One limitation in high energy and high-efficiency electron acceleration by laser-driven plasma wakefield is the dephasing due to the accelerated electrons surpassing the acceleration phase of the wake. Here, by utilizing multi-stage plasma channels with different densities, we show in simulations that electrons can jump from a back acceleration bubble into a front one before getting into the deceleration phase and obtain relay acceleration in the front bubble when the laser steps into a new stage of the plasma channel. In our numerical studies, the final maximum energy of the electrons by such relay acceleration can be several times higher than electrons accelerated in a single-stage plasma channel. The defocusing effects on the beam emittance and charge, caused by electrons crossing the high-density electron layer located between the neighboring bubbles, can be suppressed by appropriately connecting the staged channels. The current scheme helps to increase the acceleration energy and efficiency of laser wakefield accelerators.
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