  The search for a possible critical point in the QCD phase diagram is ongoing
in heavy ion collision experiments at RHIC which scan the phase diagram by
scanning the beam energy; a coming upgrade will increase the luminosity and
extend the rapidity acceptance of the STAR detector. In fireballs produced in
RHIC collisions, the baryon density depends on rapidity. By employing Ising
universality together with a phenomenologically motivated freezeout
prescription, we show that the resulting rapidity dependence of cumulant
observables sensitive to critical fluctuations is distinctive. The dependence
of the kurtosis (of the event-by-event distribution of the number of protons)
on rapidity near mid-rapidity will change qualitatively if a critical point is
passed in the scan. Hence, measuring the rapidity dependence of cumulant
observables can enhance the prospect of discovering a critical point, in
particular if it lies between two energies in the beam energy scan.
