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 and turbulent electromagnetic fields. First, the formation of turbulent fields due to plasma instabilities is treated, where especially the non-linear behavior of the resulting unstable wave modes is discussed. Second, the analytical and the numerical side of high-energy particle propagation will be reviewed by presenting non-linear analytical theories and Monte-Carlo simulations. For the example of the solar wind, the impact of anisotropic and dynamical turbulence models will be discussed. In addition, it will be shown how further complications can be treated that arise from the large-scale magnetic field geometry and turbulent electric fields. The transport properties of energetic particles can thus be calculated for current turbulence models so that they withstand a comparison with measurements taken in the solar wind.
This work provides a concrete implementation of E. Fermi's model of particle acceleration in magnetohydrodynamic (MHD) turbulence, connecting the rate of energization to the gradients of the velocity of magnetic field lines, which it characterizes within a multifractal picture of turbulence intermittency. It then derives a transport equation in momentum space for the distribution function. This description is shown to be substantiated by a large-scale numerical simulation of strong MHD turbulence. The present, general framework can be used to model particle acceleration in a variety of environ…
This whitepaper was submitted to the 2019-2020 APS-DPP-CPP (American Physical Society Division of Plasma Physics Community Planning Process) on plasma discovery science. It highlights the need for diverse computational approaches including global and local models, as well as the need for a hierarchy of physics models in complex and multi-scale magnetically and flow-dominated astrophysical systems. Examples of turbulent small-scale vs. large-scale dynamos and turbulent vs. ordered zonal flows in such systems are discussed.
Alfvénic-type turbulence in strongly magnetized, low-beta pair plasmas is investigated. A coupled set of equations for the evolution of the magnetic and flow potentials are derived, covering both fluid and kinetic scales. In the fluid (MHD) range those equations are the same as for electron-ion plasmas, so turbulence at those scales is expected to be of the Alfvénic nature, exhibiting critical balance, dynamic alignment, and transition to a tearing mediated regime at small scales. The critical scale at which a transition to a tearing-mediated range occurs is derived, and the spectral slope in …
Particle Acceleration in Magnetized Shear-Driven Turbulence
University of Michigan（密歇根大学）；University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；Princeton University（普林斯顿大学）；University of Chicago（芝加哥大学）；University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）
We propose that pressure anisotropy causes weakly collisional turbulent plasmas to self-organize so as to resist changes in magnetic-field strength. We term this effect "magneto-immutability" by analogy with incompressibility (resistance to changes in pressure). The effect is important when the pressure anisotropy becomes comparable to the magnetic pressure, suggesting that in collisionless, weakly magnetized (high-$β$) plasmas its dynamical relevance is similar to that of incompressibility. Simulations of magnetized turbulence using the weakly collisional Braginskii model show that magneto-im…
A high concentration of ultra-high-energy cosmic ray (UHECR) events, called a hotspot, was reported by the Telescope Array (TA) experiment, but its origin still remains unsolved. One of the obstacles is that there is no astronomical object, which could be the source, behind the TA hotpot. In an effort to understand the origin of the TA hotspot, we suggested a model based on the magnetized cosmic web structure. The UHECRs were produced from sources in the Virgo cluster and were initially confined by cluster magnetic fields for a certain period. Next, some of them preferentially escaped to and p…
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…
Large-scale extragalactic magnetic fields may induce conversions between very-high-energy photons and axionlike particles (ALPs), thereby shielding the photons from absorption on the extragalactic background light. However, in simplified "cell" models, used so far to represent extragalactic magnetic fields, this mechanism would be strongly suppressed by current astrophysical bounds. Here we consider a recent model of extragalactic magnetic fields obtained from large-scale cosmological simulations. Such simulated magnetic fields would have large enhancement in the filaments of matter. As a resu…
Structure formation shocks are believed to be the largest accelerators of cosmic rays in the Universe. However, little is still known about their efficiency in accelerating relativistic electrons and protons as a function of their magnetization properties, i.e. of their magnetic field strength and topology. In this work, we analyzed both uniform and adaptive mesh resolution simulations of large-scale structures with the magnetohydrodynamical grid code Enzo, studying the dependence of shock obliquity with different realistic scenarios of cosmic magnetism. We found that shock obliquities are mor…
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 use a global magnetohydrodynamic simulation of a geometrically thin accretion disk to investigate the locality and detailed structure of turbulence driven by the magnetorotational instability (MRI). The model disk has an aspect ratio $H / R \simeq 0.07$, and is computed using a higher-order Godunov MHD scheme with accurate fluxes. We focus the analysis on late times after the system has lost direct memory of its initial magnetic flux state. The disk enters a saturated turbulent state in which the fastest growing modes of the MRI are well-resolved, with a relatively high efficiency of angula…
We conduct global galactic--scale magnetohydrodynamical (MHD) simulations of the cosmic--ray driven dynamo. We assume that exploding stars deposit small--scale, randomly oriented, dipolar magnetic fields into the differentially rotating ISM, together with a portion of cosmic rays, accelerated in supernova shocks. Our simulations are performed with the aid of a new parallel MHD code PIERNIK. We demonstrate that dipolar magnetic fields supplied on small SN--remnant scales, can be amplified exponentially by the CR--driven dynamo to the present equipartition values, and transformed simultaneously …
Collisionless, magnetized turbulence offers a promising framework for the generation of non-thermal high-energy particles in various astrophysical sites. Yet, the detailed mechanism that governs particle acceleration has remained subject to debate. By means of 2D and 3D PIC, as well as 3D (incompressible) magnetohydrodynamic (MHD) simulations, we test here a recent model of non-resonant particle acceleration in strongly magnetized turbulence~\cite{2021PhRvD.104f3020L}, which ascribes the energization of particles to their continuous interaction with the random velocity flow of the turbulence, …
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…
Astrophysical fluids are turbulent, magnetized and frequently partially ionized. As an example of astrophysical turbulence, the interstellar turbulence extends over a remarkably large range of spatial scales and participates in key astrophysical processes happening in different ranges of scales. A significant progress has been achieved in the understanding of the magnetohydrodynamic (MHD) turbulence since the turn of the century, and this enables us to better describe turbulence in magnetized and partially ionized plasmas. In fact, the modern revolutionized picture of the MHD turbulence physic…
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…
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…
(Abridged) X-ray observations of synchrotron rims in supernova remnant (SNR) shocks show evidence of strong magnetic field amplification (a factor of ~100 between the upstream and downstream medium). This amplification may be due to plasma instabilities driven by shock-accelerated cosmic rays (CRs). One candidate is the cosmic ray current-driven (CRCD) instability (Bell 2004), caused by the electric current of large Larmor radii CRs propagating parallel to the upstream magnetic field. Particle-in-cell (PIC) simulations have shown that the back-reaction of the amplified field on CRs would limit…
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 …
Radio, X-ray and infrared observations of the inner few hundred pc of the Galactic center have highlighted two characteristics to the ISM. The cosmic ray ionization rate derived from molecular ions such as H$^+_3$, is at least two to three orders of magnitudes higher than in the Galactic disk. The other is bipolar X-ray and radio emission away from the Galactic plane. These features are consistent with a scenario in which high cosmic ray pressure drives large-scale winds away from the Galactic plane. The interaction of such a wind with stellar wind bubbles may explain the energetic nonthermal …
Charged particles at the crust of compact stars may be ejected and accelerated by the electric field generated due to the rotation of the magnetized star. For neutron or hybrid stars, the negatively charged particles are usually electrons, and the positively charged particles are mainly protons and Iron. Whereas the existence of strange stars also includes the possibility of ejection of strangelets from the star surface. The flux of such strangelets emitted from all known pulsars is in the range of $10^9-10^{10}$ GeV. Therefore, such massive strangelets can be one of the candidates for the sou…
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…
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 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…
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…
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…
Molecular clouds are complex magnetized structures, with variations over a broad range of length scales. Ionization in dense, shielded clumps and cores of molecular clouds is thought to be caused by charged cosmic rays (CRs). These CRs can also contribute to heating the gas deep within molecular clouds, and their effect can be substantial in environments where CRs are abundant. CRs propagate predominantly by diffusion in media with disordered magnetic fields. The complex magnetic structures in molecular clouds therefore determine the propagation and spatial distribution of CRs within them, and…
We use adaptive-mesh magnetohydrodynamic simulations to study the effect of magnetic fields on ram pressure stripping of galaxies in the intracluster medium (ICM). Although the magnetic pressure in typical clusters is not strong enough to affect the gas mass loss rate from galaxies, magnetic fields can affect the morphology of stripped galaxies. ICM magnetic fields are draped around orbiting galaxies and aligned with their stripped tails. Magnetic fields suppress shear instabilities at the galaxy-ICM interface, and magnetized tails are smoother and narrower than tails in comparable hydrodynami…
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…
Both global dynamics and turbulence in magnetized weakly collisional cosmic plasmas are described by general magnetofluid equations that contain pressure anisotropies and heat fluxes that must be calculated from microscopic plasma kinetic theory. It is shown that even without a detailed calculation of the pressure anisotropy or the heat fluxes, one finds the macroscale dynamics to be generically unstable to microscale Alfvenically polarized fluctuations. Two instabilities are considered in detail: the parallel firehose instability (including the finite-Larmor-radius effects that determine the …
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…
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…
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…
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 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…
A subcritical transition to turbulence in magnetized Keplerian shear flows is investigated using a statistical approach. Three-dimensional numerical simulations of the shearing box equations with zero net magnetic flux are employed to determine the transition from decaying to sustained turbulence as a function of the magnetic Reynolds number Rm. The results reveal no clear transition to sustained turbulence as the average lifetime of the transients grows as an exponential function of Rm, in accordance with a type-II supertransient law.
