  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. The cutoff energy of the primary curvature emission is regulated below
several GeV even for young pulsars, because the gap thickness, and hence the
acceleration electric field is suppressed by the polarization of the produced
pairs.
