Semiclassical theory of charged pion radiation by nucleons in a strong homogeneous magnetic field

Charged pions produced in very high energy hadronic interactions might be the dominant source of cosmic neutrinos in the GeV--TeV range. Spectral energy power of \pi^+ radiation by high energy protons moving in strong magnetic fields typical for magnetars is determined with a semiclassical treatment of the effective pion-nucleon model. The main characteristics emerging from a saddle point approximation to the summation over the allowed range of Landau levels is a sharp lower cut: E_\pi>0.25 E_p. The magnitude of the spectral power agrees in this region with the synchrotron radiation spectra of neutral pions.