  We present an analytical study on the effects of the transverse plasma
gradient in the blowout regime of a plasma wakefield accelerator (PWA). The
analysis departs from a simple ballistic model of plasma electrons that 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.
