We present results of a model for the energetics of electrons accelera
ted by the large electric fields generated by a rotating highly magnet
ized neutron star. The energy-loss mechanisms we consider in our calcu
lations include magnetic Compton scattering of thermal X-ray photons,
triplet pair production, and curvature radiation emission. The electro
n acceleration mechanism is assumed to operate only to a height above
the polar cap approximately equal to the polar cap radius. We find sev
eral interesting results. First, magnetic Compton scattering is the do
minant energy-loss process when the electron Lorentz factors are less
than a few x 10(6) for typical gamma-ray pulsar magnetic fields and su
rface temperatures measured by ROSAT. The amount of energy converted t
o photons by accelerated electrons ranges from similar to 10% to simil
ar to 100% of y(0) m(e)c(2), where y(0) is the maximum Lorentz factor
an electron can attain with no radiative losses. We also find that if
B > 10(13) G and T > 3 x 10(6) K, the Lorentz factors of the electrons
can be limited to values less than or similar to 10(3), assuming valu
es for the size of the neutron star thermal polar cap comparable to th
e polar cap size determined by the open field lines. Such small Lorent
z factors may be capable of explaining the gamma-ray emission from PSR
1509-58 which is observed only at energies less than or similar to 1
MeV. We calculated the fraction of the electron's kinetic energy that
is converted to gamma rays for the three gamma-ray pulsars which show
thermal X-ray spectra, namely, Vela, Geminga, and PSR 1055-52. Using t
he pulsar parameters derived by Ogelman (1995), we found that we can e
xpect these pulsars to have between similar to 5% (Geminga) and simila
r to 60% (Vela) of the accelerated electron luminosity converted to ga
mma-ray luminosity.