Stable acceleration of high-quality beams in plasma-based accelerators

A number of recent theoretical works proposed various promising methods for the generation of high-quality witness beams in present and future plasma-wakefield accelerators. However, before such beams are to be used in applications, the crucial question of the stable, quality-preserving acceleration and transport needs to be studied. An overview of the challenges regarding the stable, quality-preserving acceleration and transport of beams in single- and multi-stage plasma-wakefield accelerators will be presented with focus on methods for the emittance preservation and for the mitigation of the hose instability