The transverse stability of the target is crucial for obtaining high quality ion beams using the laser radiation pressure acceleration (RPA) mechanism. In this letter, a theoretical model and supporting two-dimensional (2D) Particle-in-Cell (PIC) simulations are presented to clarify the physical mechanism of the transverse instability observed in the RPA process. It is shown that the density ripples of the target foil are mainly induced by the coupling between the transverse oscillating electrons and the quasi-static ions, a mechanism similar to the transverse two stream instability in the inertial confinement fusion (ICF) research. The predictions of the mode structure and the growth rates from the theory agree well with the results obtained from the PIC simulations in various regimes, indicating the model contains the essence of the underlying physics of the transverse break-up of the target.
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