A longitudinal accumulation scheme based on a triple-frequency RF system, in which the static radio frequency(RF) bucket is lengthened to be compatible with the realizable raise time of a fast pulse kicker, is proposed in this paper. With this technique, the bunch from a booster can be captured by the longitudinal acceptance without any disturbance to the stored bunch, which remains at the center. This composite RF system consists of three different frequencies, which can be regarded as the conventional bunch lengthening RF system(usually containing fundamental and third harmonic cavities) extended by an additional second harmonic RF cavity. In this paper, we discuss the RF jitter and the transverse mode-coupling instability(TMCI) when using this special RF system. Considering several different bunch profiles, we discuss the beam stability with regard to the RF jitter. However, for the TMCI we assume an ideal bunch profile, where the bunch is exactly lengthened to the maximum extent. While macroparticle simulation is the main method used to study the impact of the RF jitter, numerical analysis and simulations for the TMCI while using a triple-frequency RF system are also presented in this paper. An approximation formula, based on the existing model, is also derived to estimate the impact of the TMCI on the single bunch current threshold when using harmonic cavities.
