Gamma-ray pulsars and multipole fields

Eight gamma-ray pulsars have been discovered among about 600 radio pulsars. It is very interesting to investigate how are the gamma-ray pulsars formed. Based on the Arons-Scharlemann model of pulsar radiation, we discuss the emission of gamma-ray from pulsars when both the dipole and quadrupole fields exist. The curvature radius of field line and the energy of curvature radiation are calculated in this case. We also compute the generation order parameters (in cascade process) xi = xi(P, (P) over dot, k) where P is the period of pulsar, P is the derivative of period of pulsar, k the ratio of quadrupole to dipole field. For eight discovered pulsars, we find that their k are between 0.5 and 1 when xi = 2. It means that quadrupole plays an important role in forming these discovered gamma-ray pulsars.