Emittance growth from rotated quadrupoles in heavy ion accelerators

We derive a set of moment equations which incorporates linear quadrupolar focusing and space-charge defocusing, in the presence of rotational misalignments of the quadrupoles about the direction of beam propagation. Although the usual beam emittance measured relative to fixed transverse x and y coordinate axes is not constant, a conserved emittance-like quantity has been found. Implications for alignment tolerances in accelerators for heavy-ion inertial fusion are discussed.