The new Affordable Robust Compact (ARC) fusion reactor, which, compared to larger machines like ITER, aims to achieve its goal of fusion energy in a less expensive and smaller but even more powerful and faster way with new high-field, high-temperature superconducting magnets, has been designed in the United States. The research tokamak aimed at the development of many ARC technologies is called SPARC. Ignitor is the proposed compact high-field tokamak that shares some design concepts with SPARC and ARC and shows the convenience of this tokamak design development line. Neutronics and radiation damage scoping studies have been carried out for both designs. A general-purpose macroscopic model set up by some of the authors in previous studies has been used to estimate the radiation damage on selected machine components for the two cases. Solutions to solve the problem of radiation damage of the toroidal field coil and poloidal field coil materials have been explored.