Compact low emittance light sources based on longitudinal gradient bending magnets

The horizontal emittance of a storage ring beam can be reduced below the theoretical minimum of a given magnet structure if a variation of the longitudinal field is introduced in the bending magnets. The optimum longitudinal field variation for the generation of the lowest emittance has been calculated numerically - and analytically for different classes of simple functions: exponential-, power-, hyperbolic- and step-function. Constraints have been introduced for the maximum field and the minimum beta function in the magnet. The distribution of the deflection angles to the different magnet types has been optimized. The optimization results have been applied to an exemplary design of a lattice for a light source with limited circumference as for instance the Swiss Light Source.