Turbulent amplification of magnetic field driven by dynamo effect at rippled shocks

We derive analytically the vorticity generated downstream of a two-dimensional rippled hydromagnetic shock neglecting fluid viscosity and resistivity. The growth of the turbulent component of the downstream magnetic field is driven by the vortical eddies motion. We determine an analytic time-evolution of the magnetic field amplification at shocks, so far described only numerically, until saturation occurs due to seed-field reaction to field lines whirling. The explicit expression of the amplification growth rate and of the non-linear field back-reaction in terms of the parameters of shock and interstellar density fluctuations is derived from MHD jump conditions at rippled shocks. A magnetic field saturation up to the order of milligauss and a short-time variability in the $X$-ray observations of supernova remnants can be obtained by using reasonable parameters for the interstellar turbulence.Comment: 9 pages, 4 figures, The Astrophyical Journal in pres

Vortical field amplification and particle acceleration at rippled shocks

Supernova Remnants (SNRs) shocks are believed to accelerate charged particles and to generate strong turbulence in the post-shock flow. From high-energy observations in the past decade, a magnetic field at SNR shocks largely exceeding the shock-compressed interstellar field has been inferred. We outline how such a field amplification results from a small-scale dynamo process downstream of the shock, providing an explicit expression for the turbulence back-reaction to the fluid whirling. The spatial scale of the $X-$ray rims and the short time-variability can be obtained by using reasonable parameters for the interstellar turbulence. We show that such a vortical field saturation is faster than the acceleration time of the synchrotron emitting energetic electrons.Comment: 4 pages, 3 figures; to appear in the proceedings of the RICAP-13, Roma International Conference on AstroParticle Physic

Early-time velocity autocorrelation for charged particles diffusion and drift in static magnetic turbulence

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 early-time charged particle transport. Using the computed diffusion coefficients, we exploit the particle velocity autocorrelation to investigate the time-scale over which the particles "decorrelate" from the solution to the unperturbed equation of motion. Decorrelation time-scales are evaluated for parallel and perpendicular motions, including the drift of the particles from the local magnetic field line. The regimes of strong and weak magnetic turbulence are compared for various values of the ratio of the particle gyroradius to the correlation length of the magnetic turbulence. Our simulation parameters can be applied to energetic particles in the interplanetary space, cosmic rays at the supernova shocks, and cosmic-rays transport in the intergalactic medium.Comment: 10 pages, 11 figures, The Astrophyical Journal in pres