Underdense plasma lens with a transverse density gradient

We explore the implications of a transverse density gradient on the performance of an underdense plasma lens and nonlinear plasma-based accelerator. Transverse density gradients are unavoidable in plasma sources formed in the outflow of standard gas jets, which are used heavily in plasma accelerator communities. These density gradients lead to longitudinal variations in the transverse wakefields, which can transversely deflect an electron beam within the blowout wake. We present a theoretical model of the fields within the plasma blowout cavity based on empirical analysis of 3D particle-in-cell (PIC) simulations. Using this model, the transverse beam dynamics may be studied analytically, allowing for an estimation of the net kick of a witness electron bunch from an underdense plasma lens and for density uniformity tolerance studies in plasma accelerators and plasma lenses. This model is compared to PIC simulations with a single electron bunch and constant density profile, and to PIC simulations with two bunches and a thin, underdense plasma lens density profile with density ramps.