The behavior of the electron distribution function within mirror mode
waves in the Earth's magnetosheath is studied using observations made
by the electron experiment on Active Magnetospheric Particle Tracer Ex
plorers United Kingdom Subsatellite (AMPTE UKS). The results of a deta
iled pitch angle analysis show that in the mirror mode troughs the ele
ctron distribution displays two distinct features related to particle
trapping: (1) The ''deeply''' trapped electrons (those with pitch angl
es close to 90 degrees in the magnetic field troughs) are significantl
y cooled with respect to the rest of the electron population and (2) t
he ''shallowly'' trapped electrons (those with pitch angles just great
er than the critical pitch angle for trapping) are significantly heate
d with respect to the rest of the electron population. This is explain
ed as a result of the trapped electron population undergoing a combina
tion of Fermi acceleration and deceleration and betatron deceleration.
The untrapped electron population appears to behave adiabatically as
it travels alternately through mirror mode peaks and troughs. This beh
avior is confirmed by the use of Liouville mapping techniques, which a
lso allow us to estimate the electric potential associated with the mi
rror mode wave.