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Register a new userAsymmetric diffusion of cosmic rays
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Added by
Mikhail V. Medvedev
Publication date
2015
fields
Physics
and research's language is
English
Authors
Mikhail V. Medvedev
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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 becomes 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.
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The propagation of charged particles, including cosmic rays, in a partially ordered magnetic field is characterized by a diffusion tensor whose components depend on the particles Larmor radius $R_L$ and the degree of order in the magnetic field. Most studies of the particle diffusion presuppose a scale separation between the mean and random magnetic fields (e.g., there being a pronounced minimum in the magnetic power spectrum at intermediate scales). Scale separation is often a good approximation in laboratory plasmas, but not in most astrophysical environments such as the interstellar medium (ISM). Modern simulations of the ISM have numerical resolution of order 1 pc, so the Larmor radius of the cosmic rays that dominate in energy density is at least $10^{6}$ times smaller than the resolved scales. Large-scale simulations of cosmic ray propagation in the ISM thus rely on oversimplified forms of the diffusion tensor. We take the first steps towards a more realistic description of cosmic ray diffusion for such simulations, obtaining direct estimates of the diffusion tensor from test particle simulations in random magnetic fields (with the Larmor radius scale being fully resolved), for a range of particle energies corresponding to $10^{-2}lesssim R_L/l_c lesssim 10^{3}$, where $l_c$ is the magnetic correlation length. We obtain explicit expressions for the cosmic ray diffusion tensor for $R_L/l_c ll 1$, that might be used in a sub-grid model of cosmic ray diffusion. The diffusion coefficients obtained are closely connected with existing transport theories that include the random walk of magnetic lines.
Fluid approximations to cosmic ray (CR) transport are often preferred to kinetic descriptions in studies of the dynamics of the interstellar medium (ISM) of galaxies, because they allow simpler analytical and numerical treatments. Magnetohydrodynamic (MHD) simulations of the ISM usually incorporate CR dynamics as an advection-diffusion equation for CR energy density, with anisotropic, magnetic field-aligned diffusion with the diffusive flux assumed to obey Ficks law. We compare test-particle and fluid simulations of CRs in a random magnetic field. We demonstrate that a non-Fickian prescription of CR diffusion, which corresponds to the telegraph equation for the CR energy density, can be easily calibrated to match the test particle simulations with great accuracy. In particular, we consider a random magnetic field in the fluid simulation that has a lower spatial resolution than that used in the particle simulation to demonstrate that an appropriate choice of the diffusion tensor can account effectively for the unresolved (subgrid) scales of the magnetic field. We show that the characteristic time which appears in the telegraph equation can be physically interpreted as the time required for the particles to reach a diffusive regime and we stress that the Fickian description of the CR fluid is unable to describe complex boundary or initial conditions for the CR energy flux.
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 magnetic field, leading to a new type of parallel diffusion. This diffusion is in general slower than the diffusion of non-bouncing CRs with small pitch angles that undergo gyroresonant scattering. The critical pitch angle at the balance between magnetic mirroring and pitch-angle scattering is important for determining the diffusion coefficients of both bouncing and non-bouncing CRs and their scalings with the CR energy. We find non-universal energy scalings of diffusion coefficients, depending on the properties of MHD turbulence.
We study the problem of the escape and transport of Cosmic-Rays (CR) from a source embedded in a fully ionised, hot phase of the interstellar medium (HIM). In particular, we model the CR escape and their propagation in the source vicinity taking into account excitation of Alfvenic turbulence by CR streaming and mechanisms damping the self-excited turbulence itself. Our estimates of escape radii and times result in large values (100 pc, $2times10^5$ yr) for particle energies $lesssim20$ GeV and smaller values for particles with increasing energies (35 pc and 14 kyr at 1 TeV). These escape times and radii, when used as initial conditions for the CR propagation outside the source, result in relevant suppression of the diffusion coefficient (by a factor 5-10) on time-scales comparable with their (energy dependent) escape time-scale. The damping mechanisms are fast enough that even on shorter time scales the Alfvenic turbulence is efficiently damped, and the ratio between random and ordered component of the magnetic field is $delta B/B_0ll 1$, justifying the use of quasi-linear theory. In spite of the suppressed diffusion coefficient, and then the increased residence time in the vicinity (<200 pc) of their source, the grammage accumulated by CRs after their escape is found to be negligible (at all energies) as compared to the one accumulated while diffusing in the whole Galaxy, due to the low density of the HIM.
The origin of the bulk of cosmic rays (CRs) observed at Earth is the topic of a century long investigation, paved with successes and failures. From the energetic point of view, supernova remnants (SNRs) remain the most plausible sources of CRs up to rigidity ? 10^6-10^7 GV. This confidence somehow resulted in the construction of a paradigm, the so-called SNR paradigm: CRs are accelerated through diffusive shock acceleration in SNRs and propagate diffusively in the Galaxy in an energy dependent way. Qualitative confirmation of the SNR acceleration scenario has recently been provided by gamma ray and X-ray observations. Diffusive propagation in the Galaxy is probed observationally through measurement of the secondary to primary nuclei flux ratios (such as B/C). There are however some weak points in the paradigm, which suggest that we are probably missing some physical ingredients in our models. The theory of diffusive shock acceleration at SNR shocks predicts spectra of accelerated particles which are systematically too hard compared with the ones inferred from gamma ray observations. Moreover, hard injection spectra indirectly imply a steep energy dependence of the diffusion coefficient in the Galaxy, which in turn leads to anisotropy larger than the observed one. Moreover recent measurements of the flux of nuclei suggest that the spectra have a break at rigidity ? 200 GV, which does not sit well with the common wisdom in acceleration and propagation. In this paper I will review these new developments and suggest some possible implications.
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