| Summary: | In this work we provide an in-depth analysis of mechanisms which mitigate the hose instability in the blowout regime in plasma-wakefield accelerators. We show by means of theory and three-dimensional particle-in-cell simulations that the mitigation mechanisms related to a beam energy spread are effective for parameters as used in major plasma-wakefield accelerator experiments and for various beam energies, beam current profiles, and types of hosing seed. In addition, we establish the theoretical principles for the reduction of the initial hosing seed in tapered vacuum-to-plasma transitions and derive respective analytic predictions which are successfully benchmarked against particle-in-cell simulations. We also investigate the possibility to facilitate efficient and stable acceleration of witness beams in the blowout regime. This work therefore provides a deepened understanding for the methods that allow for the mitigation of hosing, a crucial prerequisite to facilitate stable acceleration of high quality beams in plasma-wakefield accelerators.
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