Abstract
AbstractWe report here an exact analytical travelling wave solution for a non‐linear electron plasma wave excited by an intense ultra‐relativistic proton beam. It demonstrates the underlying physics of longitudinal electric field characteristics of the excited wake wave formed behind the drive beam. The results are further supplemented by a fully relativistic particle‐in‐cell code OSIRIS in two‐dimensional geometry. The investigation is further extended by providing an analytical description of the wake wave excited by an equi‐spaced train of small proton bunches with the inclusion of the non‐relativistic plasma ion dynamics. Our results show that the amplitude of the wake field does not grow indefinitely with the increase in the number of proton bunches. On the contrary, it saturates to a definitive limit.
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