  We consider E polarized bound states in the radiation continuum (BICs) in
circular periodical arrays of $N$ infinitely long dielectric rods. We find that
each true BIC which occurs in an infinite linear array has its counterpart in
the circular array as a near-BIC with extremely large quality factor. We argue
analytically as well as numerically that the quality factor of the symmetry
protected near-BICs diverges as $e^{\lambda N}$ where $\lambda$ is a material
parameter dependent on the radius and the refraction index of the rods. By
tuning of the radius of rods we also find numerically non-symmetry protected
near-BICs. These near-BICs are localized with exponential accuracy outside the
circular array but fill the whole inner space of the array carrying orbital
angular momentum.
