[show abstract][hide abstract] ABSTRACT: We present an analytic method to determine the directions of the three-dimensional (3D) heliospheric current sheet (HCS) drift for any tilt angle based on Parker's heliospheric magnetic field and compare it with published two-dimensional and quasi-3D methods. We also present a new approach to determine the magnitude of the 3D HCS drift numerically. Implications of these new methods for the solar modulation of Galactic cosmic rays are considered and compared with results from prior methods reported in the literature. Our results support the concept that HCS drift plays an important role in the solar modulation of cosmic rays.
The Astrophysical Journal 12/2011; 744(2):170. · 6.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: During the recent solar minimum the intensity of Galactic cosmic rays in the inner heliosphere reached a new space age high. Several factors have been proposed to explain this, for example, an unusually low magnetic field strength, a flattened current sheet, a low pressure solar wind, and a larger diffusion coefficient. This work focuses on a new 3D treatment of drift near the wavy heliospheric current sheet (HCS). We present solutions of Parker's equation using this new treatment of HCS drift and discuss implications for solar modulation during the recent extraordinary solar minimum. This work is supported by NASA grant NNX07AH73G and NNX08BA62G.
[show abstract][hide abstract] ABSTRACT: 1] We present a detailed description of our newly developed stochastic approach for solving Parker's transport equation, which we believe is the first attempt to solve it with time dependence in 3‐D, evolving from our 3‐D steady state stochastic approach. Our formulation of this method is general and is valid for any type of heliospheric magnetic field, although we choose the standard Parker field as an example to illustrate the steps to calculate the transport of galactic cosmic rays. Our 3‐D stochastic method is different from other stochastic approaches in the literature in several ways. For example, we employ spherical coordinates to integrate directly, which makes the code much more efficient by reducing coordinate transformations. What is more, the equivalence between our stochastic differential equations and Parker's transport equation is guaranteed by Ito's theorem in contrast to some other approaches. We generalize the technique for calculating particle flux based on the pseudoparticle trajectories for steady state solutions and for time‐dependent solutions in 3‐D. To validate our code, first we show that good agreement exists between solutions obtained by our steady state stochastic method and a traditional finite difference method. Then we show that good agreement also exists for our time‐dependent method for an idealized and simplified heliosphere which has a Parker magnetic field and a simple initial condition for two different inner boundary conditions. (2010), A general time‐dependent stochastic method for solving Parker's transport equation in spherical coordinates, J. Geophys. Res., 115, A12107, doi:10.1029/2010JA015721.
Journal of Geophysical Research 01/2010; 115. · 3.17 Impact Factor
[show abstract][hide abstract] ABSTRACT: A proper understanding of the different behavior of intensities of galactic cosmic rays in different solar cycle phases requires solving the modulation equation with time dependence. We present a detailed description of our newly developed stochastic approach for cosmic ray modulation which we believe is the first attempt to solve the time dependent Parker equation in 3D evolving from our 3D steady state stochastic approach, which has been benchmarked extensively by using the finite difference method. Our 3D stochastic method is different from other stochastic approaches in literature (Ball et al 2005, Miyake et al 2005, and Florinski 2008) in several ways. For example, we employ spherical coordinates which makes the code much more efficient by reducing coordinate transformations. What's more, our stochastic differential equations are different from others because our map from Parker's original equation to the Fokker-Planck equation extends the method used by Jokipii and Levy 1977 while others don't although all 3D stochastic methods are essentially based on Ito formula. The advantage of the stochastic approach is that it also gives the probability information of travel times and path lengths of cosmic rays besides the intensities. We show that excellent agreement exists between solutions obtained by our steady state stochastic method and by the traditional finite difference method. We also show time dependent solutions for an idealized heliosphere which has a Parker magnetic field, a planar current sheet, and a simple initial condition.
[show abstract][hide abstract] ABSTRACT: We calculate the cosmic ray diffusion tensor based on a recently developed model of magnetohydrodynamic (MHD) turbulence in the expanding solar wind [Breech et al., 2008.]. Parameters of this MHD model are tuned by using published observations from Helios, Voyager 2, and Ulysses. We present solutions of two turbulence parameter sets and derive the characteristics of the cosmic ray diffusion tensor for each. We determine the parallel diffusion coefficient of the cosmic ray following the method presented in Bieber et al. . We use the nonlinear guiding center (NLGC) theory to obtain the perpendicular diffusion coefficient of the cosmic ray [Matthaeus et al. 2003]. We find that (1) the radial mean free path decreases from 1 AU to 20 AU for both turbulence scenarios; (2) after 40 AU the radial mean free path is nearly constant; (3) the radial mean free path is dominated by the parallel component before 20 AU, after which the perpendicular component becomes important; (4) the rigidity P dependence of the parallel component of the diffusion tensor is proportional to P.404 for one turbulence scenario and P.374 for the other at 1 AU from 0.1 GVto 10 GV, but in the outer heliosphere its dependence becomes stronger above 4 GV; (5) the rigidity P dependence of the perpendicular component of the diffusion tensor is very weak. Supported by NASA Heliophysics Guest Investigator grant NNX07AH73G and by NASA Heliophysics Theory grant NNX08AI47G.
Journal of Geophysical Research 12/2008; · 3.17 Impact Factor