Three cases of large-amplitude, small spatial-scale interplanetary particle gradients observed by the anticoincidence shield (ACS) aboard the INTEGRAL spacecraft in 2006 are investigated. The high data rates provided by the INTEGRAL ACS allow an unprecedented ability to probe the fine structure of GCR propagation in the inner Heliosphere. For two of the three cases, calculating perpendicular and parallel cosmic ray diffusion coefficients based on both field and particle data results in parallel diffusion appearing to satisfy a convection gradient current balance, provided that the magnetic scattering of the particles can be described by quasi-linear theory. In the third case, perpendicular diffusion seems to dominate. The likelihood of magnetic flux rope topologies within solar ejecta affecting the local modulation is considered, and its importance in understanding the field-particle interaction for the astrophysics of nonthermal particle phenomena is discussed.
A Forbush Decrease (FD) is a global transient decrease in Galactic Cosmic-Ray (GCR) intensity followed by a substantially slower recovery. Since Scott Forbush’s discovery and description of these phenomena in the late 1930s, FDs have been put into context with increasing developments within heliospheric physics. In particular, detailed observations of coronal mass ejections (CMEs) and in situ observations of the solar wind and energetic particles have greatly increased understanding of the underlying physics of FDs (see review articles by [
This investigation focuses on small amplitude and high-frequency variability in the GCR corresponding to timescales less than a few hours, much shorter than that described by the classical FD. However, small-amplitude, mHz variability in the GCR is an experimental challenge in that very large instrumental geometric factors are required in order to make statistically significant measurements of the GCR in time periods of a few minutes or less. Therefore, only a few of these investigations can be found in the literature. Among these studies, [
Exploring the detailed relationship between particle intensity and magnetic field variability within the substructure of solar wind transients exhibiting large, short-period GCR fluctuations may yield new insight into energetic particle propagation within the Heliosphere. The authors of [
In Section
Particle data for this investigation is obtained from the large-area ACS of the SPI spectrometer mounted on the ESA INTEGRAL gamma-ray satellite. With a 24
In addition to ACSSAT and GEDSAT, the system has an ACS channel that counts all triggers in the system above
Three periods of very rapid GCR intensity decrease were selected from 2006 INTEGRAL data, DOY 103 (orbit 427), DOY 117/118 (orbit 432), and DOY 1276/127 (orbit 435). Figure
Five-minute sums of GEDSAT and ACSSAT count rates are plotted for Orbit 427.
Five-minute sums of GEDSAT and ACSSAT count rates are plotted for Orbit 427.
The amplitude of the FD in which the sudden drop seen in both figures is encompassed is of magnitude
The data plotted in Figure
It has long been known that an FD has a similar time history to the evolution of Dst during the time period of the Forbush effect [
ACSSAT for Orbit 427 plotted with the time history of Dst.
ACSSAT for Orbit 427 plotted with the time history of Dst shifted to earlier time by fourteen hours.
Figure
ACS is plotted for Orbit 427 along with the magnitude of the interplanetary field as seen by ACE.
The ACS countrate is plotted with the countrate of the McMurdo neutron monitor for the time period of Orbit 427.
Looking at the solar wind data during this time shows the existence of an ICME. The interplanetary magnetic field and plasma conditions during a four-day period bracketing the ICME are shown in Figure
Wind and ACE IMF, plasma, and electron strahl (165 eV) data for 04-13 through 04-14 2006. INTEGRAL ACS data (unshifted) is shown in the bottom panel. The leading and trailing boundaries of the ICME are shown by vertical lines.
A faster, warmer region is observed just downstream of the trailing ICME boundary. Taking a closer look at days 103 and 104 (04-13-06 and 04-14-06) shows some interesting details in the electron heat flux and ACS data during the period around the ICME. Inside the leading edge, sporadic bidirectional electron heat flux persists through the end of day 103, as shown in Figure
At the beginning of day 104 (Figure
Figure
ACS count rate over entire period encompassing the three ICME events studied together with solar wind field and plasma components from ACE and electron strahl from Wind. Highlighted regions indicate presence of flux ropes.
The most basic derivation of the parallel diffusion coefficient can be found in [
Even within the context of the assumption of transverse waves, the
Using the equation of motion for particles with unperturbed positions
Various models are then chosen which define the perturbed fields via Fourier transforms representing the wave motion or turbulent, convected field structure. The integral to be performed in (
Substituting (
The symbol
Under the approximation that the power spectrum of transverse fluctuations was proportional to
Subsequent work, on
The approximation of (
Concerning perpendicular diffusion, we again start by describing the well-known and easily accessible approximation, before mentioning analytical improvements to the theory and computational approaches which will allow an assessment of the error involved with the adopted equation. Since particles of small Larmor radii compared with the dominant scale of field fluctuations attempt to follow field lines, it is not surprising that deviation from a mean direction is thought of as a combination of motion of guiding centers following wandering field lines and diffusive scattering perpendicular to these lines. In [
Later, Foreman et al. [
Subsequent analytical work, especially [
It has been assumed that the relation between the perpendicular velocity and the perpendicular field perturbation, assuming axial symmetry, is
The work of [
Suppressing the effects of parallel scattering allows this equation to tend to the field line wandering limit while restricting the power spectra to slab and axisymmetric perpendicular disturbance allows the results of [
An alternative approach to incorporating 3D turbulence lies in computations similar to those described in [
In applying the aforementioned expressions to field data, we employ ACE 4-minute component averages, using 0.71 of a day’s data for convenience relating to the Matlab algorithm employed. We obtain the power in a typical perpendicular component by doing fast Fourier transforms to find the power in solar radial, tangential, and normal components as a function of frequency and then finding the sum of resolving each component in a direction perpendicular to the mean field. Power laws are used to fit these summed components. Field magnitudes are found from averages of the 4-minute total field magnitudes because the particles are actually attempting to follow the fluctuation field direction, rather than the mean field over 0.71 of a day. Solar wind data from ACE is used to determine the mean flow velocity of each selected period. Applying the aforementioned results to the field/plasma data of DOY 103, 2006 and the pairs of DOY 117, 118 and 126, 127 yields for 200 MeV protons the results of Table
Diffusion coefficients obtained from power spectra and particle gradients in cm2, sec−1.
DOY 103 | DOY 117 | DOY 118 | DOY 126 | DOY 127 | |
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68 | 24.8 | 45.5 | 75.8 | 45.7 |
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The maximum GCR drop in intensity during day 103 occurs between 103.6 and 103.8 Assuming that this is due to spatial convection of the feature, as is likely from previous studies of such events [
If we assume that a quasi-equilibrium is still maintained between convective outflow, adiabatic energy loss, and diffusive inflow,
Similar estimates are made for the other events, days 117/118 and 126/127. These cosmic-ray-derived diffusion coefficients,
Inspection of Figure
All three field components exhibit large changes but only one event clearly fits a flux rope model. A bidirectional heat flux persisting through to the end of day 103 has already been noted. We have already discussed the flux rope as a suitable GCR barrier [
We have set out to demonstrate the likely validity of a model for significant short-term reduction of the GCR intensity and the use of this model to obtain information on energetic particle diffusion. Approximate theoretical values of the parallel and perpendicular diffusion coefficients have been obtained appropriate to the actual field turbulence present at the time of passage of three selected events. Reference to previous analytical and Monte Carlo numerical studies taking into account 2- or 3-dimensional field representations, not present in the slab approximation of the adopted calculation of the coefficients, allowed an assessment of errors in our procedure to be made. A sufficiently satisfactory explanation of the three events was provided by the idea of a quasi-equilibrium field/particle structure being convected past the Earth with a single, dominant mode of diffusive propagation, either parallel or perpendicular to the mean field of the event. Reasonable self-consistency between diffusion coefficients derived by particle gradient and analytic theory was achieved. Nevertheless, there is every reason to urge the application of more comprehensive modeling, for example, by the methods of [
Three-dimensional models of the overall heliospheric modulation assume diffusive scattering varying smoothly over large spatial scales with at most a dependence on angle with respect to the solar equatorial plane. The relative importance of this, near isotropic and homogeneous turbulence model, compared with barrier effects discussed in this work must depend on the abundance of flux rope magnetic topologies within the solar wind.
In terms of the wider, astrophysical significance, the method proposed here of using local particle conditions to check diffusion coefficients with locally derived plasma parameters seems unprecedented as a way of validating the ability to model cosmic wave-particle interaction in a collisionless regime. One only has to point to the extensive use made of quasi-linear theory for the interaction in nonthermal astrophysical shock modeling to appreciate the worth of the investigation.
D. N. A. Shaul acknowledges Science & Technology Facilities Council (STFC) support. T. Mulligan and J. B. Blake acknowledge the support for this work under NASA Grant CG189307NGA. The authors would like to thank the INTEGRAL team for supplying the INTEGRAL data, the ACE MAG and SWEPAM teams for making their data available on the ACE Science Center website (