The diffusive motion of charged particles in synthetic magnetic turbulence with different properties is investigated by using numerical simulations with unprecedented dynamical range, which allow us to ensure that both the inertial range and the long wavelength part of the turbulent spectrum are properly described. This is of particular importance in evaluating previous suggestions that parallel and perpendicular diffusion coefficients differ in their energy dependence, an assertion at odds with the many claims of universality of the $D_{\perp}$ and $D_{\parallel}$ as functions of particle energy. Cases with and without an ordered magnetic field are discussed. Results of the numerical simulations are compared with available theoretical models, for slab, slab/2D and isotropic turbulence. We find widespread evidence that universality is broken, and that the ratio $D_{\perp}/D_{\parallel}$ is not independent of energy. The implications of this finding for the physics of cosmic ray transport are discussed in depth.
Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence w…
Astrophysical plasmas are turbulent and magnetized. The interaction between cosmic rays (CRs) and magnetohydrodynamic (MHD) turbulence is a fundamental astrophysical process. Based on the current understanding of MHD turbulence, we revisit the trapping of CRs by magnetic mirrors in the context of MHD turbulence. In compressible MHD turbulence, isotropic fast modes dominate both trapping and gyroresonant scattering of CRs. The presence of trapping significantly suppresses the pitch-angle scattering and the spatial diffusion of CRs along the magnetic field. The resulting parallel diffusion coeff…
Cosmic ray propagation is determined by the properties of interstellar turbulence. The multiphase nature of interstellar medium (ISM) and diversity of driving mechanisms give rise to spatial variation of turbulence properties. Meanwhile, precision astroparticle experiments pose challenges to the conventional picture of homogeneous and isotropic transport of cosmic rays (CRs). We are opening a new horizon for CR propagation research when studies of particle transport and interstellar turbulence confront each other. Here we review our recent developement on understandings of magnetohydrodynamic …
We study the damping from neutral-ion collisions of both incompressible and compressible magnetohydrodynamic (MHD) turbulence in partially ionized medium. We start from the linear analysis of MHD waves applying both single-fluid and two-fluid treatments. The damping rates derived from the linear analysis are then used in determining the damping scales of MHD turbulence. The physical connection between the damping scale of MHD turbulence and cutoff boundary of linear MHD waves is investigated. Our analytical results are shown to be applicable in a variety of partially ionized interstellar mediu…
Cosmic ray (CR) transport and acceleration is essential for many astrophysical problems, e.g., CMB foreground, ionization of molecular clouds and all high energy phenomena. Recent advances in MHD turbulence call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall address the issue of the transport of CRs, both parallel and perpendicular to the magnetic field and show that the issue of cosmic ray subdiffusion is…
We review some recent findings on diffusion of cosmic rays (CRs) in magnetohydrodynamic (MHD) turbulence obtained by adopting the numerically-tested model of MHD turbulence, including perpendicular superdiffusion of CRs, inefficient gyroresonant scattering by Alfvén and slow modes with scale-dependent turbulence anisotropy, resonance-broadened Transit Time Damping (TTD) interaction, and mirror diffusion. As the diffusion behavior of CRs strongly depends on the properties of MHD turbulence, theoretical modeling of CR diffusion, its numerical testing, and interpretation of CR-related observation…
The propagation of cosmic rays can be described as a diffusive motion in most galactic environments. High-energy gamma-rays measured by Fermi have allowed inference of a gradient in the cosmic-ray density and spectral energy behavior in the Milky Way, which is not predicted by models. Here, a turbulence-dependent diffusion model is used to probe different types of cosmic-ray diffusion tensors. Crucially, it is demonstrated that the observed gradients can be explained through turbulence-dependent energy-scaling of the diffusion tensor.
We study the nonlinear growth of kinetic gyroresonance instability of cosmic rays (CRs) induced by large scale compressible turbulence. This feedback of cosmic rays on turbulence was shown to induce an important scattering mechanism in addition to direct interaction with the compressible turbulence. The linear growth is bound to saturate due to the wave-particle interactions. By balancing increase of CR anisotropy via the large scale compression and its decrease via the wave-particle scattering, we find the steady state solutions. The nonlinear suppression due to the wave-particle scattering l…
This paper studies cosmic ray (CR) transport in magneto hydrodynamic (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…
The problem of cosmic-ray scattering in the turbulent electromagnetic fields of the interstellar medium and the solar wind is of great importance due to the variety of applications of the resulting diffusion coefficients. Examples are diffusive shock acceleration, cosmic-ray observations, and, in the solar system, the propagation of coronal mass ejections. In recent years, it was found that the simple diffusive motion that had been assumed for decades is often in disagreement both with numerical and observational results. Here, an overview is given of the interaction processes of cosmic rays a…
We study the role of local interstellar turbulence in shaping the large-scale anisotropy in the arrival directions of TeV-PeV cosmic-rays (CRs) on the sky. Assuming pitch-angle diffusion of CRs in a magnetic flux tube containing the Earth, we compute the CR anisotropy for Goldreich-Sridhar turbulence, and for isotropic fast modes. The narrow deficits in the 400 TeV and 2 PeV data sets of IceTop can be fitted for some parameters of the turbulence. The data also rule out a part of the parameter space. The shape of the CR anisotropy may be used as a local probe of the still poorly known propertie…
Alfvénic component of MHD turbulence damps Alfvénic waves. The consequences of this effect are important for many processes, from cosmic ray (CR) propagation to launching outflows and winds in galaxies and other magnetized systems. We discuss the differences in the damping of the streaming instability by turbulence and the damping of a plane parallel wave. The former takes place in the system of reference aligned with the local direction of magnetic field along which CRs stream. The latter is in the reference frame of the mean magnetic field and traditionally considered in plasma studies. We a…
As the fundamental physical process with many astrophysical implications, the diffusion of cosmic rays (CRs) is determined by their interaction with magnetohydrodynamic (MHD) turbulence. We consider the magnetic mirroring effect arising from MHD turbulence on the diffusion of CRs. Due to the intrinsic superdiffusion of turbulent magnetic fields, CRs with large pitch angles that undergo mirror reflection, i.e., bouncing CRs, are not trapped between magnetic mirrors, but move diffusively along the turbulent magnetic field, leading to a new type of parallel diffusion, i.e., mirror diffusion. This…
Cosmic ray (CR) transport and acceleration is determined by the properties of magnetic turbulence. Recent advances in MHD turbulence call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall address the issue of the transport of CRs, both parallel and perpendicular to the magnetic field. We shall demonstrate compressible fast modes are dominant cosmic ray scatterer from both quasilinear and nonlinear theories. W…
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 dependencies on the energy and the fluctuation amplitudes in the limit of wea…
In the standard picture of cosmic ray transport the propagation of charged cosmic rays through turbulent magnetic fields is described as a random walk with cosmic rays scattering on magnetic field turbulence. This is in good agreement with the highly isotropic cosmic ray arrival directions as this diffusion process effectively isotropizes the cosmic ray distribution. High-statistics observatories like IceCube and HAWC have however observed significant deviations from isotropy down to very small angular scales. This is in strong tension with this standard picture of cosmic ray propagation. Whil…
Cosmic-ray acceleration at non-relativistic shocks relies on scattering by turbulence that the cosmic rays drive upstream of the shock. We explore the rate of energy transfer from cosmic rays to non-resonant Bell modes and the spectral softening it implies. Accounting for the finite time available for turbulence driving at supernova-remnant shocks yields a smaller spectral impact than found earlier with steady-state considerations. Generally, for diffusion scaling with the Bohm rate by a factor $η$, the change in spectral index is at most $η$ divided by the Alfvénic Mach number of the thermal …
Recently a new transport theory of cosmic rays in magnetized space plasmas extending the quasilinear approximation to the particle orbit has been developed for the case of an axisymmetric incompressible magnetic turbulence. Here we generalize the approach to the important physical case of a compressible plasma. As previously obtained in the case of an incompressible plasma we allow arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field. For the case of quasi-stationary and spatially homogeneous magnetic turbulence we derive in the small Larmor radius ap…
We revisit propagation of galactic cosmic rays (CRs) in light of recent advances in CR diffusion theory in realistic interstellar turbulence. We use a tested model of turbulence in which it has been shown that fast modes dominate scattering of CRs. As a result, propagation becomes inhomogeneous and environment dependent. By adopting the formalism of the nonlinear theory developed by Yan & Lazarian, we calculate the diffusion of CRs self-consistently from first principles. We assume a two- phase model for the Galaxy to account for different damping mechanisms of the fast modes, and we find that…
We make quantitative estimates of the power supplied to the Galactic cosmic ray population by second-order Fermi acceleration in the interstellar medium, or as it is usually termed in cosmic ray propagation studies, diffusive reacceleration. Using recent results on the local interstellar spectrum from the Voyager missions we show that for parameter values, in particular the Alfvén speed, typically used in propagation codes such as Galprop to fit the B/C ratio, the power contributed by diffusive reacceleration is significant and can be of order 50\% of the total Galactic cosmic ray power. The i…
Revisiting the role of cosmic-ray driven Alfvén waves in pre-existing magnetohydrodynamic turbulence. I. Turbulent damping rates and feedback on background fluctuations
We calculate the shape of the large-scale anisotropy of TeV-PeV cosmic-rays (CR) in different models of the interstellar turbulence. In general, the large-scale CR anisotropy (CRA) is not a dipole, and its shape can be used as a new probe of the turbulence. The 400 TeV and 2 PeV data sets of IceTop can be fitted with Goldreich-Sridhar turbulence and a broad resonance function, but other possibilities are not excluded. We then present our first numerical calculations of the CRA down to 3 TeV energies in 3D isotropic Kolmogorov turbulence. At these low energies, the large-scale CRA aligns well w…
This paper considers turbulent damping of Alfven waves in magnetized plasmas. We identify two cases of damping, one related to damping of cosmic rays streaming instability, the other related to damping of Alfven waves emitted by a macroscopic wave source, e.g. stellar atmosphere. The physical difference between the two cases is that in the former case the generated waves are emitted in respect to the local direction of magnetic field, in the latter in respect to the mean field. The scaling of damping is different in the two cases. We the regimes of turbulence ranging from subAlfvenic to superA…
We calculate the large-scale cosmic-ray (CR) anisotropies predicted for a range of Goldreich-Sridhar (GS) and isotropic models of interstellar turbulence, and compare them with IceTop data. In general, the predicted CR anisotropy is not a pure dipole; the cold spots reported at 400 TeV and 2 PeV are consistent with a GS model that contains a smooth deficit of parallel-propagating waves and a broad resonance function, though some other possibilities cannot, as yet, be ruled out. In particular, isotropic fast magnetosonic wave turbulence can match the observations at high energy, but cannot acco…
Cosmic rays propagating in the Galaxy may excite a streaming instability when their motion is super-alfvenic, thereby producing the conditions for their own diffusion. We present the results of a self-consistent solution of the transport equation where diffusion occurs because of the self-generated turbulence together with a preexisting turbulence injected, for instance, by supernova explosions and cascading to smaller scales. All chemicals are included in our calculations, so that we are able to show the secondary to primary ratios in addition to the spectra of the individual elements. All pr…
Recent gamma-ray observations reveal inhomogeneous diffusion of cosmic rays (CRs) in the interstellar medium (ISM). This is expected as the diffusion of CRs depends on the properties of turbulence, which can vary widely in the multi-phase ISM. We focus on the mirror diffusion arising in highly compressible turbulence in molecular clouds (MCs) around supernova remnants (SNRs), where the magnetic mirroring effect results in significant suppression of diffusion of CRs near CR sources. Significant energy loss via proton-proton interactions due to slow diffusion flattens the low-energy CR spectrum,…
The transport of charged energetic particles in the presence of strong intermittent heliospheric turbulence is computationally analyzed based on known properties of the interplanetary magnetic field and solar wind plasma at 1 Astronomical Unit (AU). The turbulence is assumed to be static, composite, and quasi-three-dimensional with a varying energy distribution between a one-dimensional Alfvénic (slab) and a structured two-dimensional component. The spatial fluctuations of the turbulent magnetic field are modeled either as homogeneous with a Gaussian probability distribution function (PDF), or…
We show that the complex shape of the cosmic ray (CR) spectrum, as recently measured by PAMELA and inferred from Fermi-LAT gamma-ray observations of molecular clouds in the Gould belt, can be naturally understood in terms of basic plasma astrophysics phenomena. A break from a harder to a softer spectrum at blue rigidity R\simeq 10 GV follows from a transition from transport dominated by advection of particles with Alfven waves to a regime where diffusion in the turbulence generated by the same CRs is dominant. A second break at R\simeq 200 GV happens when the diffusive propagation is no longer…
The interaction of magnetic turbulence and relativistic particles is a important process for understanding particles propagation and acceleration in many astrophysical environments. Large-scale turbulence can be generated in the intra-cluster-medium (ICM) during mergers between galaxy clusters and affects their non-thermal properties. Giant radio halos, Mpc-scale synchrotron sources observed in merging clusters, may probe the connection between turbulence and non-thermal cluster-scale emission. After discussing relevant aspects of the physics of turbulence and turbulent acceleration in the ICM…
Recent advances in both the MHD turbulence theory and cosmic ray observations call for revisions in the paradigm of cosmic ray transport. We use the models of magnetohydrodynamic turbulence that were tested in numerical simulation, in which turbulence is injected at large scale and cascades to to small scales. We shall present the nonlinear results for cosmic ray transport, in particular, the cross field transport of CRs and demonstrate that the concept of cosmic ray subdiffusion in general does not apply and the perpendicular motion is well described by normal diffusion with M_A^4 dependence.…
Context. Supernova remnants are known as sources of galactic cosmic rays for their non-thermal emission of radio waves, X-rays, and gamma-rays. However, the observed soft broken power-law spectra are hard to reproduce within standard acceleration theory based on the assumption of Bohm diffusion and steady-state calculations. Aims. We point out that a time-dependent treatment of the acceleration process together with a self-consistent treatment of the scattering turbulence amplification is necessary. Methods. We numerically solve the coupled system of transport equations for cosmic rays and iso…
In order for diffusive shock acceleration (DSA) to accelerate particles to high energies, the energetic particles must be able to interact with magnetic turbulence over a broad wavelength range. The weakly anisotropic distribution of accelerated particles, i.e., cosmic rays (CRs), is believed capable of producing this turbulence in a symbiotic relationship where the magnetic turbulence required to accelerate the CRs is created by the accelerated CRs themselves. In efficient DSA, this wave-particle interaction can be strongly nonlinear where CRs modify the plasma flow and the specific mechanism…
We propose a novel model to produce ultrahigh-energy cosmic-rays (UHECRs) in gamma-ray burst jets. After the prompt gamma-ray emission, hydrodynamical turbulence is excited in the GRB jets at or before the afterglow phase. The mildly relativistic turbulence stochastically accelerates protons. The acceleration rate is much slower than the usual first-order shock acceleration rate, but in this case it can be energy-independent. The resultant UHECR spectrum is so hard that the bulk energy is concentrated in the highest energy range, resulting in a moderate requirement for the typical cosmic ray l…
In the energy range from ~ 10^12 eV to ~ 10^15 eV, the Galactic cosmic ray flux has anisotropies both on large scales, with an amplitude of the order of 0.1%, and on scales between ~ 10 and ~ 30 degrees, with amplitudes smaller by a factor of a few. With a diffusion coefficient inferred from Galactic cosmic ray chemical abundances, the diffusion approximation predicts a dipolar anisotropy of comparable size, but does not explain the smaller scale anisotropies. We demonstrate here that energy dependent smaller scale anisotropies naturally arise from the local concrete realization of the turbule…
Low-energy cosmic rays, in particular protons with energies below 1 GeV, are significant drivers of the thermochemistry of molecular clouds. However, these cosmic rays are also greatly impacted by energy losses and magnetic field transport effects in molecular gas. Explaining cosmic ray ionization rates of $10^{-16}$ s$^{-1}$ or greater in dense gas requires either a high external cosmic ray flux, or local sources of MeV-GeV cosmic ray protons. We present a new local source of low-energy cosmic rays in molecular clouds: first order Fermi-acceleration of protons in regions undergoing turbulent …
Cosmic rays propagating in the Galaxy may excite a streaming instability when their motion is super-alfvenic, thereby producing the conditions for their own diffusion. In this paper we present the results of a self-consistent solution of the transport equation where diffusion occurs because of the self-generated turbulence together with a pre-existing turbulence injected, for instance, by supernova explosions and cascading to smaller scales. All chemicals are included in our calculations, so that we are able to show the secondary to primary ratios in addition to the spectra of the individual e…
Observations have shown that spatially extended "TeV halos" are a common (and potentially generic) feature surrounding young and middle-aged pulsars. However, their morphology is not understood. They are larger than the "compact" region where the stellar remnant dominates the properties of the interstellar medium, but smaller than expected in models of cosmic-ray diffusion through the standard interstellar medium. Several explanations have been proposed, but all have shortcomings. Here, we revisit a class of models where the cosmic-ray gradient produced by the central source induces a streamin…
Galactic cosmic rays are believed to be mostly accelerated at supernova shocks. However, the interstellar magnetic field is too weak to efficiently accelerate galactic cosmic rays up to the highest energies, i.e. $10^{15}$ eV. A stronger magnetic field in the pre-shock region could provide the efficiency required. Bell's cosmic-ray nonresonant streaming instability has been claimed to be responsible for the amplification of precursor magnetic fields. However, an alternative mechanism has been proposed in which the cosmic-ray pressure gradient forms the shock precursor and drives turbulence, am…
We have performed magnetohydrodynamical simulations to study the amplification of magnetic fields in the precursors of shock waves. Strong magnetic fields are required in the precursors of the strong shocks that occur in supernova remnants. Observations also suggest that magnetic field amplification takes place in the weak shocks that occur in galaxy clusters and that produce so-called radio relics. Here, we extend the study of magnetic field amplification by cosmic-ray driven turbulence to weak shocks. The amplification is driven by turbulence that is produced by the cosmic-ray pressure actin…
Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfvén, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show h…
The diffusive paradigm for the transport of Galactic cosmic rays is central to our understanding of the origin of these high energy particles. However, it is worth recalling that the normalization, energy dependence, and spatial extent of the diffusion coefficient in the interstellar medium are fitted to the data and typically are not derived from more basic principles. Here, we discuss a scenario in which the diffusion properties of cosmic rays are derived from a combination of wave self-generation and advection from the Galactic disc, where the sources of cosmic rays are assumed to be locate…
We show that an alpha effect is driven by the cosmic ray Bell instability exciting left-right asymmetric turbulence. Alfven waves of a preferred polarization have maximally helical motion, because the transverse motion of each mode is parallel to its curl. We show how large-scale Alfven modes, when rendered unstable by cosmic ray streaming, can create new net flux over any finite region, in the direction of the original large-scale field. We perform direct numerical simulations (DNS) of an MHD fluid with a forced cosmic ray current and use the test-field method to determine the alpha effect an…
Cosmic-ray transport in astrophysical environments is often dominated by the diffusion of particles in a magnetic field composed of both a turbulent and a mean component. This process, which is two-fold turbulent mixing in that the particle motion is stochastic with respect to the field lines, needs to be understood in order to properly model cosmic-ray signatures. One of the most important aspects in the modeling of cosmic-ray diffusion is that fully resonant scattering, the most effective such process, is only possible if the wave spectrum covers the entire range of propagation angles. By ta…
We propose a model for Diffusive Shock Acceleration (DSA) in which stochastic magnetic fields in the shock precursor are generated through purely fluid mechanisms of a so-called small-scale dynamo. This contrasts with previous DSA models that considered magnetic fields amplified through cosmic ray streaming instabilities; i.e., either by way of individual particles resonant scattering in the magnetic fields, or by macroscopic electric currents associated with large-scale cosmic ray streaming. Instead, in our picture, the solenoidal velocity perturbations that are required for the dynamo to wor…
The magnetic fields associated with young stellar objects are expected to have an hour-glass geometry, i.e., the magnetic field lines are pinched as they thread the equatorial plane surrounding the forming star but merge smoothly onto a background field at large distances. With this field configuration, incoming cosmic rays experience both a funneling effect that acts to enhance the flux impinging on the circumstellar disk and a magnetic mirroring effect that acts to reduce that flux. To leading order, these effects nearly cancel out for simple underlying magnetic field structures. However, th…
The presence of relativistic particles at the center of our galaxy is evidenced by the diffuse TeV emission detected from the inner $\sim$$2^\circ$ of the Galaxy. Although it is not yet entirely clear whether the origin of the TeV photons is due to hadronic or leptonic interactions, the tight correlation of the intensity distribution with the distribution of molecular gas along the Galactic ridge strongly points to a pionic-decay process involving relativistic protons. In earlier work, we concluded that point-source candidates, such as the supermassive black hole Sagittarius A* (identified wit…
Understanding the time scales for diffusive processes and their degree of anisotropy is essential for modelling cosmic-ray transport in turbulent magnetic fields. We show that the diffusion time scales are isotropic over a large range of energy and turbulence levels, notwithstanding the high degree of anisotropy exhibited by the components of the diffusion tensor for cases with an ordered magnetic field component. The predictive power of the classical scattering relation as a description for the relation between the parallel and perpendicular diffusion coefficients is discussed and compared to…
Using test-particle simulations, we investigate the temporal dependence of the two-point velocity correlation function for charged particles scattering in a time-independent spatially fluctuating magnetic field derived from a three-dimensional isotropic turbulence power spectrum. Such a correlation function allowed us to compute the spatial coefficients of diffusion both parallel and perpendicular to the average magnetic field. Our simulations confirm the dependence of the perpendicular diffusion coefficient on turbulence energy density and particle energy predicted previously by a model for e…
