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

Particle acceleration by collisionless shocks containing large-scale magnetic-field variations

Diffusive shock acceleration at collisionless shocks is thought to be the source of many of the energetic particles observed in space. Large-scale spatial variations of the magnetic field has been shown to be important in understanding observations. The effects are complex, so here we consider a simple, illustrative model. Here, we solve numerically the Parker transport equation for a shock in the presence of large-scale sinusoidal magnetic-field variations. We demonstrate that the familiar planar-shock results can be significantly altered as a consequence of large-scale, meandering magnetic lines of force. Because perpendicular diffusion coefficient $\kappa_\perp$ is generally much smaller than parallel diffusion coefficient $\kappa_\parallel$, the energetic charged particles are trapped and preferentially accelerated along the shock front in the regions where the connection points of magnetic field lines intersecting the shock surface converge, and thus create the "hot spots" of the accelerated particles. For the regions where the connection points separate from each other, the acceleration to high energies will be suppressed. Further, the particles diffuse away from the "hot spot" regions and modify the spectra of downstream particle distribution. These features are qualitatively similar to the recent Voyager's observation in the Heliosheath. These results are potentially important for particle acceleration at shocks propagating in turbulent magnetized plasmas as well as those which contain large-scale nonplanar structures. Examples include anomalous cosmic rays accelerated by the solar wind termination shock, energetic particles observed in propagating heliospheric shocks, and galactic cosmic rays accelerated by supernova blast waves, etc.Comment: accepted to Ap

Evidence of Confinement of Solar-energetic Particles to Interplanetary Magnetic Field Lines

We present new observations of solar-energetic particles (SEPs) associated with impulsive solar flares that show evidence for their confinement to interplanetary magnetic field lines. Some SEP events exhibit intermittent intensity dropouts becausemagnetic field lines filledwith and empty of particle flux mix together. The edges of these dropouts are observed to be very sharp, suggesting that particles cannot easily move from a filled to an empty field line in the time available during their transport from the Sun. In this paper, we perform high time-resolution observations of intensity fall-off at the edges of observed SEP dropouts in order to look for signatures of particle motion off field lines. However, the statistical study is dominated by one particularly intense event. The inferred length scale of the intensity decay is comparable to the gyroradii of the particles, suggesting that particles only rarely scatter off magnetic field lines during interplanetary transport

Effects of interplanetary transport on derived energetic particle source strengths

We study the transport of solar energetic particles (SEPs) in the inner heliosphere in order to relate observations made by an observer at 1 AU to the number and total energy content of accelerated particles at the source, assumed to be near the Sun. We use a numerical simulation that integrates the trajectories of a large number of individual particles moving in the interplanetary magnetic field. We model pitch angle scattering and adiabatic cooling of energetic ions with energies from 50 keV nucleon^(−1) to 100 MeV nucleon^(−1). Among other things, we determine the number of times that particles of a given energy cross 1 AU and the average energy loss that they suffer because of adiabatic deceleration in the solar wind. We use a number of different forms of the interplanetary spatial diffusion coefficient and a wide range of scattering mean-free paths and consider a number of different ion species in order to generate a wide range of simulation results that can be applied to individual SEP events. We apply our simulation results to observations made at 1 AU of the 20 February 2002 solar energetic particle event, finding the original energy content of several species. We find that estimates of the source energy based on SEP measurements at 1 AU are relatively insensitive to the mean-free path and scattering scheme if adiabatic cooling and multiple crossings are taken into account

Vortical amplification of magnetic field at inward shock of supernova remnant Cassiopeia A

We present an interpretation of the time variability of the $X$-ray flux recently reported from a multi-epoch campaign of $15$ years observations of the supernova remnant Cassiopeia A by {\it Chandra}. We show for the first time quantitatively that the $[4.2-6]$ keV non-thermal flux increase up to $50\%$ traces the growth of the magnetic field due to vortical amplification mechanism at a reflection inward shock colliding with inner overdensities. The fast synchrotron cooling as compared with shock-acceleration time scale qualitatively supports the flux decrease.Comment: 5 pages, 2 figures, PRL in pres

The mixing of interplanetary magnetic field lines: A significant transport effect in studies of the energy spectra of impulsive flares

Using instrumentation on board the ACE spacecraft we describe short-time scale (~3 hour) variations observed in the arrival profiles of ~20 keV nucleon^(–1) to ~2 MeV nucleon^(–1) ions from impulsive solar flares. These variations occurred simultaneously across all energies and were generally not in coincidence with any local magnetic field or plasma signature. These features appear to be caused by the convection of magnetic flux tubes past the observer that are alternately filled and devoid of flare ions even though they had a common flare source at the Sun. In these particle events we therefore have a means to observe and measure the mixing of the interplanetary magnetic field due to random walk. In a survey of 25 impulsive flares observed at ACE between 1997 November and 1999 July these features had an average time scale of 3.2 hours, corresponding to a length of ~0.03 AU. The changing magnetic connection to the flare site sometimes lead to an incomplete observation of a flare at 1 AU; thus the field-line mixing is an important effect in studies of impulsive flare energy spectra

ENERGETIC PARTICLE DIFFUSION IN CRITICALLY BALANCED TURBULENCE

Observations and modeling suggest that the fluctuations in magnetized plasmas exhibit scale-dependent anisotropy, with more energy in the fluctuations perpendicular to the mean magnetic field than in the parallel fluctuations and the anisotropy increasing at smaller scales. The scale dependence of the anisotropy has not been studied in full-orbit simulations of particle transport in turbulent plasmas so far. In this paper, we construct a model of critically balanced turbulence, as suggested by Goldreich & Sridhar, and calculate energetic particle spatial diffusion coefficients using full-orbit simulations. The model uses an enveloped turbulence approach, where each two-dimensional wave mode with wavenumber k ⊥ is packed into envelopes of length L following the critical balance condition, Lk –2/3 ⊥, with the wave mode parameters changing between envelopes. Using full-orbit particle simulations, we find that both the parallel and perpendicular diffusion coefficients increase by a factor of two, compared to previous models with scale-independent anisotropy