The Effect of a Fisk-type Heliospheric Magnetic Field on Cosmic Ray Modulation

Physics

Scientific paper

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2104 Cosmic Rays, 2134 Interplanetary Magnetic Fields

Scientific paper

A heliospheric magnetic field (HMF) with a meridional component, such as the model of Fisk, leads to a more complicated form of the transport equation (TPE) for cosmic rays than is the case for the Parker model of the HMF. The number of terms with mixed derivatives increases and as a result the three-dimensional numerical codes used to solve the TPE becomes unstable more easily. In this paper we present a hybrid Fisk/Parker HMF, which is a pure Fisk HMF at mid-latitudes, but changes to a Parker HMF in the solar equatorial plane and above the solar poles. Although this field will under-estimate the full effects of the Fisk field to some degree, it's use should give some insight into the effect of an HMF with a periodic meridional component on cosmic-ray modulation. To study this hybrid field, we solve the three-dimensional steady-state TPE in a system corotating with the Sun, using spherical coordinates in an ADI numerical scheme which covers the entire heliopshere. The solar wind speed is assumed to be independent of latitude. For the parallel diffusion coefficient we use a standard QLT expression. The perpendicular diffusion coefficients have the same spatial dependence as the parallel diffusion coefficient, but have a flatter rigidity dependence. We use the standard weak-scattering form for the drift coefficient and a wavy current sheet with a small tilt angle. We present results for galactic cosmic-ray protons and electrons, covering an energy range from 10 GeV down to a few MeV. We find that the 27-day intensity variations are more pronounced when the latitudinal gradient is large. The latitudinal gradient itself is reduced with respect to the gradient for a pure Parker HMF. This reduction does not change the rigidity at which the maximum latitudinal gradient occurs for either protons or electrons.

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