We have proposed a method to reduce the size of a compact x-ray lithography machine used for etching the next-generation high-density computer chips. A high gradient electron accelerator powered by a relativistic klystron is used in place of the conventional linac as an injector to a superconducting synchrotron radiation ring to produce intense x-rays. Recent experimental results have demonstrated that electrons can reach the same final energy in a much shorter section of the high gradient accelerator than the conventional linac. The proposed machine is therefore much smaller than the conventional x-ray synchrotron machines. The compact machine enables manufacturers to utilize high-energy, high-intensity x- rays to produce various high-density computer chips in a factory environment. In Phase I of this research, we will perform conceptual studies for the injection system, and will consider the related physics and engineering issues for combining the relativistic klystron high gradient accelerator (RK/HGA) and the superconducting synchrotron radiation ring (SSRR) into a single x-ray production machine. Particular consideration will be given to the compatibility of the extremely short pulses produced by the RK/HGA and the macropulses required by the SSRR, to the preservation of electron beam emittance, and to tradeoff studies of various kicker magnet configurations in order to ensure efficient transfer of the beam from the RK/HGA to the SSRR.