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We use a relativistic ionization front to provide various initial transverse wakefield amplitudes for the self-modulation of a long proton bunch in plasma. We show experimentally that, with sufficient initial amplitude ($ge(4.1pm0.4)$ MV/m), the phase of the modulation along the bunch is reproducible from event to event, with 3 to 7% (of 2$pi$) rms variations all along the bunch. The phase is not reproducible for lower initial amplitudes. We observe the transition between these two regimes. Phase reproducibility is essential for deterministic external injection of particles to be accelerated.
Seeded self-modulation in a plasma can transform a long proton beam into a train of micro-bunches that can excite a strong wakefield over long distances, but this needs the plasma to have a certain density profile with a short-scale ramp up. For the
AWAKE is a proton-driven plasma wakefield acceleration experiment. % We show that the experimental setup briefly described here is ready for systematic study of the seeded self-modulation of the 400,GeV proton bunch in the 10,m-long rubidium plasma w
We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported in arXiv:2007.14894
We analyze the electromagnetic field of a small bunch that uniformly moves in a circular waveguide and transverses a boundary between an area filled up with cold magnetized electron plasma and a vacuum area. The magnetic field is supposed to be stron
If a charged particle bunch propagates near a plasma-vacuum boundary, it excites a surface wave and experiences a force caused by the boundary. For the linearly responding plasma and ultra-relativistic bunch, the spatial distribution of excited field