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Journal articles on the topic 'Cosmic-ray diffusion'

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Author: Grafiati

Published: 10 December 2022

Last updated: 29 January 2023

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1

Duffy, Peter. "Bohm Diffusion and Cosmic-Ray-Modified Shocks." International Astronomical Union Colloquium 142 (1994): 981–83. http://dx.doi.org/10.1017/s0252921100078428.

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AbstractA numerical solution to the problem of self-consistent diffusive shock acceleration is presented. The cosmic rays are scattered, accelerated and exert a back-reaction on the gas through their interaction with turbulence frozen into the local fluid frame. Using a grid with a hierarchical spacetime structure the physically interesting limit of Bohm diffusion (к ∝ pv), which introduces a wide range of diffusion lengthscales and acceleration timescales, can be studied. Some implications for modified shocks and particle acceleration are presented.Subject headings: acceleration of particles — cosmic rays — diffusion — shock waves

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2

Zhang, Yiran, Siming Liu, and Dejin Wu. "Cosmic-Ray Convection–Diffusion Anisotropy." Astrophysical Journal 938, no. 2 (October 1, 2022): 106. http://dx.doi.org/10.3847/1538-4357/ac8f28.

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Abstract Under nonuniform convection, the distribution of diffusive particles can exhibit dipole and quadrupole anisotropy induced by the fluid inertial and shear force, respectively. These convection-related anisotropies, unlike the Compton–Getting effect, typically increase with the cosmic-ray (CR) energy, and are thus candidate contributors for the CR anisotropy. In consideration of the inertial effect, CR observational data can be used to set an upper limit on the average acceleration of the local interstellar medium in the equatorial plane to be on the order of 100 μm s−2. Using Oort constants, the quadrupole anisotropy above 200 TeV may be modeled with the shear effect arising from the Galactic differential rotation.

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3

Reichherzer, P., J. Becker Tjus, E. G. Zweibel, L. Merten, and M. J. Pueschel. "Turbulence-level dependence of cosmic ray parallel diffusion." Monthly Notices of the Royal Astronomical Society 498, no. 4 (August 21, 2020): 5051–64. http://dx.doi.org/10.1093/mnras/staa2533.

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ABSTRACT Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic ray transport. The transition from a ballistic to a diffusive-propagation regime is presented in direct numerical calculations of diffusion coefficients for homogeneous magnetic field lines subject to turbulent perturbations. Simulation results are compared with theoretical derivations of the parallel diffusion coefficient’s dependences on the energy and the fluctuation amplitudes in the limit of weak turbulence. The present study shows that the widely used extrapolation of the energy scaling for the parallel diffusion coefficient to high turbulence levels predicted by quasi-linear theory does not provide a universally accurate description in the resonant-scattering regime. It is highlighted here that the numerically calculated diffusion coefficients can be polluted for low energies due to missing resonant interaction possibilities of the particles with the turbulence. Five reduced-rigidity regimes are established, which are separated by analytical boundaries derived in this work. Consequently, a proper description of cosmic ray propagation can only be achieved by using a turbulence-level-dependent diffusion coefficient and can contribute to solving the Galactic cosmic ray gradient problem.

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4

Schlickeiser, Reinhard. "Cosmic-Ray Transport and Acceleration." International Astronomical Union Colloquium 142 (1994): 926–36. http://dx.doi.org/10.1017/s0252921100078337.

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AbstractWe review the transport and acceleration of cosmic rays concentrating on the origin of galactic cosmic rays. Quasi-linear theory for the acceleration rates and propagation parameters of charged test particles combined with the plasma wave viewpoint of modeling weak cosmic electromagnetic turbulence provides a qualitatively and quantitatively correct description of key observations. Incorporating finite frequency effects, dispersion, and damping of the plasma waves are essential in overcoming classical discrepancies with observations as the Kfit - Kql discrepancy of solar particle events. We show that the diffusion-convection transport equation in its general form contains spatial convection and diffusion terms as well as momentum convection and diffusion terms. In particular, the latter momentum diffusion term plays a decisive role in the acceleration of cosmic rays at super-Alfvénic supernova shock fronts, and in the acceleration of ultra-high-energy cosmic rays by distributed acceleration in our own galaxy.Subject headings: acceleration of particles — convection — cosmic rays — diffusion — shock waves

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5

Commerçon, Benoît, Alexandre Marcowith, and Yohan Dubois. "Cosmic-ray propagation in the bi-stable interstellar medium." Astronomy & Astrophysics 622 (February 2019): A143. http://dx.doi.org/10.1051/0004-6361/201833809.

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Context. Cosmic rays propagate through the galactic scales down to the smaller scales at which stars form. Cosmic rays are close to energy equipartition with the other components of the interstellar medium and can provide a support against gravity if pressure gradients develop. Aims. We study the propagation of cosmic rays within the turbulent and magnetised bi-stable interstellar gas. The conditions necessary for cosmic-ray trapping and cosmic-ray pressure gradient development are investigated. Methods. We derived an analytical value of the critical diffusion coefficient for cosmic-ray trapping within a turbulent medium, which follows the observed scaling relations. We then presented a numerical study using 3D simulations of the evolution of a mixture of interstellar gas and cosmic rays, in which turbulence is driven at varying scales by stochastic forcing within a box of 40 pc. We explored a large parameter space in which the cosmic-ray diffusion coefficient, the magnetisation, the driving scale, and the amplitude of the turbulence forcing, as well as the initial cosmic-ray energy density, vary. Results. We identify a clear transition in the interstellar dynamics for cosmic-ray diffusion coefficients below a critical value deduced from observed scaling relations. This critical diffusion depends on the characteristic length scale L of Dcrit ≃ 3.1 × 1023 cm2 s−1(L/1 pc)q+1, where the exponent q relates the turbulent velocity dispersion σ to the length scale as σ ~ Lq. Hence, in our simulations this transition occurs around Dcrit ≃ 1024–1025 cm2 s−1. The transition is recovered in all cases of our parameter study and is in very good agreement with our simple analytical estimate. In the trapped cosmic-ray regime, the induced cosmic-ray pressure gradients can modify the gas flow and provide a support against the thermal instability development. We discuss possible mechanisms that can significantly reduce the cosmic-ray diffusion coefficients within the interstellar medium. Conclusions. Cosmic-ray pressure gradients can develop and modify the evolution of thermally bi-stable gas for diffusion coefficients D0 ≤ 1025 cm2 s−1 or in regions where the cosmic-ray pressure exceeds the thermal one by more than a factor of ten. This study provides the basis for further works including more realistic cosmic-ray diffusion coefficients, as well as local cosmic-ray sources.

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6

Armillotta, Lucia, Eve C. Ostriker, and Yan-Fei Jiang. "Cosmic-Ray Transport in Simulations of Star-forming Galactic Disks." Astrophysical Journal 922, no. 1 (November 1, 2021): 11. http://dx.doi.org/10.3847/1538-4357/ac1db2.

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Abstract Cosmic-ray transport on galactic scales depends on the detailed properties of the magnetized, multiphase interstellar medium (ISM). In this work, we postprocess a high-resolution TIGRESS magnetohydrodynamic simulation modeling a local galactic disk patch with a two-moment fluid algorithm for cosmic-ray transport. We consider a variety of prescriptions for the cosmic rays, from a simple, purely diffusive formalism with constant scattering coefficient, to a physically motivated model in which the scattering coefficient is set by the critical balance between streaming-driven Alfvén wave excitation and damping mediated by local gas properties. We separately focus on cosmic rays with kinetic energies of ∼1 GeV (high-energy) and ∼30 MeV (low energy), respectively important for ISM dynamics and chemistry. We find that simultaneously accounting for advection, streaming, and diffusion of cosmic rays is crucial for properly modeling their transport. Advection dominates in the high-velocity, low-density hot phase, while diffusion and streaming are more important in higher-density, cooler phases. Our physically motivated model shows that there is no single diffusivity for cosmic-ray transport: the scattering coefficient varies by four or more orders of magnitude, maximal at density n H ∼ 0.01 cm−3. The ion-neutral damping of Alfvén waves results in strong diffusion and nearly uniform cosmic-ray pressure within most of the mass of the ISM. However, cosmic rays are trapped near the disk midplane by the higher scattering rate in the surrounding lower-density, higher-ionization gas. The transport of high-energy cosmic rays differs from that of low-energy cosmic rays, with less effective diffusion and greater energy losses for the latter.

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7

Maiti, Snehanshu, Kirit Makwana, Heshou Zhang, and Huirong Yan. "Cosmic-ray Transport in Magnetohydrodynamic Turbulence." Astrophysical Journal 926, no. 1 (February 1, 2022): 94. http://dx.doi.org/10.3847/1538-4357/ac46c8.

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Abstract This paper studies cosmic-ray (CR) transport in magnetohydrodynamic (MHD) turbulence. CR transport is strongly dependent on the properties of the magnetic turbulence. We perform test particle simulations to study the interactions of CR with both total MHD turbulence and decomposed MHD modes. The spatial diffusion coefficients and the pitch angle scattering diffusion coefficients are calculated from the test particle trajectories in turbulence. Our results confirm that the fast modes dominate the CR propagation, whereas Alfvén and slow modes are much less efficient and have shown similar pitch-angle scattering rates. We investigate the cross field transport on large and small scales. On large/global scales, normal diffusion is observed and the diffusion coefficient is suppressed by M A ζ compared to the parallel diffusion coefficients, with ζ closer to 4 in Alfvén modes than that in total turbulence, as theoretically expected. For the CR transport on scales smaller than the turbulence injection scale, both the local and global magnetic reference frames are adopted. Superdiffusion is observed on such small scales in all the cases. Particularly, CR transport in Alfvén modes show clear Richardson diffusion in the local reference frame. The diffusion transitions smoothly from the Richardson’s one with index 1.5 to normal diffusion as the particle mean free path decreases from λ ∥ ≫ L to λ ∥ ≪ L, where L is the injection/coherence length of turbulence. Our results have broad applications to CRs in various astrophysical environments.

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8

ZIRAKASHVILI, VLADIMIR N. "COSMIC RAY ANISOTROPY PROBLEM." International Journal of Modern Physics A 20, no. 29 (November 20, 2005): 6858–60. http://dx.doi.org/10.1142/s0217751x05030314.

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The anisotropy of cosmic rays, produced by Galactic supernovae is calculated. It is a factor 100 ÷ 1000 larger than the observed value at 1 PeV. It is shown that this contradiction can be explained if a cosmic ray diffusion coefficient is small in the local vicinity of the Sun.

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Chan, T. K., D. Kereš, P. F. Hopkins, E. Quataert, K.-Y. Su, C. C. Hayward, and C.-A. Faucher-Giguère. "Cosmic ray feedback in the FIRE simulations: constraining cosmic ray propagation with GeV γ-ray emission." Monthly Notices of the Royal Astronomical Society 488, no. 3 (July 10, 2019): 3716–44. http://dx.doi.org/10.1093/mnras/stz1895.

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ABSTRACT We present the implementation and the first results of cosmic ray (CR) feedback in the Feedback In Realistic Environments (FIRE) simulations. We investigate CR feedback in non-cosmological simulations of dwarf, sub-L⋆ starburst, and L⋆ galaxies with different propagation models, including advection, isotropic, and anisotropic diffusion, and streaming along field lines with different transport coefficients. We simulate CR diffusion and streaming simultaneously in galaxies with high resolution, using a two-moment method. We forward-model and compare to observations of γ-ray emission from nearby and starburst galaxies. We reproduce the γ-ray observations of dwarf and L⋆ galaxies with constant isotropic diffusion coefficient $\kappa \sim 3\times 10^{29}\, {\rm cm^{2}\, s^{-1}}$. Advection-only and streaming-only models produce order of magnitude too large γ-ray luminosities in dwarf and L⋆ galaxies. We show that in models that match the γ-ray observations, most CRs escape low-gas-density galaxies (e.g. dwarfs) before significant collisional losses, while starburst galaxies are CR proton calorimeters. While adiabatic losses can be significant, they occur only after CRs escape galaxies, so they are only of secondary importance for γ-ray emissivities. Models where CRs are ‘trapped’ in the star-forming disc have lower star formation efficiency, but these models are ruled out by γ-ray observations. For models with constant κ that match the γ-ray observations, CRs form extended haloes with scale heights of several kpc to several tens of kpc.

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10

Exarhos, G., and X. Moussas. "On the heliolatitudinal variation of the galactic cosmic-ray intensity. Comparison with Ulysses measurements." Annales Geophysicae 21, no. 6 (June 30, 2003): 1341–45. http://dx.doi.org/10.5194/angeo-21-1341-2003.

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Abstract. We study the dependence of cosmic rays with heliolatitude using a simple method and compare the results with the actual data from Ulysses and IMP spacecraft. We reproduce the galactic cosmic-ray heliographic latitudinal intensity variations, applying a semi-empirical, 2-D diffusion-convection model for the cosmic-ray transport in the interplanetary space. This model is a modification of our previous 1-D model (Exarhos and Moussas, 2001) and includes not only the radial diffusion of the cosmic-ray particles but also the latitudinal diffusion. Dividing the interplanetary region into "spherical magnetic sectors" (a small heliolatitudinal extension of a spherical magnetized solar wind plasma shell) that travel into the interplanetary space at the solar wind velocity, we calculate the cosmic-ray intensity for different heliographic latitudes as a series of successive intensity drops that all these "spherical magnetic sectors" between the Sun and the heliospheric termination shock cause the unmodulated galactic cosmic-ray intensity. Our results are compared with the Ulysses cosmic-ray measurements obtained during the first pole-to-pole passage from mid-1994 to mid-1995.Key words. Interplanetary physics (cosmic rays; interplanetray magnetic fields; solar wind plasma)

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11

Tjus, Julia Becker. "Plasmas, particles and photons—spotlights on multimessenger astronomy." Plasma Physics and Controlled Fusion 64, no. 4 (March 14, 2022): 044013. http://dx.doi.org/10.1088/1361-6587/ac57ce.

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Abstract During the past decennia, progress in the area of high-energy astroparticle physics was exceptional, mainly due to the great success of the bridging of particle- and astrophysics both in theory and in the instrumentation of astroparticle physics observatories. Multimessenger data coming from charged cosmic-ray-, gamma-ray- and neutrino-observatories start to shed more and more light on the nature and origin of cosmic rays. At the same time, the development of methods for the investigation of cosmic-ray transport, acceleration and interaction has advanced to the true potential of tying these different pieces of multimessenger data together, this way closing in on the origin of cosmic rays. In recent years, this rapid interplay between modeling and observations has made it clear that it is essential to add the ingredient of plasma physics to the problem. It has been shown that even the interpretation of data of highly relativistic cosmic rays at TeV energies and above is in need of a proper modeling of the plasma physics involved. One of the most important examples is the understanding of wave-particle interactions. In simulations of cosmic-ray transport in the Galaxy, the cosmic-ray diffusion coefficient is typically approximated with a Kolmogorov-type cascade model, resulting in an energy-dependent parallel diffusion coefficient κ ∥ ∝ E γ with γ = 1 / 3 . Here, we show how the energy dependence of the diffusion coefficient can be investigated systematically as a function of δ B / B . The complex energy behavior that goes well beyond a simple powerlaw interpretation will be presented together with a formal definition of an energy range that indeed can be approximated as a powerlaw. These results are applied to cosmic-ray transport in the Milky Way. Finally, the transition between the ballistic and diffusive regime will be investigated for astrophysical sources with special focus on relativistic plasmoids of active galaxies.

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12

Uchaikin, V. V. "Fractional phenomenology of cosmic ray anomalous diffusion." Physics-Uspekhi 56, no. 11 (November 30, 2013): 1074–119. http://dx.doi.org/10.3367/ufne.0183.201311b.1175.

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13

Fedorov, Yu I. "Cosmic ray streaming in the diffusion approximation." Kinematika i fizika nebesnyh tel (Online) 37, no. 3 (May 1, 2021): 3–23. http://dx.doi.org/10.15407/kfnt2021.03.003.

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14

Fedorov, Yu I. "Cosmic Ray Flux in the Diffusion Approximation." Kinematics and Physics of Celestial Bodies 37, no. 3 (May 2021): 107–20. http://dx.doi.org/10.3103/s088459132103003x.

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15

Pei, C., J. W. Bieber, B. Breech, R. A. Burger, J. Clem, and W. H. Matthaeus. "Cosmic ray diffusion tensor throughout the heliosphere." Journal of Geophysical Research: Space Physics 115, A3 (March 2010): n/a. http://dx.doi.org/10.1029/2009ja014705.

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16

Duffy, Peter. "Bohm diffusion and cosmic-ray-modified shocks." Astrophysical Journal Supplement Series 90 (February 1994): 981. http://dx.doi.org/10.1086/191936.

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17

Uchaikin, Vladimir V. "Fractional phenomenology of cosmic ray anomalous diffusion." Uspekhi Fizicheskih Nauk 183, no. 11 (2013): 1175–223. http://dx.doi.org/10.3367/ufnr.0183.201311b.1175.

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18

Kachelrieß, M. "Anisotropic diffusion and the cosmic ray anisotropy." Journal of Physics: Conference Series 1181 (February 2019): 012039. http://dx.doi.org/10.1088/1742-6596/1181/1/012039.

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19

McKibben, R. B. "Cosmic-ray diffusion in the inner heliosphere." Advances in Space Research 35, no. 4 (January 2005): 518–31. http://dx.doi.org/10.1016/j.asr.2005.01.022.

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20

Rodgers-Lee, D., A. A. Vidotto, and A. L. Mesquita. "Charting nearby stellar systems: the intensity of Galactic cosmic rays for a sample of solar-type stars." Monthly Notices of the Royal Astronomical Society 508, no. 4 (October 2, 2021): 4696–704. http://dx.doi.org/10.1093/mnras/stab2788.

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ABSTRACT Cosmic rays can penetrate planetary atmospheres driving the formation of prebiotic molecules, which are important for the origin of life. We calculate the Galactic cosmic ray fluxes in the habitable zone (HZ) of five nearby, well-studied solar-type stars and at the orbits of two known exoplanets. We model the propagation of Galactic cosmic rays through the stellar winds using a combined 1.5D stellar wind and 1D cosmic ray transport model. We find that the HZ of 61 Cyg A has comparable Galactic cosmic ray fluxes to present-day Earth values. For the other four systems (ϵ Eri, ϵ Ind, ξ Boo B, and π1 UMa), the fluxes are orders of magnitude smaller than Earth values. Thus, it is unlikely that any as-of-yet undetected Earth-like planets in their HZs would receive a higher radiation dose than is received on Earth. $\epsilon \,$Ind b, a Jupiter-like planet orbiting at ∼11 au, receives higher Galactic cosmic ray fluxes than Earth. We find the suppression of Galactic cosmic rays is influenced by whether diffusion or advection dominates at GeV energies and at distances where the wind has reached its’ terminal velocity. For advectively dominated winds (∼younger systems), varying the astrospheric size influences the suppression significantly. For diffusion-dominated systems (∼older systems), the astrospheric size, and therefore knowledge of the interstellar medium properties, are not very important. This reduces the Galactic cosmic ray flux uncertainties in the HZ for diffusion-dominated systems. Whether a system is advection- or diffusion-dominated can be determined from the stellar wind properties.

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21

Ahlers, M. "The power spectrum of cosmic ray arrival directions." ASTRA Proceedings 2 (October 7, 2015): 45–49. http://dx.doi.org/10.5194/ap-2-45-2015.

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Abstract. Various experiments show that the arrival directions of multi-TeV cosmic rays show significant anisotropies at small angular scales. It was recently argued that this small scale structure may arise naturally by cosmic ray diffusion in a large-scale cosmic ray gradient in combination with deflections in local turbulent magnetic fields. We show via analytical and numerical methods that the non-trivial power spectrum in this setup is a direct consequence of Liouville's theorem and can be related to properties of relative diffusion.

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22

Jones, Frank C. "Static versus Dynamical Cosmic-ray Halos." Symposium - International Astronomical Union 144 (1991): 359–68. http://dx.doi.org/10.1017/s0074180900089300.

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The dynamical halo of the Galaxy offers a natural explanation for the form of the variation of cosmic-ray path length with energy. The variation above 1 GeV per nucleon can be understood as due to the variation of the diffusion coefficient, and hence the resident time in the galaxy, with energy. The flattening of the curve below 1 GeV per nucleon is seen to mark a transition to a convection dominated regime where the variation of the diffusion coefficient is no longer a determining factor. It is possible that the random motion of the cosmic rays about the galaxy that prevents us from seeing their sources in a clear manner may enable us to extract information about the galaxy at large and learn something about its large scale motions.

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23

Dashyan, Gohar, and Yohan Dubois. "Cosmic ray feedback from supernovae in dwarf galaxies." Astronomy & Astrophysics 638 (June 2020): A123. http://dx.doi.org/10.1051/0004-6361/201936339.

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The regulation of the baryonic content in dwarf galaxies is a long-standing problem. Supernovae (SNe) are supposed to play a key role in forming large-scale galactic winds by removing important amounts of gas from galaxies. SNe are efficient accelerators of non-thermal particles, so-called cosmic rays (CRs), which can substantially modify the dynamics of the gas and conditions to form large-scale galactic winds. We investigate how CR injection by SNe impacts the star formation and the formation of large-scale winds in dwarf galaxies, and whether it can produce galaxy star-formation rates (SFR) and wind properties closer to observations. We ran CR magneto-hydrodynamical simulations of dwarf galaxies at high resolution (9 pc) with the adaptive mesh refinement code RAMSES. Those disc galaxies are embedded in isolated halos of mass of 1010 and 1011 M⊙, and CRs are injected by SNe. We included CR isotropic and anisotropic diffusion with various diffusion coefficients, CR radiative losses, and CR streaming. The injection of CR energy into the interstellar medium smooths out the highest gas densities, which reduces the SFR by a factor of 2–3. Mass outflow rates are significantly greater with CR diffusion, by 2 orders of magnitudes for the higher diffusion coefficients. Without diffusion and streaming, CRs are inefficient at generating winds. CR streaming alone allows for the formation of winds but which are too weak to match observations. The formation of galactic winds strongly depends on the diffusion coefficient: for low coefficients, CR energy stays confined in high density regions where CR energy losses are highest, and higher coefficients, which allow for a more efficient leaking of CRs out of dense gas, produce stronger winds. CR diffusion leads to colder and denser winds than without CRs, and brings outflow rates and mass loading factors much closer to observations.

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WEBB, G. M., A. ZAKHARIAN, and G. P. ZANK. "Wave mixing and instabilities in cosmic-ray-modified shocks and flows." Journal of Plasma Physics 61, no. 4 (May 1999): 553–99. http://dx.doi.org/10.1017/s0022377898007466.

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Wave mixing equations describing the interaction of short-wavelength sound waves and entropy waves in two-fluid cosmic ray hydrodynamics in a non-uniform, large-scale, background flow in one Cartesian space dimension are investigated. The wave interaction coefficients depend on large-scale gradients in the background flow, and consist of two physically distinct components. The first component consists of wave-damping terms due to the diffusing cosmic rays, plus squeezing instability terms associated with the large-scale cosmic ray pressure gradient. These effects were first investigated by Drury and Dorfi in a study of the propagation of short-wavelength WKB sound waves in cosmic-ray-modified flows and shocks. The second component describes gas dynamical wave mixing effects due to gradients of the gas entropy S and the gas dynamical Riemann invariants (R±) of the background flow. A Green function solution is used to illustrate the coupling of the backward and forward sound waves for the case of a uniform background flow, in which the coupling coefficients depend on the parameter α = a2c/2κ, where ac is the cosmic-ray ‘sound speed’ and κ is the hydrodynamical cosmic-ray diffusion coefficient. Analytical WKB approximation methods and numerical simulations are used to investigate the modifications of the cosmic ray squeezing instability by wave mixing in cosmic-ray-modified shocks and pressure balance structures. Astrophysical applications to instabilities in supernova remnant shocks are discussed.

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Uchaikin, V. V., and R. T. Sibatov. "On fractional differential models for cosmic ray diffusion." Gravitation and Cosmology 18, no. 2 (April 2012): 122–26. http://dx.doi.org/10.1134/s0202289312020132.

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Jaekel, Uwe. "Magnetic mirroring and cosmic ray pitch-angle diffusion." Physical Review E 58, no. 3 (September 1, 1998): 4033–36. http://dx.doi.org/10.1103/physreve.58.4033.

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Weinhorst, B., A. Shalchi, and H. Fichtner. "The Cosmic‐Ray Diffusion Tensor in Nonaxisymmetric Turbulence." Astrophysical Journal 677, no. 1 (April 10, 2008): 671–75. http://dx.doi.org/10.1086/529121.

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Mathews, William G., and Fulai Guo. "COSMIC RAY DIFFUSION FRONTS IN THE VIRGO CLUSTER." Astrophysical Journal 736, no. 1 (June 28, 2011): 6. http://dx.doi.org/10.1088/0004-637x/736/1/6.

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29

Lagutin, A. A., and V. V. Uchaikin. "Anomalous diffusion equation: Application to cosmic ray transport." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 201, no. 1 (January 2003): 212–16. http://dx.doi.org/10.1016/s0168-583x(02)01362-9.

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Schlickeiser, R., and A. Shalchi. "Cosmic‐Ray Diffusion Approximation with Weak Adiabatic Focusing." Astrophysical Journal 686, no. 1 (October 10, 2008): 292–302. http://dx.doi.org/10.1086/591237.

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Tautz, R. C., and I. Lerche. "Cosmic-ray diffusion modeling: Solutions using variational methods." Journal of Mathematical Physics 54, no. 5 (May 2013): 053303. http://dx.doi.org/10.1063/1.4806649.

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32

Lasuik, J., and A. Shalchi. "Solutions of the cosmic ray velocity diffusion equation." Advances in Space Research 60, no. 7 (October 2017): 1532–46. http://dx.doi.org/10.1016/j.asr.2017.06.035.

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Shimoda, Jiro, and Shu-ichiro Inutsuka. "The Effects of Cosmic-Ray Diffusion and Radiative Cooling on the Galactic Wind of the Milky Way." Astrophysical Journal 926, no. 1 (February 1, 2022): 8. http://dx.doi.org/10.3847/1538-4357/ac4110.

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Abstract The effects of cosmic-ray diffusion and radiative cooling on the structure of the Galactic wind are studied using a steady-state approximation. It is known that realistic cooling processes suppress the wind from launching. The effects of cosmic-ray diffusion are also supposed to be unfavorable for launching the wind. Both of these effects have not been studied simultaneously in a steady-state approximation of the wind. We find 327,254 solutions of the steady-state Galactic wind and confirm that: the effect of the cosmic-ray pressure depends on the Alfvén Mach number, the mass flux carried by the wind does not depend on the cosmic-ray pressure directly (but depends on the thermal pressure), and the typical conditions found in the Galaxy may correspond to the wind solution that provides metal-polluted matter at a height of ∼300 kpc from the disk.

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SCHLICKEISER, R., and F. JENKO. "Cosmic ray transport in non-uniform magnetic fields: consequences of gradient and curvature drifts." Journal of Plasma Physics 76, no. 3-4 (January 8, 2010): 317–27. http://dx.doi.org/10.1017/s0022377809990444.

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AbstractLarge-scale spatial variations of the guide magnetic field of interplanetary and interstellar plasmas give rise to the mirror force −(p⊥2/2mγB)∇B). The parallel component of this mirror force causes adiabatic focusing of the cosmic ray guiding center whereas the perpendicular component of the mirror force gives rise to the gradient and curvature drifts of the cosmic ray guiding center. Adiabatic focusing and the gradient and curvature drift terms additionally enter the Fokker–Planck transport equation for the gyrotropic cosmic ray particle phase space density in partially turbulent non-uniform magnetic fields. For magnetohydrodynamic turbulence with dominating magnetic fluctuations, the diffusion approximation is justified, which results in a modification of the diffusion–convection transport equation for the isotropic part of the gyrotropic phase space density from the additional focusing and drift terms. For axisymmetric undamped slab Alfvenic turbulence we show that all perpendicular spatial diffusion coefficients are caused by the non-vanishing gradient and curvature drift terms. For a specific (symmetric in μ) choice of the pitch-angle Fokker–Planck coefficients we show that the ratio of the perpendicular to parallel spatial diffusion coefficients apart from a constant is determined by the spatial first derivatives of the non-constant cosmic ray Larmor radius in the non-uniform magnetic field.

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BELL, A. R. "SELF-SIMILAR SOLUTIONS FOR THE ACCELERATION OF COSMIC RAYS AT A SUPERNOVA SHOCK PROPAGATING INTO A CIRCUMSTELLAR WIND." International Journal of Modern Physics D 17, no. 10 (September 2008): 1787–93. http://dx.doi.org/10.1142/s0218271808013418.

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Cosmic ray acceleration may occur at a supernova shock expanding into a circumstellar wind. Self-similar solutions for the cosmic ray distribution are derived firstly when diffusion is isotropic and secondly when the wind sustains a magnetic field in the form of a Parker spiral.

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36

Krumholz, Mark R., Roland M. Crocker, Siyao Xu, A. Lazarian, M. T. Rosevear, and Jasper Bedwell-Wilson. "Cosmic ray transport in starburst galaxies." Monthly Notices of the Royal Astronomical Society 493, no. 2 (February 18, 2020): 2817–33. http://dx.doi.org/10.1093/mnras/staa493.

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ABSTRACT Starburst galaxies are efficient γ-ray producers, because their high supernova rates generate copious cosmic ray (CR) protons, and their high gas densities act as thick targets off which these protons can produce neutral pions and thence γ-rays. In this paper, we present a first-principles calculation of the mechanisms by which CRs propagate through such environments, combining astrochemical models with analysis of turbulence in weakly ionized plasma. We show that CRs cannot scatter off the strong large-scale turbulence found in starbursts, because efficient ion-neutral damping prevents such turbulence from cascading down to the scales of CR gyroradii. Instead, CRs stream along field lines at a rate determined by the competition between streaming instability and ion-neutral damping, leading to transport via a process of field line random walk. This results in an effective diffusion coefficient that is nearly energy independent up to CR energies of ∼1 TeV. We apply our computed diffusion coefficient to a simple model of CR escape and loss, and show that the resulting γ-ray spectra are in good agreement with the observed spectra of the starbursts NGC 253, M82, and Arp 220. In particular, our model reproduces these galaxies’ relatively hard GeV γ-ray spectra and softer TeV spectra without the need for any fine-tuning of advective escape times or the shape of the CR injection spectrum.

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Shaikh, Zubair I., Anil N. Raghav, and Geeta Vichare. "Evolution of planar magnetic structure within the stream interaction region and its connection with a recurrent Forbush decrease." Monthly Notices of the Royal Astronomical Society 494, no. 4 (May 7, 2020): 5075–80. http://dx.doi.org/10.1093/mnras/staa1039.

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ABSTRACT In general, stream interaction region (SIR)-induced Forbush decreases are recurrent and low magnitude in nature. The diffusion–convection associated with the SIR plays an important role in their modulation. Here, we study the evolution of planar magnetic structure (PMS) within the SIR and its contribution to cosmic ray modulation. Interestingly, we found the presence of PMS structures within the SIR from the leading part of the SIR to the minimum of the cosmic ray intensity in two events. The PMS may have originated due to the high compression caused by the fast solar wind, which amplifies and aligns the pre-existing discontinuities in the ambient slow solar wind. The study also suggests that the existence of PMS, enhanced initial mass function (IMF) strength, and associated turbulent regions decreases the perpendicular diffusion coefficient and causes a decrease in the cosmic ray intensity observed on Earth. Moreover, a slow decrease in IMF magnitude concurs with the recovery phase of cosmic ray intensity.

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Kuwabara, Takuhito, Kenji Nakamura, and Chung-Ming Ko. "The Effect of Cosmic-Ray Diffusion for Parker Instability." Symposium - International Astronomical Union 217 (2004): 230–32. http://dx.doi.org/10.1017/s0074180900197621.

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We studied the effect of anisotropic cosmic-ray (CR) diffusion for Parker instability by two-dimensional magnetohydrodynamic (MHD) simulation. We investigated two cases: a mechanical perturbation case and an explosional perturbation case. In the former case, the growth rate is proportional to the value of the diffusion coefficient of the CR. In the latter case, the growth rate becomes large in the early stages as the value of diffusion coefficient of the CR is getting small. But, after all, the result becomes the same as the former case in the late stages.

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39

Ferreira, Stefan E. S. "Theory of cosmic ray modulation." Proceedings of the International Astronomical Union 4, S257 (September 2008): 429–38. http://dx.doi.org/10.1017/s1743921309029664.

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AbstractThis work aims to give a brief overview on the topic of cosmic ray modulation in the heliosphere. The heliosphere, heliospheric magnetic field, transport parameters and the transport equation together with modulation models, which solve this equation in various degree of complexity, are briefly discussed. Results from these models are then presented where first it is shown how cosmic rays are globally distributed in an asymmetrical heliosphere which results from the relative motion between the local interstellar medium and the Sun. Next the focus shifts to low-energy Jovian electrons. The intensities of these electrons, which originate from a point source in the inner heliosphere, exhibit a unique three-dimensional spiral structure where most of the particles are transported along the magnetic field lines. Time-dependent modulation is also discussed where it is shown how drift effects together with propagating diffusion barriers are responsible for modulation over a solar cycle.

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40

Mertsch, P., and S. Funk. "A solution to the cosmic ray anisotropy problem." ASTRA Proceedings 2 (October 8, 2015): 51–55. http://dx.doi.org/10.5194/ap-2-51-2015.

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Abstract. Observations of the cosmic ray (CR) anisotropy are widely advertised as a means of finding nearby sources. This idea has recently gained currency after the discovery of a rise in the positron fraction and is the goal of current experimental efforts, e.g., with AMS-02 on the International Space Station. Yet, even the anisotropy observed for hadronic CRs is not understood, in the sense that isotropic diffusion models overpredict the dipole anisotropy in the TeV–PeV range by almost two orders of magnitude. Here, we consider two additional effects normally not considered in isotropic diffusion models: anisotropic diffusion due to the presence of a background magnetic field and intermittency effects of the turbulent magnetic fields. We numerically explore these effect by tracking test-particles through individual realisations of the turbulent field. We conclude that a large misalignment between the CR gradient and the background field can explain the observed low level of anisotropy.

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41

Setthahirun, Suwitchaya, and Maneenate Wechakama. "Constraining the annihilation of dark matter via cosmic-ray positrons and electrons." Journal of Physics: Conference Series 2145, no. 1 (December 1, 2021): 012007. http://dx.doi.org/10.1088/1742-6596/2145/1/012007.

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Abstract We aim to constrain the properties of dark matter particles by several measurements of positrons and electrons from cosmic-rays. We assume that collisions of dark matter particles and dark matter anti-particles can produce positrons and electrons. The electron-positron propagation is explained by a diffusion-loss equation including loss rates, diffusion, as well as source function. We use data of cosmic-ray positrons and electrons detected by PAMELA, H.E.S.S., AMS-02 and Fermi-LAT. We compare the observational data with the electron and positron spectrum from five annihilation channels in our model to derive constraining factors regarding the cross-section of the annihilation of dark matter. The tightest constraint is provided by cosmic-ray positrons of AMS-02 for the electron channel. Dark matter with mass below a few GeV gets excluded by the cosmic-ray positrons of AMS-02 for the electron, muon and tau channels.

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42

Ndiitwani, D. C., S. E. S. Ferreira, M. S. Potgieter, and B. Heber. "Modelling cosmic ray intensities along the Ulysses trajectory." Annales Geophysicae 23, no. 3 (March 30, 2005): 1061–70. http://dx.doi.org/10.5194/angeo-23-1061-2005.

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Abstract. Time dependent cosmic ray modulation in the inner heliosphere is studied by comparing results from a 2-D, time-dependent cosmic ray transport model with Ulysses observations. A compound approach, which combines the effects of the global changes in the heliospheric magnetic field magnitude with drifts to establish a realistic time-dependence, in the diffusion and drift coefficients, are used. We show that this model results in realistic cosmic ray modulation from the Ulysses launch (1990) until recently (2004) when compared to 2.5-GV electron and proton and 1.2-GV electron and Helium observations from this spacecraft. This approach is also applied to compute radial gradients present in 2.5-GV cosmic ray electron and protons in the inner heliosphere. The observed latitude dependence for both positive and negative charged particles during both the fast latitude scan periods, corresponding to different solar activity conditions, could also be realistically computed. For this an additional reduction in particle drifts (compared to diffusion) toward solar maximum is needed. This results in a realistic charge-sign dependent modulation at solar maximum and the model is also applied to predict charge-sign dependent modulation up to the next expected solar minimum.

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43

Schlickeiser, R., U. Dohle, R. C. Tautz, and A. Shalchi. "A New Type of Cosmic‐Ray Anisotropy from Perpendicular Diffusion. I. Modification of the Spatial Diffusion Tensor and the Diffusion‐Convection Cosmic‐Ray Transport Equation." Astrophysical Journal 661, no. 1 (May 20, 2007): 185–89. http://dx.doi.org/10.1086/514813.

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44

Giacinti, G., M. Kachelrieẞ, and D. V. Semikoz. "Reconciling cosmic ray diffusion with Galactic magnetic field models." Journal of Cosmology and Astroparticle Physics 2018, no. 07 (July 23, 2018): 051. http://dx.doi.org/10.1088/1475-7516/2018/07/051.

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Lerche, Ian, and R. C. Tautz. "Cosmic ray diffusion: Detailed investigation of a recent model." Physics of Plasmas 18, no. 8 (August 2011): 082305. http://dx.doi.org/10.1063/1.3625277.

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46

Beresnyak, A., H. Yan, and A. Lazarian. "NUMERICAL STUDY OF COSMIC RAY DIFFUSION IN MAGNETOHYDRODYNAMIC TURBULENCE." Astrophysical Journal 728, no. 1 (January 20, 2011): 60. http://dx.doi.org/10.1088/0004-637x/728/1/60.

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47

Uchaikin, V. V., and R. T. Sibatov. "Nonlocal relativistic diffusion (NoRD) model of cosmic ray propagation." Journal of Physics: Conference Series 798 (January 2017): 012029. http://dx.doi.org/10.1088/1742-6596/798/1/012029.

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48

Shadmehri, Mohsen. "Thermal instability and the effects of cosmic-ray diffusion." Monthly Notices of the Royal Astronomical Society 397, no. 3 (August 11, 2009): 1521–27. http://dx.doi.org/10.1111/j.1365-2966.2009.15047.x.

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49

Bieber, John W., and William H. Matthaeus. "Perpendicular Diffusion and Drift at Intermediate Cosmic‐Ray Energies." Astrophysical Journal 485, no. 2 (August 20, 1997): 655–59. http://dx.doi.org/10.1086/304464.

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50

Snodin, A. P., A. Brandenburg, A. J. Mee, and A. Shukurov. "Simulating field-aligned diffusion of a cosmic ray gas." Monthly Notices of the Royal Astronomical Society 373, no. 2 (December 1, 2006): 643–52. http://dx.doi.org/10.1111/j.1365-2966.2006.11034.x.

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