  In this short note we derive an approximate expression for the mode density
of modes carrying orbital angular momentum (OAM) in a cylindrical cavity which
is large compared to the inverse wavevector in any direction. We argue that in
the large cavity limit the modes asymptotically converges to the corresponding
OAM modes in free space. We compare the result to Weyl's law. It is found, as
expected, that the mode density does not depend on whether or not the modes
carry OAM.
