Measurement of the Saturation Length of the Self-Modulation Instability

Abstract: The self-modulation (SM) instability transforms a long charged particle bunch traveling in plasma into a train of microbunches that resonantly drives large-amplitude wakefields. We present the first determination of the saturation length of SM using experimental and numerical results. The saturation length is the distance over which wakefields reach their maximum amplitude along the plasma. By varying the plasma length and measuring the radius of the transverse distribution of the bunch, we find that the saturation length of SM decreases with plasma density and initial field amplitude, e.g., when seeding. The saturation length is a fundamental parameter of the instability, and these results are key for understanding SM and designing plasma wakefield accelerators driven by long bunches, such as AWAKE, or by long laser pulses for radiation production.