Modelling the effects of scattering parameters on particle-drift in the solar modulation of galactic cosmic rays

It is well known that particle drift motions are suppressed by diffusive scattering as established by direct numerical simulations. The effect of constant scattering on the drift velocities of charged particles has always been included in numerical modulation models provided that the weak scattering drift velocity is scaled down in magnitude, although in an empirical manner as comparison between drift models and observations required. What has not yet been established is the spatial dependence of the scattering parameter (ωτ), with ω the gyro-frequency and τ a time scale defined by diffusive scattering. In this work, current knowledge about the spatial and rigidity dependence of ωτ is used to illustrate and discuss its effect on the drift coefficient in the modulation of cosmic ray Carbon in the heliosphere. This is done with a well-established numerical model which includes all four major modulation processes, also the solar wind termination shock (TS) and the heliosheath. We estimate that a reasonable range in the value of ωτ is 0 ⩽ ωτ ⩽ 5, applicable to modulation studies inside and outside the TS. Furthermore, it is found that the considered different scenarios for ωτ cause significant modifications to the weak scattering drift coefficient and as such on the subsequent computed differential intensities in both solar magnetic polarity cycles. For example, it is found that when ωτ decreases rapidly over the heliospheric polar regions, the resulting drift coefficient at 1 AU becomes smaller at the poles compared to its value in the equatorial plane. This is contrary to the generally assumed spatial dependence of the maximal weak scattering drift coefficient. The consequent effect is that in the equatorial plane the A < 0 spectra are higher than the A > 0 spectra at all energies primarily because of drifts; which is unexpected from a classical drift modelling point of view. This feature persists for the equatorial plane modulation even when the explicit enhancement of perpendicular polar diffusion is neglected. Thus, scenarios of ωτ with strong decreases over the heliospheric polar regions seem unlikely for the modulation of galactic cosmic rays in the upstream region of the TS.