Time dependent Solar Modulation of GCRs using a Monte-Carlo simulation

In characterising solar modulation of galactic cosmic rays, an often used parameter is the so called modulation parameter φ, whose value vary by a factor of more than 2 from the solar maximum to the solar minimum, reflecting the effects of different levels of solar activities on the modulation. Simple and elegant, this approach however, is based on the assumption that the current of GCRs is small and can be taken to be zero at all times, leading to a steady state solution of the transport equation. Recently, Wiedenbeck et al, using data from CRIS/ACE and ground neutron monitor, found that, for the declining phase of the solar cycle 23, the neutron monitor counting rate has been at a level of 4 percents higher than during the period when φ had comparable values during the rising phase of solar cycle 23. In this work, we examine this differences of neutron monitor counting rates (or alternatively, the difference of φ themselves) between the rising phase and declining phase of solar cycle. We show that the modulation of low energy GCRs is more sensitive to the phase of the solar cycle than high energy GCRs. We present in this work, the first time, a formalism to solve a time dependent transport equation using a stochastic method.