  We study pion production by proton synchrotron radiation in the presence of a
strong magnetic field when the Landau numbers of the initial and final protons
are $n_{i,f} \sim 10^4 - 10^5$. We find in our relativistic field theory
calculations that the pion decay width depends only on the field strength
parameter which previously was only conjectured based upon semi-classical
arguments. Moreover, we also find new results that the decay width satisfies a
robust scaling relation, and that the polar angular distribution of emitted
pion momenta is very narrow and can be easily obtained. This scaling implies
that one can infer the decay width in more realistic magnetic fields of
$10^{15}$G, where $n_{i,f} \sim 10^{12} - 10^{13}$, from the results for
$n_{i,f} \sim 10^4 - 10^5$. The resultant pion intensity and angular
distributions for realistic magnetic field strengths are presented and their
physical implications discussed.
