  In this paper, we study the local well-posedness of classical solutions to
the ideal Hall-MHD equations whose magnetic field is supposed to be azimuthal
in the $L^2$-based Sobolev spaces. By introducing a good unknown coupling with
the original unknowns, we overcome difficulties arising from the lack of
magnetic resistance, and establish a self-closed $H^m$ with $(3\leq
m\in\mathbb{N})$ local energy estimate of the system. Here, a key cancellation
related to $\theta$ derivatives is discovered. In order to apply this
cancellation, part of the high-order energy estimates is performed in the
cylindrical coordinate system, even though our solution is not assumed to be
axially symmetric.
  During the proof, high-order derivative tensors of unknowns in the
cylindrical coordinates system are carefully calculated, which would be useful
in further researches on related topics.
