  We study experimentally the longitudinal and transverse wakefields driven by
a highly relativistic proton bunch during self-modulation in plasma. We show
that the wakefields' growth and amplitude increase with increasing seed
amplitude as well as with the proton bunch charge in the plasma. We study
transverse wakefields using the maximum radius of the proton bunch distribution
measured on a screen downstream from the plasma. We study longitudinal
wakefields by externally injecting electrons and measuring their final energy.
Measurements agree with trends predicted by theory and numerical simulations
and validate our understanding of the development of self-modulation.
Experiments were performed in the context of the Advanced Wakefield Experiment
(AWAKE).
