  Josephson radiation is a useful signature for detecting Majorana zero modes
in topological superconductors. We study the Josephson radiation of the
underdamped topological Josephson junction within the quantum resistively and
capacitively shunted junction model. We show that the quantum dynamics of the
Majorana two-level system induce oscillatory patterns in the Josephson emission
spectra. With the Floquet method, we obtain analytical results for these
oscillatory patterns and find that they are well described by Bessel functions.
We perform numerical simulations to verify the analytical results and
demonstrate that these Bessel radiation patterns exist for a wide range of
junction parameters.
