The injection of plasma sheet ion to inner magnetosphere plays an important role during the time of magnetic sub-storm and storm periods. In the past, researches of such injection were all processed by the method of drift path theory of certain magnetic moment particles. In this article, we will extend the past certain magnetic moment magnetosphere particle drift path theory in (U,B) coordinate to certain energy magnetosphere particle drift path theory. Because particle's drift orbit is associated with its charge, we will take proton as an example. Then we will discuss the characters of different energy particles' boundary between their open and close drift path and its variation with Kp index during their transportation to the Earth. In high energy situation, the radial distance to the Earth of plasma sheet ions' boundary will increase with their energy, and the distance in dawn side is much larger than that in dusk side. But in low energy situation, such thing will completely change. The radial distance will decrease with ion energy and the radial distance in dusk side will be larger than that in dawn side. Our simulation results also show that with the increase of Kp index, all boundaries of various energy particles in the plasma sheet will move towards the Earth. But performances of ion boundaries in high and low situations are different. To low energy situation, the inner boundary shape of ion almost keeps constant with the increase of Kp index. To high energy situation, its shape will change remarkably with Kp index. In two extreme cases, that is, E=20 keV, Kp=6 and E=10 keV,Kp=3, the ion boundaries even show two different regions, one is the closed circling Earth region and the other is the isolated tapered region in dawn side. The boundary of plasma sheet certain-energy-E particles is just the connection of energy-E point in various magnetic moments Alfven layer.