Proof of the nonexistence of a linear solution for the CR2 injection region of the CLIC drive beam

In this paper we present a mathematical proof to show that there exists no linear system of optics which can simultaneously close an orbit bump and correct the dispersion in the CR2 injection region. Due to the requirements of the CR2 injection region, several different trajectories will exist through the injection region which are off-axis; therefore the orbit and dispersion functions need to be corrected. In this paper, we determine the properties of a hypothetical linear lattice which is capable of closing the orbit and dispersion functions and then show that the resulting solutions are either unphysical or trivial. Geneva.