Recent observational, theoretical, and experimental work strongly suggest that the damping of Alfvén waves is responsible for the heating of solar coronal holes. In order to experimentally investigate potential damping mechanisms, we have performed a series of experiments at the Large PlasmaDevice (LAPD) at the University of California, Los Angeles. Under experimental conditions scaled to approximate coronal holes, we have studied the propagation of Alfvén waves propagating through a gradient parallel or perpendicular to the magnetic field in both the kinetic regime (electron thermal speed ≫ Alfvén speed) and inertial regime (electron thermal speed ≪ Alfvén speed). In the recent laboratory experiment of kinetic Alfvén wave, it is observed that, in the presence of the gradient in the Alfvén speed, the damping mechanism is not sufficient to explain the energy reduction in the plasma. In order to better understand the reduction in wave energy through the gradient, we are carrying out an analysis of Alfvén wave propagation in the inertial regime. Here we report results for Alfvén waves in the inertial regime propagating through a parallel gradient. This work is supported, in part, by grants from the NSF Solar-Terrestrial Program under grant AGS-1834822 and the U.S. Department of Energy, Office of Science, Office of FusionEnergy Science under Award Numbers DE-SC0016602 and DE-SC0021261. The experiments were performed at the Basic Plasma Science Facility (BaPSF), which is supported by the DOE and NSF, with major facility instrumentation developed via an NSF award AGS-9724366.