  The transverse self-modulation of ultra-relativistic, long lepton bunches in
high-density plasmas is explored through full-scale particle-in-cell
simulations. We demonstrate that long SLAC-type electron and positron bunches
can become strongly self-modulated over centimeter distances, leading to wake
excitation in the blowout regime with accelerating fields in excess of 20 GV/m.
We show that particles energy variations exceeding 10 GeV can occur in
meter-long plasmas. We find that the self-modulation of positively and
negatively charged bunches differ when the blowout is reached. Seeding the
self-modulation instability suppresses the competing hosing instability. This
work reveals that a proof-of-principle experiment to test the physics of bunch
self-modulation can be performed with available lepton bunches and with
existing experimental apparatus and diagnostics.
