[en] Various longitudinal distributions, resulting from the specific injection and stacking methods, are considered to minimize longitudinal and transverse instabilities and particle losses in SNS accumulator ring. The longitudinal phase space paintings by linac energy ramping, increased linac energy spread and the use of a random phase RF debunching cavity are reported. Bunch lengthening and beam in gap rate as functions of injection energy spread RF voltage and injection energy error is summarized. Finally, the energy error tolerance is concluded