  The effects of turbulence in the very local interstellar medium (VLISM) have
been proposed by Giacalone & Jokipii (2015) to be important in determining the
structure of the Interstellar Boundary Explorer (IBEX) ribbon via particle
trapping by magnetic mirroring. We further explore this effect by simulating
the motion of charged particles in a turbulent magnetic field superposed on a
large-scale mean field, which we have considered to be either spatially-uniform
or a mean field derived from a 3D MHD simulation. We find that the ribbon is
not double-peaked, in contrast to Giacalone & Jokipii (2015). However, the
magnetic mirror force still plays an important role in trapping particles.
Furthermore, the ribbon$'$s thickness is considerably larger if the large-scale
mean field is draped around the heliosphere. Voyager 1 observations in the
VLISM show a turbulent field component that is stronger than previously
thought, which we test in our simulation. We find that the inclusion of
turbulent fluctuations at scales ${\gtrsim}$100 au and power consistent with
Voyager 1 observations produces a ribbon whose large-scale structure is
inconsistent with IBEX observations. However, restricting the fluctuations to
${\sim}$10 au or smaller produces a smoother ribbon structure similar to IBEX
observations. Different turbulence realizations produce different small-scale
features ${\lesssim}10{\deg}$ in the ribbon, but its large-scale structure is
robust if the maximum fluctuation size is ${\sim}$10 au. This suggests that the
magnetic field structure at scales ${\lesssim}$10 au is determined by the
heliosphere$'$s interaction with the VLISM and cannot entirely be represented
by homogeneous interstellar turbulence.
