We investigate the electrodynamic structure of a pulsar outer-magnetospheric particle accelerator and the resultant gamma-ray emission. By considering the condition for the accelerator to be self-sustained, we derive how the trans-magnetic-field thickness of the accelerator evolves with the pulsar age. It is found that the thickness is small but increases steadily if the neutron-star envelope is contaminated by sufficient light elements.
For such a light element envelope, the gamma-ray luminosity of the accelerator is kept approximately constant as a function of age in the initial ten thousand years, forming the lower bound of the observed distribution of the gamma-ray luminosity of rotation-powered pulsars. If the envelope consists of only heavy elements, on the other hand, the thickness is greater but increases less rapidly than what a light element envelope has.
For such a heavy element envelope, the gamma-ray luminosity decreases relatively rapidly, forming the upper bound of the observed distribution. The gamma-ray luminosity of a general pulsar resides between these two extreme cases, reflecting the envelope composition and the magnetic inclination angle with respect to the rotation axis.