  In this paper, the feasibility of the electron-positron collider based on
plasma accelerator is proved by simulation experiments. Starting from the
17.612cm proton beam provided by SPS (super proton synchrotron), the simulation
shows that the long proton beam can form several high quality proton bunches
through seeded self-modulation in the first half of the long proton beam in a
uniform plasma. Then we use these high-quality bunches to excite the wakefield
in a uniform plasma and accelerate witness positrons and witness electrons. The
simulation results show that the average energy of witness bunches after about
90 meters acceleration is about 125 GeV, and the average acceleration gradient
is about 1.3 GeV/m. The center-of-mass (CoM) energy of positron-electron
collision is about 125 GeV. The energy spread, witness particle survival rate,
emittances and luminorsity of the output witness bunches are also discussed.
