Li, Y. M. Lotov, K.V. Sosedkin, A. Xia, G.X. Zhao, Y. JACoW Publishing Geneva, Switzerland 978-3-95450-184-7 10.18429/JACoW-IPAC2018-TUPML023 English 1585-1588 TUPML023 Contribution to a conference proceedings 2018 2018-06 https://doi.org/10.18429/JACoW-IPAC2018-TUPML023 http://jacow.org/ipac2018/papers/tupml023.pdf Seeded Self-modulation (SSM) has been demonstrated to transform a long proton bunch into many equidistant micro-bunches (e.g., the AWAKE case), which then resonantly excite strong wakefields. However, the wakefields in a uniform plasma suffer from a quick amplitude drop after reaching the peak. This is caused by a significant decrease of the wake phase velocity during self-modulation. A large number of protons slip out of focusing and decelerating regions and get lost, and thus cannot contribute to the wakefield growth. Previously suggested solutions incorporate a sharp or a linear plasma longitudinal density increase which can compensate the backward phase shift and therefore enhance the wakefields. In this paper, we propose a new plasma density profile, which can further boost the wakefield amplitude by 30%. More importantly, almost 24% of protons initially located along one plasma period survive in a micro-bunch after modulation. The underlying physics is discussed.