  In the lattice designs for the next generation storage ring light sources,
longitudinal gradient bending magnets and anti-bending magnets have been
adopted. A logical question raised by the trend of varying the longitudinal
distribution of dipole strength is: what are the optimal distributions of the
dipole and quadrupole fields in a lattice cell for the purpose of minimizing
the natural emittance? We studied this problem by numerically optimizing the
dipole and quadrupole distributions of the normalized cell optics using the
particle swarm optimization algorithm. The results reveal the features of the
longitudinal field variation of the optimized cell and show that when the
quadrupole gradient is increased enough, the cell tends to split into two
identical cells with similar features.
