We recently extended our Parker-type transport equation for energetic particle interaction with numerous dynamic small-scale magnetic flux ropes (SMFRs) to include perpendicular diffusion in addition to parallel diffusion. We present a new analytical solution to this equation assuming heliocentric spherical geometry with spherical symmetry for all SMFR acceleration mechanisms present in the transport theory. With the goal of identifying the dominant mechanism(s) through which particles are accelerated by SMFRs, a search was launched to identify events behind interplanetary shocks that could be explained by our new solution and not classical diffusive shock acceleration. Two new SMFR acceleration events were identified in situ for the first time within heliocentric distances of 1 astronomical unit (au) in Helios A data. A Metropolis–Hastings algorithm is employed to fit the new solution to the energetic proton fluxes so that the relative strength of the transport coefficients associated with each SMFR acceleration mechanism can be determined. We conclude that the second-order Fermi mechanism for particle acceleration by SMFRs is more important than first-order Fermi acceleration due to the mean compression of the SMFRs regions during these new events. Furthermore, with the aid of SMFR parameters determined via the Grad–Shafranov reconstruction method, we find that second-order Fermi SMFR acceleration is dominated by the turbulent motional electric field parallel to the guide/background field. Finally, successful reproduction of energetic proton flux data during these SMFR acceleration events also required efficient particle escape from the SMFR acceleration regions.
Understanding the time-scales for diffusive processes and their degree of anisotropy is essential for modelling cosmic ray transport in turbulent magnetic fields. We show that the diffusion time-scales are isotropic over a large range of energy and turbulence levels, notwithstanding the high degree of anisotropy exhibited by the components of the diffusion tensor for cases with an ordered magnetic field component. The predictive power of the classical scattering relation as a description for the relation between the parallel and perpendicular diffusion coefficients is discussed and compared to numerical simulations. Very good agreement for a large parameter space is found, transforming classical scattering relation predictions into a computational prescription for the perpendicular component. We discuss and compare these findings, in particular, the time-scales to become diffusive with the time-scales that particles reside in astronomical environments, the so-called escape time-scales. The results show that, especially at high energies, the escape times obtained from diffusion coefficients may exceed the time-scales required for diffusion. In these cases, the escape time cannot be determined by the diffusion coefficients.
more » « less- Award ID(s):
- 2007323
- NSF-PAR ID:
- 10368106
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 514
- Issue:
- 2
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 2658-2666
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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