In this chapter, we review some features of particle acceleration in astrophysical jets. We begin by describing four observational results relating to the topic, with particular emphasis on jets in active galactic nuclei and parallels between different sources. We then discuss the ways in which particles can be accelerated to high energies in magnetised plasmas, focusing mainly on shock acceleration, second-order Fermi and magnetic reconnection; in the process, we attempt to shed some light on the basic conditions that must be met by any mechanism for the various observational constraints to be satisfied. We describe the limiting factors for the maximum particle energy and briefly discuss multimessenger signals from neutrinos and ultrahigh energy cosmic rays, before describing the journey of jet plasma from jet launch to cocoon with reference to the different acceleration mechanisms. We conclude with some general comments on the future outlook.
The results of MHD numerical simulations of the formation and development of magnetized jets are presented. Similarity criteria for comparisons of the results of laboratory laser experiments and numerical simulations of astrophysical jets are discussed. The results of laboratory simulations of jets generated in experiments at the Neodim laser installation are presented.
In this review, analytical results obtained for a wide class of stationary axisymmetric flows in the vicinity of compact astrophysical objects are analyzed, with an emphasis on quantitative predictions for specific sources. Recent years have witnessed a great increase in understanding the formation and properties of astrophysical jets. This is due not only to new observations but also to advances in analytical theory which has produced fairly simple relations, and to what can undoubtedly be called a breakthrough in numerical simulation which has enabled confirmation of theoretical predictions.…
We review the plasma phenomenology in the astrophysical sources which show appreciable radio emissions, namely Radio-Jets from Pulsars, Microquasars, Quasars and Radio-Active Galaxies. A description of their basic features is presented, then we discuss in some details the links between their morphology and the mechanisms that lead to the different radio-emissions, investigating especially the role played by the plasma configurations surrounding compact objects (Neutron Stars, Black Holes). For the sake of completeness, we briefly mention observational techniques and detectors, whose structure …
Jets, collimated outflows of particles and fields, are observed in a wide variety of astrophysical systems, including Active Galactic Nuclei of various types, microquasars, gamma-ray bursts, and young stellar objects. Despite intensive efforts along several decades of observational and theoretical research, there are still many uncertainties and open questions related to how jets are produced and what is their composition. In this review I offer an outline of some current views on the content and basic properties of astrophysical jets.
We report new experimental results obtained on three different laser facilities that show directed laser-driven relativistic electron-positron jets with up to 30 times larger yields than previously obtained and a quadratic (~ E^2) dependence of the positron yield on the laser energy. This favorable scaling stems from a combination of higher energy electrons due to increased laser intensity and the recirculation of MeV electrons in the mm-thick target. Based on this scaling, first principles simulations predict the possibility of using such electron-positron jets, produced at upcoming high-ener…
Relativistic magnetized jets from active galaxies are among the most powerful cosmic accelerators, but their particle acceleration mechanisms remain a mystery. We present a new acceleration mechanism associated with the development of the helical kink instability in relativistic jets, which leads to the efficient conversion of the jet's magnetic energy into nonthermal particles. Large-scale three-dimensional ab initio simulations reveal that the formation of highly tangled magnetic fields and a large-scale inductive electric field throughout the kink-unstable region promotes rapid energization…
The use of Z-pinch facilities makes it possible to carry out well-controlled and diagnosable laboratory experiments to study laboratory jets with scaling parameters close to those of the jets from young stars. This makes it possible to observe processes that are inaccessible to astronomical observations. Such experiments are carried out at the PF-3 facility ("plasma focus", Kurchatov Institute), in which the emitted plasma emission propagates along the drift chamber through the environment at a distance of one meter. The paper presents the results of experiments with helium, in which a success…
Magnetized jets in GRBs and AGNs are thought to be efficient accelerators of particles, however, the process responsible for the acceleration is still a matter of active debate. In this work, we study the kink-instability in non-rotating force-free jets using first-principle particle-in-cell simulations. We obtain similar overall evolution of the instability as found in MHD simulations. The instability first generates large scale current sheets, which at later times break up into small-scale turbulence. Reconnection in these sheets proceeds in the strong guide field regime, which results in a …
A laboratory simulation of astrophysical processes is one of the intensively developed areas of plasma physics. A new series of experiments has been launched recently on the Plasma Focus type facility in NRC Kurchatov Institute. The main goal is to study the mechanisms of the jet stabilization, due to which it can propagate at distances much greater than their transverse dimensions. The experiments with stationary gas filling revealed regimes in which a narrowly collimated plasma jet was formed, the head of which was no wider than several centimeters at jet propagation distances of up to 100 c…
The conservation of the energy flux in turbulent jets which propagate in the intergalactic medium (IGM) allows deducing the law of motion in the classical and relativistic cases. Three types of IGM are considered: constant density, hyperbolic and inverse power law decrease of density. An analytical law for the evolution of the magnetic field along the radio-jets is deduced using a linear relation between the magnetic pressure and the rest density. Astrophysical applications are made to the centerline intensity of synchrotron emission in NGC315 and to the magnetic field of 3C273.
We study a possible mechanism for astrophysical jet production from a neutron star composed by a partially bosonized npe-gas. We obtain that the expulsion of a stable stream of matter might be triggered by the quantum magnetic collapse of one or various components of the gas, while its collimation is due to the formation of a strong self-generated magnetic field.
Broadband emission from relativistic outflows (jets) of active galactic nuclei (AGN) and gamma-ray bursts (GRBs) contains valuable information about the nature of the jet itself, and about the central engine which launches it. Using special relativistic hydrodynamics and magnetohydronamics simulations we study the dynamics of the jet and its interaction with the surrounding medium. The observational signature of the simulated jets is computed using a radiative transfer code developed specifically for the purpose of computing multi-wavelength, time-dependent, non-thermal emission from astrophys…
The composition of the astrophysical relativistic jets remains uncertain. By kinetic particle-in-cell simulations, we show that the baryon component in the jet, or the so-called baryon loading effect (BLE), heavily affects relativistic jets transport dynamics in the interstellar medium. On the one hand, with the BLE, relativistic jets can transport in a much longer distance, because jet electrons draw a significant amount of energy from jet baryons via the Buneman-induced electrostatic waves and the Weibel-mediated collisionless shock; on the other hand, the jet electron phase space distributi…
This is a brief review of the recent developments in the theory of magnetic acceleration of relativistic jets. We attempt to explain the key results of this complex theory using basic physical arguments and simple calculations. The main focus is on the standard model, which describes steady-state axisymmetric ideal MHD flows. We argue that this model is over-restrictive and discuss various alternatives.
We investigate the self-consistent particle acceleration physics associated with the development of the kink instability (KI) in nonrelativistic, electron-ion plasma jets. Using 3D fully kinetic particle-in-cell (PIC) simulations, we show that the KI efficiently converts the initial toroidal magnetic field energy into energetic ions. The accelerated ions form a nonthermal power-law tail in the energy spectrum, containing $\simeq10\%$ of the initial magnetic field energy, and with the maximum ion energy extending to the confinement energy of the jet. We find that the ions are efficiently accele…
One of the fundamental properties of astrophysical magnetic fields is their ability to change topology through reconnection and in doing so, to release magnetic energy, sometimes violently. In this work, we review recent results on the role of magnetic reconnection and associated heating and particle acceleration in jet/accretion disk systems, namely young stellar objects (YSOs), microquasars, and active galactic nuclei (AGNs).
Jets are found in a variety of astrophysical sources, from young stellar objects to active galactic nuclei. In all the cases the jet propagates with a supersonic velocity through the external medium, which can be inhomogeneous, and inhomogeneities could penetrate into the jet. The interaction of the jet material with an obstacle produces a bow shock in the jet in which particles can be accelerated up to relativistic energies and emit high-energy photons. In this work, we explore the active galactic nuclei scenario, focusing on the dynamical and radiative consequences of the interaction at diff…
Dissipation and particle acceleration in astrophysical jets with velocity and magnetic shear: Interaction of Kelvin-Helmholtz and Drift-Kink Instabilities
A brief white paper is provided, discussing how the particle acceleration mechanisms taking place within astrophysical sources may mimic or mask signatures of new physics and the role that will be played by next-generation gamma-ray observatories, such as the Cherenkov Telescope Array, in improving our understanding of these phenomena.
The origin of the extended X-ray emission in the large-scale jets of active galactic nuclei (AGNs) poses challenges to conventional models of acceleration and emission. Although the electron synchrotron radiation is considered the most feasible radiation mechanism, the formation of the continuous large-scale X-ray structure remains an open issue. As astrophysical jets are expected to exhibit some turbulence and shearing motion, we here investigate the potential of shearing flows to facilitate an extended acceleration of particles and evaluate its impact on the resultant particle distribution. …
In this paper, we investigate the acceleration in relativistic jets of high-energy proton preaccelerated in the magnetosphere of a supermassive black hole. The proton reaches maximum energy when passing the total potential difference of $U$ between the jet axis and its periphery. This voltage is created by a rotating black hole and transmitted along magnetic field lines into the jet. It is shown that the trajectories of proton in the jet are divided into three groups: untrapped, trapped and not accelerated. Untrapped particles are not kept by poloidal and toroidal magnetic fields inside the je…
The Particle-In-Cell (PIC) method has been developed by Oscar Buneman, Charles Birdsall, Roger W. Hockney, and John Dawson in the 1950s and, with the advances of computing power, has been further developed for several fields such as astrophysical, magnetospheric as well as solar plasmas and recently also for atmospheric and laser-plasma physics. Currently more than 15 semi-public PIC codes are available which we discuss in this review. Its applications have grown extensively with increasing computing power available on high performance computing facilities around the world. These systems allow…
X-ray observations of kilo-parsec scale jets indicate that a synchrotron origin of the sustained non-thermal emission is likely. This requires distributed acceleration of electrons up to near PeV energies along the jet. The underlying acceleration mechanism is still unclear. Shear acceleration is a promising candidate, as velocity-shear stratification is a natural consequence of the collimated flow of a jet. We study the details of shear acceleration by solving the steady-state Fokker-Planck-type equation and provide a simple general solution for trans-relativistic jets for a range of magnetoh…
We study the acceleration of ultra-high-energy cosmic rays (UHECRs) at FR-II radio galaxies by performing Monte Carlo simulations for the transport, scattering, and energy change of the CR particles injected into the time-evolving jet flows that are realized through relativistic hydrodynamic (RHD) simulations. Toward that end, we adopt physically motivated models for the magnetic field and particle scattering. By identifying the primary acceleration process among diffusive shock acceleration (DSA), turbulent shear acceleration (TSA), and relativistic shear acceleration (RSA), we find that CRs …
Astrophysical accretion is arguably the most prevalent physical process in the Universe; it occurs during the birth and death of individual stars and plays a pivotal role in the evolution of entire galaxies. Accretion onto a black hole, in particular, is also the most efficient mechanism known in nature, converting up to 40% of accreting rest mass energy into spectacular forms such as high-energy (X-ray and gamma-ray) emission and relativistic jets. Whilst magnetic fields are thought to be ultimately responsible for these phenomena, our understanding of the microphysics of MHD turbulence in ac…
Ejections from the Sun can be observed with a higher resolution than in any other astrophysical object: can we build up on solar results and apply them to astrophysical objects? Aim of this work is to establish whether there is any analogy between solar ejections and ejections in microquasars and AGNs. Briefly reviewing jets properties from these objects and from the Sun, we point out some characteristics they share and indicate research areas where cross-breeeding between astrophysical and solar research is likely to be productive. Preliminary results of this study suggest, for instance, that…
This paper studies acceleration processes of background thermal electrons in X-ray binary jets via turbulent stochastic interactions and shock collisions. By considering turbulent magnetized jets mixed with fluctuation magnetic fields and ordered, large-scale one, and numerically solving the transport equation along the jet axis, we explore the influence of such as magnetic turbulence, electron injections, location of an acceleration region, and various cooling rates on acceleration efficiency. The results show that (1) the existence of the dominant turbulent magnetic fields in the jets is nec…
The paper presents the results of numerical simulation of the propagation of a sequence of plasma knots in laboratory conditions and the astrophysical environment. The physical and geometric parameters of the simulation have been chosen close to the parameters of the PF-3 facility (Kurchatov Institute) and the jet of the star RW Aur. We found that the low-density region formed after the first knot propagation plays an important role for collimation of the subsequent ones. Assuming only the thermal expansion of the subsequent emissions, qualitative estimates of the time taken to fill this area …
Observations of relativistic jets from black holes systems suggest that particle acceleration often occurs at fixed locations within the flow. These sites could be associated with critical points that allow the formation of standing shock regions, such as the magnetosonic modified fast point. Using the self-similar formulation of special relativistic magnetohydrodynamics by Vlahakis & Königl, we derive a new class of flow solutions that are both relativistic and cross the modified fast point at a finite height. Our solutions span a range of Lorentz factors up to at least 10, appropriate for mo…
Espresso is a novel acceleration model for Ultra-High-Energy Cosmic Rays (UHECRs), where lower-energy CRs produced in supernova remnants experience a one-shot reacceleration in the relativistic jets of powerful Active Galactic Nuclei (AGNs) to reach energies up to $10^{20}$ eV. To test the espresso framework, we follow UHECR acceleration bottom-up from injection to the highest energies by propagating 100,000 particles in realistic 3D magneto-hydrodynamic (MHD) simulations of ultra-relativistic jets. We find that simulations agree well with analytical expectations in terms of trajectories of in…
Diverging supersonic flows are accelerating, as in the case of a de Laval nozzle, and the same concept has been applied for acceleration of magnetohydrodynamic flows in the universe. Here, we study the dynamics of "non-diverging" cylindrical supersonic flows and show that they can be accelerated by effects of radiative cooling and the tangled magnetic field. In addition to radiative cooling of the jet materials (cooling effect), conversion of the ordered magnetic field into the turbulent one (conversion effect) and dissipation of the turbulent magnetic field (dissipation effect) are formulated…
When a magnetically-dominated super-fast magnetosonic GRB jet leaves the progenitor star the external pressure support may drop and the jet may enter the regime of ballistic expansion during which its magnetic acceleration becomes highly ineffective. However, recent numerical simulations suggested that the transition to this regime is accompanied by a sudden "burst" of acceleration. We confirm this finding and attribute the acceleration to the sideways expansion of the jet - the magnetic energy is converted into the kinetic one in the strong magnetosonic rarefaction wave, which is launched whe…
We study the acceleration, transport, and emission of particles in relativistic jets. Localized stochastic particle acceleration, spatial diffusion, and synchrotron as well as synchrotron self-Compton emission are considered in a leptonic model. To account for inhomogeneity, we use a 2D axi-symmetric cylindrical geometry for both relativistic electrons and magnetic field. In this first phase of our work, we focus on steady-state spectra that develop from a time-dependent model. We demonstrate that small isolated acceleration region in a much larger emission volume are sufficient to accelerate …
Multi-messenger astronomy provides for the observation of the same astronomical event with different kind of telescopes at the same time: optical observations, X-rays, gamma-ray bursts, neutrinos and, most recently, gravitational waves are just few examples of the several points of view from which an astronomical event can be observed and analyzed. Cosmic rays play an important role in multi-messenger astronomy and, for this reason, it is important to deepen the study of their sources and to understand the mechanisms behind their acceleration in astronomical environments.
Relativistic jets are collimated plasma outflows with relativistic speeds. Astrophysical objects involving relativistic jets are a system comprising a compact object such as a black hole, surrounded by rotating accretion flows, with the relativistic jets produced near the central compact object. The most accepted models explaining the origin of relativistic jets involve magnetohydrodynamic (MHD) processes. Over the past few decades, many general relativistic MHD (GRMHD) codes have been developed and applied to model relativistic jet formation in various conditions. This short review provides a…
Context: Understanding the acceleration mechanism of astrophysical jets has been a cumbersome endeavor from both the theoretical and observational perspective. Although several breakthroughs have been achieved in recent years, on all sides, we are still missing a comprehensive model for the acceleration of astrophysical jets. Aims: In this work we attempt to construct a simple toy model that can account for several observational and theoretical results and allow us to probe different aspects of blazar jets usually inaccessible to observations. Methods: We used the toy model and Lorentz factor …
Recently it was shown that the centrifugal instability may be important in the dynamics of astrophysical jets undergoing reconfinement by external pressure. However, these studies were limited to the case of unmagnetised flows. Here we explore the role of the magnetic field within both the Newtonian and relativistic frameworks. Since the jet problem is rather complicated, we focus instead on the simpler problem of cylindrical rotation and axial magnetic field, which shares significant similarity with the jet problem, and consider only axisymmetric perturbations. The studied equilibrium configu…
X-ray polarimetry promises us an unprecedented look at the structure of magnetic fields and on the processes at the base of acceleration of particles up to ultrarelativistic energies in relativistic jets. Crucial pieces of information are expected from observations of blazars (that are characterized by the presence of a jet pointing close to the Earth), in particular of the subclass defined by a synchrotron emission extending to the X-ray band (so-called high synchrotron peak blazars, HSP). In this review, I give an account of some of the models and numerical simulations developed to predict t…
Highly energetic, relativistic electrons are commonly present in many astrophysical systems, from solar flares to the intra-cluster medium, as indicated by observed electromagnetic radiation. However, open questions remain about the mechanisms responsible for their acceleration, and possible re-acceleration. Ubiquitous plasma turbulence is one of the possible universal mechanisms. We study the energization of transrelativistic electrons in turbulence using hybrid particle-in-cell, which provide a realistic model of Alfvénic turbulence from MHD to sub-ion scales, and test particle simulations f…
Electrons emitting non-thermal photons in blazars are possibly accelerated by turbulences developed in jets. In this paper, we consider the case so-called hard-sphere scattering as an interaction model between turbulences and electrons, in which the acceleration timescale is independent of the electron energy. We numerically simulate broad-band emission from blazar jets with a one-zone time-dependent code, taking into account the turbulence acceleration. Our model reproduces various blazar spectra with simple assumptions, such as constant particle injection rate, constant diffusion coefficient…
In the espresso scenario, ultra-high-energy (UHE) cosmic rays (CRs) are produced via a one-shot reacceleration of galactic-like CRs in the relativistic jets of active galactic nuclei, independently of the scattering rate dictated by magnetic fluctuations. In Mbarek & Caprioli (2019), we traced test-particle CRs in high-resolution magnetohyrodynamic (MHD) jet simulations and found that the associated spectral slope, chemical composition, and anisotropy are consistent with UHECR phenomenology. In this work, we extend such an analysis by including sub-grid pitch-angle scattering to model small-sc…
Particle acceleration by magnetic reconnection is now recognized as an important process in magnetically dominated regions of galactic and extragalactic black hole sources. This process helps to solve current puzzles specially related to the origin of the very high energy flare emission in these sources. In this review, we discuss this acceleration mechanism and show recent analytical studies and multidimensional numerical SRMHD and GRMHD (special and general relativistic magnetohydrodynamical) simulations with the injection of test particles, which help us to understand this process both in r…
Active Galactic Nuclei (AGN) and their relativistic jets are believed to be potential sites of ultra-high-energy (UHE) cosmic ray acceleration. This paper reviews basic observational findings as well as requirements on source energetics, and then discusses the relevance of different acceleration sites and mechanisms, such as black hole gap, shock in back-flows or jet shear acceleration. When put in context, the result suggests that Fermi-type particle acceleration at trans-relativistic shocks and/or in shearing, relativistic flows offers the most promising framework for UHECR production in AGN…
This paper describes the acceleration of high energies protons captured by electrostatic waves in the frame of jet arising in the area of instability of relativistic jet, where spiral structures are excited. The wave has a spatially heterogeneous structure of $\exp(i k_\parallel z +i m_ϕϕ)$. Protons can be captured in potential wells created by spiral waves, and thereby experience acceleration with a mechanism known as surfatron acceleration. Expressions of the maximum energy ($ E_p \simeq 10^{19} eV $) and the energy spectrum from jet parameters are obtained.
In this work, at first we present a model of studying astrophysical flows of binary systems and microquasars based on the laws of relativistic magnetohydrodynamics. Then, by solving the time independent transfer equation, we estimate the primary and secondary particle distributions within the hadronic astrophysical jets as well as the emissivities of high energy neutrinos and $γ$-rays. One of our main goals is, by taking into consideration the various energy-losses of particles into the hadronic jets, to determine through the transport equation the respective particle distributions focusing on…
Long-lived, stable jets are observed in a wide variety of systems, from protostars, through Galactic compact objects to active galactic nuclei (AGN). Magnetic fields play a central role in launching, accelerating, and collimating the jets through various media. The termination of jets in molecular clouds or the interstellar medium deposits enormous amounts of mechanical energy and momentum, and their interactions with the external medium, as well, in many cases, as the radiation processes by which they are observed, are intimately connected with the magnetic fields they carry. This review focu…
We have shown the generation/amplification of fast macro-scale plasma flows in the degenerate two-fluid astrophysical systems with initial turbulent (micro--scale) magnetic/velocity fields due to the Unified Reverse Dynamo/Dynamo mechanism. This process is simultaneous with and complementary to the micro-scale unified dynamo. It is found that the generation of macro--scale flows is an essential consequence of the magneto-fluid coupling; the generation of macro--scale fast flows and magnetic fields are simultaneous, they grow proportionately. The resulting dynamical flow acceleration is directl…
It has been proposed that blazar jets are structured, with a fast spine surrounded by a slower sheath or layer. This structured jet model explains some properties of their emission and morphology. Because of their relative motion, the radiation produced by one component is seen amplified by the other, thus enhancing the inverse Compton emission of both. Radiation is emitted anisotropically in the comoving frames, and causes the emitting plasma to recoil. As seen in the observer frame, this corresponds to a deceleration of the fastest component (the spine) and an acceleration of the slower one …
A central compact object (CCO, e.g. a black hole) with an accretion disk has been suggested as the common central engine of various astrophysical phenomena, such as gamma-ray bursts (GRBs), tidal disruption events (TDEs) and active galactic nuclei (AGNs). A jet powered by such a system might precess due to the misalignment of the angular momenta of the CCO and accretion disk. Some quasi-periodic behaviors observed in the light curves of these phenomena can be well interpreted within the framework of a precessing jet model. In this paper, we study the emission polarization of precessing jets in…
We model the multi-wavelength emission in the southern hotspot of the radio quasar 4C74.26. The synchrotron radio emission is resolved near the shock with the MERLIN radio-interferometer, and the rapid decay of this emission behind the shock is interpreted as the decay of the amplified downstream magnetic field as expected for small scale turbulence. Electrons are accelerated to only 0.3 TeV, consistent with a diffusion coefficient many orders of magnitude greater than in the Bohm regime. If the same diffusion coefficient applies to the protons, their maximum energy is only ~100 TeV.
We present a new, semi-analytic formalism to model the acceleration and collimation of relativistic jets in a gravitational potential. The gravitational energy density includes the kinetic, thermal, and electromagnetic mass contributions. The solutions are close to self-similar throughout the integration, from very close to the black hole to the region where gravity is unimportant. The field lines are tied to the conditions very close to the central object and eventually overcollimate, possibly leading to a collimation shock. This collimation shock could provide the conditions for diffusive sh…
This review aims at providing an up-to-date status and a general introduction to the subject of the numerical study of energetic particle acceleration and transport in turbulent astrophysical flows. The subject is also complemented by a short overview of recent progresses obtained in the domain of laser plasma experiments. We review the main physical processes at the heart of the production of a non-thermal distribution in both Newtonian and relativistic astrophysical flows, namely the first and second order Fermi acceleration processes. We also discuss shock drift and surfing acceleration, tw…
An accreting supermassive blackhole, the central engine of active galactic nucleus (AGN), is capable of exciting extreme amplitude Alfven waves whose wavelength (wave packet) size is characterized by its clumpiness. The pondermotive force and wakefield are driven by these Alfven waves propagating in the AGN (blazar) jet and accelerate protons/nuclei to extreme energies beyond Zetta-electron volt (ZeV$=10^{21}$ eV). Such acceleration is prompt, localized, and does not suffer from the multiple scattering/bending enveloped in the Fermi acceleration that causes excessive synchrotron radiation loss…
Relativistic jets in active galactic nuclei, galactic microquasars, and gamma-ray bursts are widely considered to be magnetohydrodynamically driven by black hole accretion systems, although conversion mechanism from Poynting into particle kinetic energy flux is still open. Recent detailed numerical and analytical studies of global structures of steady, axisymmetric magnetohydrodynamic (MHD) flows with specific boundary conditions have not reproduced as rapid an energy conversion as required by observations. In order to find more suitable boundary conditions, we focus on the flow along a poloid…
Synchrotron radio emission from non-relativistic jets powered by massive protostars has been reported, indicating the presence of relativistic electrons and magnetic fields of strength ~0.3-5 mG. We study diffusive shock acceleration and magnetic field amplification in protostellar jets with speeds between 300 and 1500 km/s. We show that the magnetic field in the synchrotron emitter can be amplified by the non-resonant hybrid (Bell) instability excited by the cosmic-ray streaming. By combining the synchrotron data with basic theory of Bell instability we estimate the magnetic field in the sync…
