White Paper: Radio Emission and Polarization Properties of Galaxy Clusters with VLASS

We outline the science case for extended radio emission and polarization in galaxy clusters which would be a scientifically important area of research for an upcoming Jansky Very Large Array Sky Survey. The survey would provide a major contribution in three key areas of the physics of clusters: 1) the active galactic nucleus population and the impact of feedback on the evolution of the intra-cluster medium, 2) the origin and evolution of diffuse cluster radio sources to probe the physics of mergers with implications for cosmology, and 3) the origin and role of magnetic fields in the ICM and in large scale structures. Considering all three areas, a survey must have sufficient spatial resolution to study the tailed galaxies which trace the cluster weather as well as the radio lobes driving energy into the cluster from the central AGN. The survey must also have sensitivity to low surface brightness emission and large angular scales to probe radio halos and relics as well as the WHIM residing in the large scale structure filaments. Finally, we note that full polarization information would be a highly valuable tool to probe a number of cluster-related issues. Due to the general steep spectral index of the emission we consider the survey is best suited to this science when conducted in P, L, or S bands. We conclude that the choices of S Band + D Configuration, L Band + C Configuration, and P Band + B Configuration offer optimal resolutions for constraining galactic interactions and feedback in cluster environments, while still probing large scale structure and the bulk cluster environment itself. While the push to probe higher redshifts and lower mass limits strongly favors a narrow and deep (or even targeted) survey strategy, we note that a wide survey covering roughly 1/4-2/3 of the sky will have significant scientific return, discovery potential, and archival value.