AbstractA synthetic scheme for accelerating the convergence of the fission source in time-dependent multigroup even-parity Sncalculations with downscatter is described. The low-order operator associated with this scheme is a one-group diffusion operator. Thus, this scheme can be thought of as a variant of diffusion synthetic acceleration. A Fourier analysis of this scheme is performed, which indicates that it is unconditionally effective for a spatially infinite model problem. Computational results are presented that show excellent performance of the method in three-dimensional calculations. Although this method is derived for the even-parity Snequations, it can easily be generalized for application to the standard first-order Snequations. The accelerated iteration equations for both the even-parity and first-order Snequations are given, but only the even-parity algorithm is computationally tested.