  We consider optimization of a rubidium atom clock that uses magnetically
trapped Bose condensed atoms in a highly elongated trap, and determine the
optimal conditions for minimum Allan variance of the clock using microwave
Ramsey fringe spectroscopy. Elimination of magnetic field shifts and
collisional shifts are considered. The effects of spin-dipolar relaxation are
addressed in the optimization of the clock. We find that for the interstate
interaction strength equal to or larger than the intrastate interaction
strengths, a modulational instability results in phase separation and symmetry
breaking of the two-component condensate composed of the ground and excited
hyperfine clock levels, and this mechanism limits the clock accuracy.
