]

    Lowe, R. E. and Burgess, D. , Doi =. The properties and causes of rippling in quasi-perpendicular collisionless shock fronts , Url =. Annales Geophysicae , Number =. 2003 , Bdsk-Url-1 =

    2003

  27. [27]

    Shock ripples observed by the

    Andreas Johlander and Andris Vaivads and Yuri V Khotyaintsev and Imogen Gingell and Steven J Schwartz and Barbara L Giles and Roy B Torbert and Christopher T Russell , Doi =. Shock ripples observed by the. Plasma Physics and Controlled Fusion , Month =

  28. [28]

    and Schwartz, S

    Johlander, A. and Schwartz, S. J. and Vaivads, A. and Khotyaintsev, Y. V. and Gingell, I. and Peng, I. B. and Markidis, S. and Lindqvist, P.-A. and Ergun, R. E. and Marklund, G. T. and Plaschke, F. and Magnes, W. and Strangeway, R. J. and Russell, C. T. and Wei, H. and Torbert, R. B. and Paterson, W. R. and Gershman, D. J. and Dorelli, J. C. and Avanov, L...

    2016

  29. [29]

    and Vaivads, A

    Johlander, A. and Vaivads, A. and Khotyaintsev, Y. V. and Retin. Ion injection at Quasi-parallel Shocks Seen by the Cluster Spacecraft , Url =. , Keywords =. 2016 , Bdsk-Url-1 =. doi:10.3847/2041-8205/817/1/L4 , Eid =

    doi:10.3847/2041-8205/817/1/l4 2016

  30. [30]

    , Keywords =

    Kinetic simulations of mildly relativistic shocks: Particle acceleration in high Mach number shocks , Url =. , Keywords =. 2019 , Bdsk-Url-1 =. doi:10.1093/mnras/stz232 , Eprint =

    doi:10.1093/mnras/stz232 2019

  31. [31]

    Weidl and Dan Winske and Christoph Niemann , Doi =

    Martin S. Weidl and Dan Winske and Christoph Niemann , Doi =. On the Background-gyroresonant Character of Bell's Instability in the Large-current Regime , Url =. The Astrophysical Journal , Month =

  32. [32]

    Jokipii, J. R. , Doi =. Propagation of cosmic rays in the solar wind , Url =. 1971 , Bdsk-Url-1 =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/RG009i001p00027 , Journal =

    doi:10.1029/rg009i001p00027 1971

  33. [33]

    The Astrophysical Journal , Month = apr, Title =

    Mignone, A and Bodo, G and Vaidya, B and Mattia, G , Doi =. The Astrophysical Journal , Month = apr, Title =. 2018 , Bdsk-Url-1 =

    2018

  34. [34]

    doi:10.1088/0004-637X/749/1/63 , Eid =

    2012 , Bdsk-Url-1 =. doi:10.1088/0004-637X/749/1/63 , Eid =. arXiv , Author =:1107.5576 , Journal =

    Pith/arXiv arXiv doi:10.1088/0004-637x/749/1/63 2012

  35. [35]

    doi:10.1111/j.1365-2966.2009.15428.x , Eprint =

    MNRAS , Keywords =. doi:10.1111/j.1365-2966.2009.15428.x , Eprint =

    doi:10.1111/j.1365-2966.2009.15428.x 2009

  36. [36]

    arXiv , Author =:1407.5223 , Journal =

    Pith/arXiv arXiv

  37. [37]

    , Keywords =

    Cambridge and New York, Cambridge University Press, 1990, 292 p. , Keywords =

    1990

  38. [38]

    doi:10.1088/1742-6596/409/1/012008 , Eid =

    Journal of Physics Conference Series , Month = feb, Number = 1, Pages =. doi:10.1088/1742-6596/409/1/012008 , Eid =

    doi:10.1088/1742-6596/409/1/012008

  39. [39]

    astro-ph/9803299 , Journal =

    Pith/arXiv arXiv

  40. [40]

    2000 , Bdsk-Url-1 =

    MNRAS , Keywords =. 2000 , Bdsk-Url-1 =. doi:10.1046/j.1365-8711.2000.03146.x , Eprint =

    doi:10.1046/j.1365-8711.2000.03146.x 2000

  41. [41]

    doi:10.1016/j.astropartphys.2010.12.008 , Eprint =

    , Month = mar, Pages =. doi:10.1016/j.astropartphys.2010.12.008 , Eprint =

    doi:10.1016/j.astropartphys.2010.12.008 2010

  42. [42]

    Phys. Rep. , Month = sep, Pages =. doi:10.1016/j.physrep.2008.05.004 , Eprint =

    doi:10.1016/j.physrep.2008.05.004 2008

  43. [43]

    , Keywords =

    ApJ Lett. , Keywords =. doi:10.1088/2041-8205/790/2/L21 , Eid =

    doi:10.1088/2041-8205/790/2/l21 2041

  44. [44]

    doi:10.1016/j.astropartphys.2010.08.010 , Eprint =

    , Pages =. doi:10.1016/j.astropartphys.2010.08.010 , Eprint =

    doi:10.1016/j.astropartphys.2010.08.010 2010

  45. [45]

    doi:10.1016/j.nuclphysbps.2009.03.069 , Eprint =

    Nuclear Physics B Proceedings Supplements , Month = may, Pages =. doi:10.1016/j.nuclphysbps.2009.03.069 , Eprint =

    doi:10.1016/j.nuclphysbps.2009.03.069 2009

  46. [46]

    , Keywords =

    ApJ Lett. , Keywords =. doi:10.1088/2041-8205/720/2/L155 , Eprint =

    doi:10.1088/2041-8205/720/2/l155 2041

  47. [47]

    2010 , Bdsk-Url-1 =

    MNRAS , Keywords =. 2010 , Bdsk-Url-1 =. doi:10.1111/j.1365-2966.2009.15784.x , Eprint =

    doi:10.1111/j.1365-2966.2009.15784.x 2010

  48. [48]

    doi:10.4236/ijaa.2014.43046 , Journal =

    2014 , Bdsk-Url-1 =. doi:10.4236/ijaa.2014.43046 , Journal =

    doi:10.4236/ijaa.2014.43046 2014

  49. [49]

    2001 , Bdsk-Url-1 =

    MNRAS , Keywords =. 2001 , Bdsk-Url-1 =. doi:10.1046/j.1365-8711.2001.04851.x , Eprint =

    doi:10.1046/j.1365-8711.2001.04851.x 2001

  50. [50]

    doi:10.1088/1367-2630/6/1/140 , Journal =

    doi:10.1088/1367-2630/6/1/140

  51. [51]

    1995 , Bdsk-Url-1 =

    Physical Review Letters , Month = jul, Pages =. 1995 , Bdsk-Url-1 =. doi:10.1103/PhysRevLett.75.386 , Eprint =

    doi:10.1103/physrevlett.75.386 1995

  52. [52]

    2012 , Bdsk-Url-1 =

    Astroparticle Physics , Month = may, Pages =. 2012 , Bdsk-Url-1 =. doi:10.1016/j.astropartphys.2012.02.004 , Eprint =

    doi:10.1016/j.astropartphys.2012.02.004 2012

  53. [53]

    arXiv , Author =:1310.5477 , Journal =

    Probing the origin of cosmic-rays with extremely high energy neutrinos using the IceCube Observatory , Volume =. arXiv , Author =:1310.5477 , Journal =

    Pith/arXiv arXiv

  54. [54]

    Astroparticle Physics , keywords =

    Cosmic ray composition and energy spectrum from 1-30 PeV using the 40-string configuration of IceTop and IceCube. Astroparticle Physics , keywords =. doi:10.1016/j.astropartphys.2012.11.003 , archivePrefix =. 1207.3455 , primaryClass =

    Pith/arXiv arXiv doi:10.1016/j.astropartphys.2012.11.003 2012

  55. [55]

    doi:10.1086/510831 , Eprint =

    , Keywords =. doi:10.1086/510831 , Eprint =

    doi:10.1086/510831

  56. [56]

    arXiv , Author =:1311.0287 , Journal =

    Pith/arXiv arXiv

  57. [57]

    and Trivelpiece, A.W

    Krall, N.A. and Trivelpiece, A.W. , Date-Added =. Principles of plasma physics , Url =. 1973 , Bdsk-Url-1 =

    1973

  58. [58]

    doi:10.1086/309533 , Eprint =

    , Keywords =. doi:10.1086/309533 , Eprint =

    doi:10.1086/309533

  59. [59]

    doi:10.1038/nphys2541 , Eprint =

    Nature Physics , Month = mar, Pages =. doi:10.1038/nphys2541 , Eprint =

    doi:10.1038/nphys2541

  60. [60]

    arXiv , Author =:1705.11096 , Journal =

    doi:10.3847/1538-4357/aa76ea , Eid =. arXiv , Author =:1705.11096 , Journal =

    Pith/arXiv arXiv doi:10.3847/1538-4357/aa76ea

  61. [61]

    Masters and A

    A. Masters and A. H. Sulaiman and N. Sergis and L. Stawarz and M. Fujimoto and A. J. Coates and M. K. Dougherty , title =. The Astrophysical Journal , abstract =. 2016 , month =. doi:10.3847/0004-637X/826/1/48 , url =

    doi:10.3847/0004-637x/826/1/48 2016

  62. [62]

    doi:10.1063/1.866765 , Journal =

    doi:10.1063/1.866765

  63. [63]

    doi:10.1093/mnras/stt100 , Eprint =

    , Keywords =. doi:10.1093/mnras/stt100 , Eprint =

    doi:10.1093/mnras/stt100

  64. [64]

    doi:10.1088/0004-637X/721/1/828 , Eprint =

    , Keywords =. doi:10.1088/0004-637X/721/1/828 , Eprint =

    doi:10.1088/0004-637x/721/1/828

  65. [65]

    doi:10.1093/mnras/stt179 , Eprint =

    MNRAS , Keywords =. doi:10.1093/mnras/stt179 , Eprint =

    doi:10.1093/mnras/stt179

  66. [66]

    MNRAS , Month = jan, Pages =

  67. [67]

    MNRAS , Month = feb, Pages =

  68. [68]

    2001 , Bdsk-Url-1 =

    MNRAS , Month = mar, Pages =. 2001 , Bdsk-Url-1 =

    2001

  69. [69]

    Bell, A. R. , Date-Added =. doi:10.1111/j.1365-2966.2004.08097.x , Journal =

    doi:10.1111/j.1365-2966.2004.08097.x 2004

  70. [70]

    doi:10.1086/591308 , Eprint =

    , Keywords =. doi:10.1086/591308 , Eprint =

    doi:10.1086/591308

  71. [71]

    astro-ph/0104064 , Journal =

    Pith/arXiv arXiv

  72. [72]

    doi:10.1051/0004-6361:20042015 , Eprint =

    A&A , Month = apr, Pages =. doi:10.1051/0004-6361:20042015 , Eprint =

    doi:10.1051/0004-6361:20042015

  73. [73]

    Akademiia Nauk SSSR Doklady , keywords =

    A regular mechanism for the acceleration of charged particles on the front of a shock wave. Akademiia Nauk SSSR Doklady , keywords =

  74. [74]

    doi:10.1086/182658 , Journal =

    1978 , Bdsk-Url-1 =. doi:10.1086/182658 , Journal =

    doi:10.1086/182658 1978

  75. [75]

    doi:10.1142/S0217732305019213 , Eprint =

    Modern Physics Letters A , Pages =. doi:10.1142/S0217732305019213 , Eprint =

    doi:10.1142/s0217732305019213

  76. [76]

    doi:10.1103/PhysRevLett.103.051104 , Eid =

    2009 , Bdsk-Url-1 =. doi:10.1103/PhysRevLett.103.051104 , Eid =. arXiv , Author =:0903.2794 , Journal =

    Pith/arXiv arXiv doi:10.1103/physrevlett.103.051104 2009

  77. [77]

    Fast electron transport in laser-produced plasmas and the

    A R Bell and A P L Robinson and M Sherlock and R J Kingham and W Rozmus , Doi =. Fast electron transport in laser-produced plasmas and the. Plasma Physics and Controlled Fusion , Month =

  78. [78]

    doi:10.1016/0021-9991(86)90076-8 , Journal =

    1986 , Bdsk-Url-1 =. doi:10.1016/0021-9991(86)90076-8 , Journal =

    doi:10.1016/0021-9991(86)90076-8 1986

  79. [79]

    2000 , Bdsk-Url-1 =

    MNRAS , Month = may, Pages =. 2000 , Bdsk-Url-1 =

    2000

  80. [80]

    doi:10.1007/BF00642346 , Journal =

    doi:10.1007/bf00642346

Showing first 80 references.