We study pion curvature radiation by a proton, i.e. pion emission by a
proton moving along a curved trajectory. We suggest an approximate se
miclassical solution and the exact solution for which we assume that a
proton moves in a fictitious magnetic field with the Larmor radius eq
ual to the curvature radius of the real trajectory. As possible applic
ation we consider the pion radiation by ultrahigh energy protons movin
g along curved magnetic field lines. Such situation can occur in the m
agnetosphere of a young pulsar, in the magnetosphere of the accretion
disk around a black hole, and in the vicinity of a superconducting cos
mic string. The decay products of these pions, such as high energy pho
tons or neutrinos, can give the observable consequences of the conside
red mechanism.