Laser wakefield acceleration of electrons usually offers an axisymmetry around the laser propagation axis. Thus, the accelerating electrons that are focused on axis often execute small transverse oscillations. In this Article, we propose a simple scheme to break this symmetry, which enhances the transverse wiggling of electrons and boosts the betatron radiation emission. Through 3D particle-in-cell simulations, we show that sending the laser with a small angle of incidence on a transverse plasma density gradient generates an asymmetric wakefield. It first provokes injection and then increases the wiggling of the electrons through the transverse shifting of the wakefield axis which occurs when the laser pulse leaves the gradient. Consequently, we show that the radiated energy per unit of charge can increase by a factor $>20$ when using this scheme, and that the critical energy of the radiation quintuples compared with a reference case without the transverse density gradient.
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