Measurement of energy reduction by inertial Alfv\'en waves propagating through parallel gradients in the Alfv\'en speed

We have studied the propagation of inertial Alfv\'en waves through parallel gradients in the Alfv\'en speed using the Large Plasma Device at the University of California, Los Angeles. The reflection and transmission of Alfv\'en waves through inhomogeneities in the background plasma is important for understanding wave propagation, turbulence, and heating in space, laboratory, and astrophysical plasmas. Here we \rev{present inertial Alfv\'en waves, under conditions relevant to solar flares and the solar corona. We find} that the transmission of the inertial Alfv\'en waves is reduced as the sharpness of the gradient is increased. Any reflected waves were below the detection limit of our experiment and reflection cannot account for all of the energy not transmitted through the gradient. Our findings indicate that, for both kinetic and inertial Alfv\'en waves, the controlling parameter for the transmission of the waves through an Alfv\'en speed gradient is the ratio of the Alfv\'en wavelength along the gradient divided by the scale length of the gradient. Furthermore, our results suggest that an as-yet-unidentified damping process occurs in the gradient.