We present the spatially self-bending solutions (the partial Bessel functions) of the Maxwell equations, where the self-bending wave can be produced through launching a group of plane waves that interfere with each other by modulating their initial phases and the emission directions. The self-bending electromagnetic waves accelerating in a circular trajectory preserve the beam shape within a certain propagation distance. Unlike Ariy wave packet, the bending angle of the new self-accelerating wave can be much larger than that of Ariy beam. The Poynting vector of the half Bessel beam shows that the main lobe maintains a propagation-invariant structure and can complete a turn close to 180°. In addition, one pair of half Bessel electromagnetic waves is forbidden to propagate inside a certain area where the designed beam generates the self-shielding region.