Experimental Investigation of Plasma Density Gradient Effect on Self-Modulation of a Proton Bunch

We study experimentally the effect of a linear plasma density gradient on the self-modulation of a long proton bunch in a dense plasma. The density gradient modifies the phase velocity of the wakefields. It can thus modify the development of the self-modulation process through the time or distance along the plasma that protons spend in the focusing or defocusing phase of the wakefields. This could change the number and the charge of micro-bunches that result from the periodic action of the wakefields. This effect varies along the bunch and along the plasma and is observed after the saturation of the process. Plasma density changing along the proton bunch path can also change the modulation period of the bunch. Experimental results obtained in the AWAKE experiment\footnote{P. Muggli et al. (AWAKE Collaboration), Plasma Physics and Controlled Fusion, 60(1) 014046 (2017)} will be presented\footnote{F. Braunmueller, T. Nechaeva et al. (AWAKE Collaboration), to be submitted}.