Cosmic-Ray Modulation: an Ab Initio Approach

Abstract

A better understanding of cosmic-ray modulation in the heliosphere can only be gained through a proper understanding of the effects of turbulence on the diffusion and drift of cosmic rays. We present an ab initio model for cosmic-ray modulation, incorporating for the first time the results yielded by a two-component turbulence transport model. This model is solved for periods of minimum solar activity, utilizing boundary values chosen so that model results are in fair to good agreement with spacecraft observations of turbulence quantities, not only in the solar ecliptic plane but also along the out-of-ecliptic trajectory of the Ulysses spacecraft. These results are employed as inputs for modelled slab and 2D turbulence energy spectra. The latter spectrum is chosen based on physical considerations, with a drop-off at the very lowest wavenumbers commencing at the 2D outerscale. There currently exist no models or observations for this quantity, and it is the only free parameter in this study. The modelled turbulence spectra are used as inputs for parallel mean free path expressions based on those derived from quasi-linear theory and perpendicular mean free paths from extended nonlinear guiding center theory. Furthermore, the effects of turbulence on cosmic-ray drifts are modelled in a self-consistent way, employing a recently developed model for drift along the wavy current sheet. The resulting diffusion coefficients and drift expressions are applied to the study of galactic cosmic-ray protons and antiprotons using a threedimensional, steady-state cosmic-ray modulation code, and sample solutions in fair agreement with multiple spacecraft observations are presented.

Forward Modeling of Reduced Power Spectra From Three-Dimensional K-Space

“…We like to point out that our analysis is also relevant to modeling cosmic ray transport in turbulent media (e.g., Jokipii, 1966;Engelbrecht & Burger, 2014, 2015. Cosmic rays are traveling with very large velocities through turbulent plasma fields while being scattered by timevariable fields, which are seen in a Lagrangian frame by the moving particles commonly described in an appropriate guiding center.…”

Numerical Test of Different Approximations Used in the Transport Theory of Energetic Particles

“…Analytical theory is required in order to achieve a complete understanding of particle motion in plasmas. Furthermore, simple analytical forms of the different diffusion parameters are necessary in investigations of solar modulation (see, e.g., Engelbrecht & Burger 2014;Siluszyk et al 2014;Zhao et al 2014;Ahluwalia & Ygbuhay 2015;Manuel et al 2015) and different shock acceleration scenarios (see, e.g., Dosch & Shalchi 2010;Li et al 2012;Ferrand et al 2014;Neergaard Parker & Zank 2014). Those can only be obtained from analytical treatments of the transport.…”