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In this work we present two new closures for the spherical harmonics (PN)method in slab geometry transport problems. Our approach begins with ananalysis of the squared-residual of the transport equation where we show thatthe standard truncation and diffusive closures do not minimize the residual ofthe PN expansion. Based on this analysis we derive two models, a moment-limiteddiffusive MLDN closure and a transient PN (TPN) closure that attempt to addressshortcomings of common closures. The form of these closures is similar toflux-limiters for diffusion with the addition of a time-derivative in thedefinition of the closure. Numerical results on a pulsed plane source problem,the Gordian knot of slab-geometry transport problems, indicate that our newclosure outperforms existing linear closures. Additionally, on a deeppenetration problem we demonstrate that the TPN closure does not suffer fromthe artificial shocks that can arise in the MN entropy-based closure. Finally,results for Reed's problem demonstrate that the TPN solution is as accurate asthe PN+3 solution. We further extend the TPN closure to 2D Cartesian geometry.The line source test problem demonstrates the model effectively dampsoscillations and negative densities

Moment Closures Based on Minimizing the Residual of the P$_N$ Angular Expansion in Radiation Transport