Lawrence Berkeley National Laboratory

Use of a one-dimensional model of longitudinal space-charge (SC) impedance has been proposed for studying the microbunching instability in single-pass delivery systems relevant for the next generation of FELs. For beams with uniform transverse density and circular cross-section of radius r_b the SC impedance can be expressed in a handy analytical form, making this model particularly convenient. In this report we show how with an appropriate choice of r_b one can use this as an effective-beam model to approximate beams with non-axis symmetric and non-uniform transverse densities.