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Active plasma lensing is a promising technology for compact focusing ofparticle beams that has seen a recent surge of interest. While these lenses canprovide strong focusing gradients of order kT/m and focusing in both transverseplanes, there are limitations from nonlinear aberrations, causing emittancegrowth in the beams being focused. One cause of such aberrations is beam-drivenplasma wakefields, present if the beam density is sufficiently high. We developsimple, but powerful analytic formulas for the effective focusing gradient fromthese wakefields, and use this to set limits on which parts of the beam andplasma parameter space permits distortion-free use of active plasma lenses. Itis concluded that the application of active plasma lenses to conventional andplasma-based linear colliders may prove very challenging, except perhaps in thefinal focus system, unless the typical discharge currents used are dramaticallyincreased, and that in general these lenses are better suited for acceleratorapplications with lower beam intensities.

Analytic plasma wakefield limits for active plasma lenses