  The large-scale magnetic structure of interplanetary coronal mass ejections
(ICMEs) has been shown to affect the galactic cosmic ray (GCR) flux measured in
situ by spacecraft, causing temporary decreases known as Forbush decreases
(Fds). In some ICMEs, the magnetic ejecta exhibits a magnetic flux rope (FR)
structure; the strong magnetic field strength and closed field line geometry of
such ICME FRs has been proposed to act as a shield to GCR transport. In this
study, we identify four ICMEs near Earth that drove Fds with similar mean
magnetic field strengths (20 - 25 nT); two ICMEs with more typical mean speeds
(~400 km/s), and two fast (~750 km/s) ICMEs. Within each speed pairing, we
identify an ICME that exhibited an open magnetic field line topology and
compare its effect on the GCR flux to that which exhibited a mostly closed
topology. We investigate the different mechanisms that contribute to the
resulting ICME-related Fds and their recovery, and determine which properties,
if any, play a more important role than others in driving Fds. We find that
much of the GCR response to the ICME events in this study is independent of the
open or closed magnetic field line topology of the flux rope, and that features
such as the fluctuations in speed, magnetic field structure, and expansion
within the FR may play more of a role in determining the smaller-scale
structure of the Fd profile.
