Exploring the role of Alfv\'en waves in heating the solar corona

The solar corona, the outer atmosphere of the Sun, is $\sim 200$ times hotter than the underlying visible surface of the Sun. Recent coronal observations find Alfv\'en wave damping at unexpectedly low heights in the corona, suggesting that Alfv\'en waves may contribute to the heating of the corona to temperatures of $\sim 10^{6}$ K. Dissipation of wave energy may occur due to gradients in the Alfv\'en speed along the coronal magnetic field lines. These gradients may cause wave reflection, which subsequently generates turbulence. Furthermore, the presence of gradients in the Alfv\'en speed across the magnetic field line may lead to phase mixing, which can promote additional nonlinear damping mechanisms. We are studying various wave dissipation processes under conditions similar to the solar corona, using the Large Plasma Device (LAPD) at the University of California, at Los Angeles. Here we will present the results of our initial experiments exploring the effectiveness of gradients in the Alfv\'en speed along the magnetic field in reflecting Alfv\'en waves and reducing the amplitude of Alfv\'en waves transmitted across a gradient