Effects of the transversely nonuniform plasma density in a blowout regime of a plasma wakefield accelerator

We present an analytical study on the effects of the transverse plasma gradient in the blowout regime of a plasma wakefield accelerator. The analysis departs from a simple ballistic model of plasma electrons and allows us to derive a complete analytic solution for the pseudopotential and, consequently, for the wakefield. We demonstrate that the transverse plasma gradient modifies the bubble shape and affects the wakefield; namely, the dipole plasma gradient results in a dipole component of the wakefield. Analysis suggests that, despite the asymmetry, the instability due to the fixed transverse plasma gradient is unlikely, as the total wakefield has a single stable point inside the bubble. The only effect that occurs is the shift of the electromagnetic center. We point out that random fluctuation of the transverse plasma gradient could become an issue.