Opportunities and challenging seeding the self-modulation instability of a long proton bunch in plasma

Long laser pulses and charged particle bunches propagating in dense plasma are subject to transverse self-modulation (SM) instabilities. SM offers the opportunity to drive large amplitude wakefields with pulses/bunches in principle too long for that purpose [M. Turner et al., Phys. Rev. Lett. 122, 054801 (2019)]. Seeding of SM offers the apportunity to control the final timing and amplitude of the SM process. We have demontrated seeding of the SM of a long proton bunch in plasma using a relativistic ionization front (RIF-SSM) [F. Batsch et al., Phys. Rev. Lett. 126, 164802 (2021)] and using a short electron bunch (eSSM) [L. Verra et al., accepeted for publication in Phys. Rev. Lett., arXiv.2203.13752]. Seeding with a "cut in the electron bunch" was also demonstarted (cSSM) [Y. Fang et al., Phys. Rev. Lett. 112, 045001 (2014)]. We will summarize the experimental results obtained so far with SM seeding. We will outline the pros and cons of the seeding metods for the purpose of using the self-modulated bunch to drive a plasma wakefield acceleration stage [P. Muggli, J. Phys.: Conf. Ser. 1596 012008 (2020)]. In particular, the RIF-SSM is intrinsically simple than RIF-SSM, but SM instability may re-appear. eSSM leads to the SM of the entire bunch, but it may induce or seed the hose instability through misalignment beteen the two bunches.