Cosmic ray propagation is diffusive because of pitch angle scattering by waves. We demonstrate that if the high-amplitude magnetohydrodynamic turbulence with $tilde B/langle Brangle sim 1$ is present on top of the mean field gradient, the diffusion b
ecomes asymmetric. As an example, we consider the vertical transport of cosmic rays in our Galaxy propagating away from a point-like source. We solve this diffusion problem analytically using a one-dimensional Markov chain analysis. We obtained that the cosmic ray density markedly differs from the standard diffusion prediction and has a sizable effect on their distribution throughout the galaxy. The equation for the continuous limit is also derived, which shows limitations of the convection-diffusion equation.
Radiative diagnostics of high-energy density plasmas is addressed in this paper. We propose that the radiation produced by energetic particles in small-scale magnetic field turbulence, which can occur in laser-plasma experiments, collisionless shocks
, and during magnetic reconnection, can be used to deduce some properties of the turbulent magnetic field. Particles propagating through such turbulence encounter locally strong magnetic fields, but over lengths much shorter than a particle gyroradius. Consequently, the particle is accelerated but not deviated substantially from a straight line path. We develop the general jitter radiation solutions for this case and show that the resulting radiation is directly dependent upon the spectral distribution of the magnetic field through which the particle propagates. We demonstrate the power of this approach in considering the radiation produced by particles moving through a region in which a (Weibel-like) filamentation instability grows magnetic fields randomly oriented in a plane transverse to counterstreaming particle populations. We calculate the spectrum as would be seen from the original particle population and as could be seen by using a quasi-monoenergetic electron beam to probe the turbulent region at various angles to the filamentation axis.
Radiation from many astrophysical sources, e.g. gamma-ray bursts and active galactic nuclei, is believed to arise from relativistically shocked collisionless plasmas. Such sources often exhibit highly transient spectra evolving rapidly, compared with
source lifetimes. Radiation emitted from these sources is typically associated with non-linear plasma physics, complex field topologies and non-thermal particle distributions. In such circumstances a standard synchrotron paradigm may fail to produce accurate conclusions regarding the underlying physics. Simulating spectral emission and spectral evolution numerically in various relativistic shock scenarios is then the only viable method to determine the detailed physical origin of the emitted spectra. In this Letter we present synthetic radiation spectra representing the early stage development of the filamentation (streaming) instability of an initially unmagnetized plasma, which is relevant for both collisionless shock formation and reconnection dynamics in relativistic astrophysical outflows, as well as for laboratory astrophysics experiments. Results were obtained using a highly efficient in situ diagnostics method, based on detailed particle-in-cell modeling of collisionless plasmas. The synthetic spectra obtained here are compared with those predicted by a semi-analytical model for jitter radiation from the filamentation instability, the latter including self-consistent generated field topologies and particle distributions obtained from the simulations reported upon here. Spectra exhibit dependence on the presence - or absence - of an inert plasma constituent, when comparing baryonic plasmas (i.e. containing protons) with pair plasmas. The results also illustrate that considerable care should be taken when using lower-dimensional models to obtain information about the astrophysical phenomena generating observed spectra.
Relativistic shocks are usually thought to occur in violent astrophysical explosions. These collisionless shocks are mediated by a plasma kinetic streaming instability, often loosely referred to as the Weibel instability, which generates strong magne
tic fields from scratch very efficiently. In this review paper we discuss the shock micro-physics and present a recent model of pre-conditioning of an initially unmagnetized upstream region via the cosmic-ray-driven Weibel-type instability.
Weibel instability turns out to be the a ubiquitous phenomenon in High-Energy Density environments, ranging from astrophysical sources, e.g., gamma-ray bursts, to laboratory experiments involving laser-produced plasmas. Relativistic particles (electr
ons) radiate in the Weibel-produced magnetic fields in the Jitter regime. Conventionally, in this regime, the particle deflections are considered to be smaller than the relativistic beaming angle of 1/$gamma$ ($gamma$ being the Lorentz factor of an emitting particle) and the particle distribution is assumed to be isotropic. This is a relatively idealized situation as far as lab experiments are concerned. We relax the assumption of the isotropy of radiating particle distribution and present the extension of the jitter theory amenable for comparisons with experimental data.
Jitter radiation is produced by relativistic electrons moving in turbulent small-scale magnetic fields such as those produced by streaming Weibel-type instabilities at collisionless shocks in weakly magnetized media. Here we present a comprehensive s
tudy of the dependence of the jitter radiation spectra on the properties of, in general, anisotropic magnetic turbulence. We have obtained that the radiation spectra do reflect, to some extent, properties of the magnetic field spatial distribution, yet the radiation field is anisotropic and sensitive to the viewing direction with respect to the field anisotropy direction. We explore the parameter space of the magnetic field distribution and its effect on the radiation spectrum. Some important results include: the presence of the harder-than-synchrotron segment below the peak frequency at some viewing angles, the presence of the high-frequency power-law tail even for a monoenergetic distribution of electrons, the dependence of the peak frequency on the field correlation length rather than the field strength, the strong correlation of the spectral parameters with the viewing angle. In general, we have found that even relatively minor changes in the magnetic field properties can produce very significant effects upon the jitter radiation spectra. We consider these results to be important for accurate interpretation of prompt gamma-ray burst spectra and possibly other sources.
Radiation from GRBs in the prompt phase, flares and an afterglow is thought to be produced by accelerated electrons in magnetic fields. Such emission may be produced at collisionless shocks of baryonic outflows or at reconnection sites (at least for
the prompt and flares) of the magnetically dominated (Poynting flux driven) outflows, where no shocks presumably form at all. An astonishing recent discovery is that during reconnection strong small-scale magnetic fields are produced via the Weibel instability, very much like they are produced at relativistic shocks. The relevant physics has been successfully and extensively studied with the PIC simulations in 2D and, to some extent, in 3D for the past few years. We discuss how these simulations predict the existence of MeV-range synchrotron/jitter emission in some GRBs, which can be observed with Fermi. Recent results on modeling of the spectral variability and spectral correlations of the GRB prompt emission in the Weibel-jitter paradigm applicable to both baryonic and magnetic-dominated outflows is reviewed with the emphasis on observational predictions.
Cosmic rays accelerated by a shock form a streaming distribution of outgoing particles in the foreshock region. If the ambient fields are negligible compared to the shock and cosmic ray energetics, a stronger magnetic field can be generated in the sh
ock upstream via the streaming (Weibel-type) instability. Here we develop a self-similar model of the foreshock region and calculate its structure, e.g., the magnetic field strength, its coherence scale, etc., as a function of the distance from the shock. Our model indicates that the entire foreshock region of thickness $sim R/(2Gamma_{rm sh}^2)$, being comparable to the shock radius in the late afterglow phase when $Gamma_{rm sh}sim1$, can be populated with large-scale and rather strong magnetic fields (of sub-gauss strengths with the coherence length of order $10^{17} {rm cm}$) compared to the typical interstellar medium magnetic fields. The presence of such fields in the foreshock region is important for high efficiency of Fermi acceleration at the shock. Radiation from accelerated electrons in the foreshock fields can constitute a separate emission region radiating in the UV/optical through radio band, depending on time and shock parameters. We also speculate that these fields being eventually transported into the shock downstream can greatly increase radiative efficiency of a gamma-ray burst afterglow shock.
We address the question of whether numerical particle-in-cell (PIC) simulations and laboratory laser-plasma experiments can (or will be able to, in the near future) model realistic gamma-ray burst (GRB) shocks. For this, we compare the radiative cool
ing time, t_cool, of relativistic electrons in the shock magnetic fields to the microscopic dynamical time of collisionless relativistic shocks -- the inverse plasma frequency of protons, omega_pp^{-1}. We obtain that for t_cool*omega_pp^{-1}lesssim ~few hundred, the electrons cool efficiently at or near the shock jump and are capable of emitiing away a large fraction of the shock energy. Such shocks are well-resolved in existing PIC simulations; therefore, the microscopic structure can be studied in detail. Since most of the emission in such shocks would be coming from the vicinity of the shock, the spectral power of the emitted radiation can be directly obtained from finite-length simulations and compared with observational data. Such radiative shocks correspond to the internal baryon-dominated GRB shocks for the conventional range of ejecta parameters. Fermi acceleration of electrons in such shocks is limited by electron cooling, hence the emitted spectrum should be lacking a non-thermal tail, whereas its peak likely falls in the multi-MeV range. Incidentally, the conditions in internal shocks are almost identical to those in laser-produced plasmas; thus, such GRB-like plasmas can be created and studied in laboratory experiments using the presently available Petawatt-scale laser facilities. An analysis of the external shocks shows that only the highly relativistic shocks, corresponding to the extremely early afterglow phase, can have efficient electron cooling in the shock transition. We emphasize the importance of radiative PIC simulations for further studies.
