The Energy Dependence of the Saturation Momentum

We study BFKL evolution and, in particular, the energy dependence of the saturation momentum in the presence of saturation boundaries limiting the region of linear BFKL evolution. In the case of fixed coupling evolution we confirm the previously found exponential term in $Q_s(Y)$ and determine the prefactor $Y$ and $\alpha$ dependences. In the running coupling case we find $Y^{1/6}$ corrections to the $Y^{1/2}$exponential behavior previously known. Geometrical scaling of the scattering amplitude is valid in a wide-range of momenta for fixed coupling evolution and in a more restricted region for running coupling evolution.