Effect of Fisk-type heliospheric magnetic fields on the latitudinal transport of cosmic rays

A heliospheric magnetic field (HMF) with a merid- ional component, such as the model of Fisk, leads to a more complicated form of the transport equation (TPE) for cos- mic rays than is the case for the Parker model. The number of mixed derivatives increases and as a result the numerical codes used to solve the TPE becomes unstable more easily. In this progress report we circumvent some of these com- plications by using restrictive transport parameters. Apart from the standard Fisk field, we also consider a second Fisk- type field. Here the motion of the footpoints of the magnetic field on the source surface are assumed to follow circles cen- tred on an axis that is perpendicular to the rotation axis of the Sun. Such footpoint motions may occur, for instance, when the orientation of the solar magnetic dipole changes. We solve the three-dimensional steady-state TPE in a sys- tem corotating with the Sun, using spherical coordinates in an ADI numerical scheme. We show that both the standard Fisk field and the second Fisk-type field may reduce the lati- tudinal cosmic-ray gradient more at low than at high rigidity. Given our choice transport parameters, we see small effects. These should however be indicative of what can be expected when the restrictions on the transport parameters are relaxed. parameters that can be used. We regard the results from our code as both preliminary and qualitative. We introduce a second type of Fisk field and show that both types of fields reduce latitudinal gradients more at low rigidity than at high rigidity. While we neglect drifts in the numerical code, we show an estimate of drift effects in a Fisk field and a comparison to drift effects in other models for the HMF. 2 Modulation model In a coordinate system corotating with the Sun the cosmic- ray transport equation (TPE) of Parker (1965) can be written in terms of the omnidirectional distribution function f(r;p) (related to the differential intensity by jT / p 2 f ) as (K´ ota