  Josephson radiation is a powerful method to probe Majorana zero modes in
topological superconductors. Recently, Josephson radiation with half the
Josephson frequency has been experimentally observed in a HgTe-based junction,
possibly from Majorana zero modes. However, this radiation vanishes above a
critical voltage, sharply contradicting previous theoretical results. In this
work, we theoretically obtain a radiation spectrum quantitatively in agreement
with the experiment after including the nonlinear dynamics of the Majorana
states into the standard resistively shunted junction model. We further predict
two new structures of the radiation spectrum for future experimental
verification: an interrupted emission line and a chaotic regime. We develop a
fixed-point analysis to understand all these features. Our results resolve an
apparent discrepancy between theory and experiments, and will inspire
reexamination of structures in radiation spectra of various topological
Josephson junctions.
