Development and saturation of self-modulation of a long proton bunch in a plasma

Self-modulation (SM) of a long laser pulse or a particle bunch [1,2] can be used to resonantly drive plasma wakefields to large amplitudes. We present experimental results showing that the SM of a 400GeV, 175ps-duration proton bunch develops and saturates, whether seeded or not [3,4], in less than 10m of plasma with density in the 1e14 to 1e15/cc range. Development and saturation are derived from dependencies of the bunch halo radius [5], and of light emitted by dissipating wakefields [6], both as a function of plasma length. This is important to understand SM, and for the AWAKE plans to use the self-modulated bunch to accelerate an externally-injected electron bunch to 50 to 200GeV for application to particle physics and strong-field QED [7].

[1] The AWAKE Collaboration, Phys. Rev. Lett. 122, 054802 (2019)

[2] M. Turner et al., AWAKE Collaboration, Phys. Rev. Lett. 122, 054801 (2019)

[3] F. Batsch et al., AWAKE Collaboration, Phys. Rev. Lett. 126, 164802 (2021)

[4] L. Verra et al., AWAKE Collaboration, Phys. Rev. Lett. 129, 024802 (2022)

[5] A. Clairembaud et al., NIMA 1073, 170265 (2025)

[6] J. Mezger et al., NIMA 1075, 170426 (2025)

[7] E. Gschwendtner et al., (AWAKE Collaboration) Symmetry, 14(8), 1680 (2022)