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

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

No Stagnation Region Before the Heliopause at Voyager 1? Inferences From New Voyager 2 Results

We present anisotropy results for anomalous cosmic-ray (ACR) protons in the energy range $\sim$0.5-35 MeV from Cosmic Ray Subsytem (CRS) data collected during calibration roll maneuvers for the magnetometer instrument when Voyager 2 (V2) was in the inner heliosheath. We use a new technique to derive for the first time the radial component of the anisotropy vector from CRS data. We find that the CRS-derived radial solar wind speeds, when converted from the radial components of the anisotropy vectors via the Compton-Getting (C-G) effect, generally agree with those similarly-derived speeds from the Low-Energy Charged Particle experiment using 28-43 keV data. However, they often differ significantly from the radial solar wind speeds measured directly by the Plasma Science (PLS) instrument. There are both periods when the C-G-derived radial solar wind speeds are significantly higher than those measured by PLS and times when they are significantly lower. The differences are not expected nor explained, but it appears that after a few years in the heliosheath the V2 radial solar wind speeds derived from the C-G method underestimate the true speeds as the spacecraft approaches the heliopause. We discuss the implications of this observation for the stagnation region reported along the Voyager 1 trajectory as it approached the heliopause inferred using the C-G method

No Stagnation Region before the Heliopause at Voyager 1? Inferences from New Voyager 2 Results

We present anisotropy results for anomalous cosmic-ray protons in the energy range ~0.5–35 MeV from Cosmic Ray Subsystem (CRS) data collected during calibration roll maneuvers for the magnetometer instrument when Voyager 2 (V2) was in the inner heliosheath. We use a new technique to derive for the first time the radial component of the anisotropy vector from CRS data. We find that the CRS-derived radial solar wind speeds, when converted from the radial components of the anisotropy vectors via the Compton–Getting (C–G) effect, generally agree with those similarly derived speeds from the Low Energy Charged Particle experiment using 28–43 keV data. However, they often differ significantly from the radial solar wind speeds measured directly by the Plasma Science (PLS) instrument. There are both periods when the C–G-derived radial solar wind speeds are significantly higher than those measured by PLS and times when they are significantly lower. The differences are not expected nor explained, but it appears that after a few years in the heliosheath the V2 radial solar wind speeds derived from the C–G method underestimate the true speeds as the spacecraft approaches the heliopause. We discuss the implications of this observation for the stagnation region reported along the Voyager 1 trajectory as it approached the heliopause inferred using the C–G method

Drift-induced deceleration of Solar Energetic Particles

We investigate the deceleration of Solar Energetic Particles (SEPs) during their propagation from the Sun through interplanetary space, in the presence of weak to strong scattering in a Parker spiral configuration, using relativistic full orbit test particle simulations. The calculations retain all three spatial variables describing particles’ trajectories, allowing to model any transport across the magnetic field. Large energy change is shown to occur for protons, due to the combined effect of standard adiabatic deceleration and a significant contribution from particle drift in the direction opposite to that of the solar wind electric field. The latter drift-induced deceleration is found to have a stronger effect for SEP energies than for galactic cosmic rays. The kinetic energy of protons injected at 1 MeV is found to be reduced by between 35 and 90% after four days, and for protons injected at 100 MeV by between 20 and 55%. The overall degree of deceleration is a weak function of the scattering mean free path, showing that, although adiabatic deceleration plays a role, a large contribution is due to particle drift. Current SEP transport models are found to account for drift-induced deceleration in an approximate way and their accuracy will need to be assessed in future work

A Re-interpretation of the STEREO/STE Observations and it's Consequences

We present an alternate interpretation of recent STEREO/STE observations that were originally attributed to energetic neutral atoms (ENA) from the heliosheath. The signal attributed to the diffuse ENA source instead shows the characteristics of a point source. We point out that the peak intensity seen by STEREO/STE is centered at the ecliptic longitude of the bright X-ray source Sco X-1. The observed energy spectrum and intensity are also consistent with the X-rays from Sco X-1. The problem of energy dissipation at the solar wind termination shock remains unsolved while current understanding of the interaction between the solar wind and interstellar wind awaits future observations.Comment: Accepted by ApJ

Cosmic-ray pitch-angle scattering in imbalanced mhd turbulence simulations

Pitch-angle scattering rates for cosmic-ray particles in magnetohydrodynamic (MHD) simulations with imbalanced turbulence are calculated for fully evolving electromagnetic turbulence. We compare with theoretical predictions derived from the quasilinear theory of cosmic-ray diffusion for an idealized slab spectrum and demonstrate how cross helicity affects the shape of the pitch-angle diffusion coefficient. Additional simulations in evolving magnetic fields or static field configurations provide evidence that the scattering anisotropy in imbalanced turbulence is not primarily due to coherence with propagating Alfven waves, but an effect of the spatial structure of electric fields in cross-helical MHD turbulence.Comment: 13 pages, 15 figures. Accepted by Ap

Energetic particle transport across the mean magnetic field: before diffusion

Current particle transport models describe the propagation of charged particles across the mean field direction in turbulent plasmas as diffusion. However, recent studies suggest that at short time- scales, such as soon after solar energetic particle (SEP) injection, particles remain on turbulently meandering field lines, which results in non-diffusive initial propagation across the mean magnetic field. In this work, we use a new technique to investigate how the particles are displaced from their original field lines, and quantify the parameters of the transition from field-aligned particle propagation along meandering field lines to particle diffusion across the mean magnetic field. We show that the initial decoupling of the particles from the field lines is slow, and particles remain within a Larmor radius from their initial meandering field lines for tens to hundreds of Larmor periods, for 0.1-10 MeV protons in turbulence conditions typical of the solar wind at 1 AU. Subsequently, particles decouple from their initial field lines and after hundreds to thousands of Larmor periods reach time-asymptotic diffusive behaviour consistent with particle diffusion across the mean field caused by the meandering of the field lines. We show that the typical duration of the pre-diffusive phase, hours to tens of hours for 10 MeV protons in 1 AU solar wind turbulence conditions, is significant for SEP propagation to 1 AU and must be taken into account when modelling SEP propagation in the interplanetary space