Curvature radiation by ultrarelativistic protons

We study pion curvature radiation by a proton, i.e. pion emission by a proton moving along a curved trajectory. We suggest an approximate semiclassical solution and the exact solution for which we assume that a proton moves in a fictitious magnetic field with the Larmor radius equal to the curvature radius of the real trajectory. As possible application we consider the pion radiation by ultrahigh energy protons moving along curved magnetic field lines. Such situation can occur in the magnetosphere of a young pulsar, in the magnetosphere of the accretion disk around a black hole, and in the vicinity of a superconducting cosmic string. The decay products of these pions, such as high energy photons or neutrinos, can give the observable consequences of the considered mechanism.