  A Fermi accelerator is a billiard with oscillating walls. A leaky accelerator
interacts with an environment of an ideal gas at equilibrium by exchange of
particles through a small hole on its boundary. Such interaction may heat the
gas: we estimate the net energy flow through the hole under the assumption that
the particles inside the billiard do not collide with each other and remain in
the accelerator for sufficiently long time. The heat production is found to
depend strongly on the type of the Fermi accelerator. An ergodic accelerator,
i.e. one which has a single ergodic component, produces a weaker energy flow
than a multi-component accelerator. Specifically, in the ergodic case the
energy gain is independent of the hole size, whereas in the multi-component
case the energy flow may be significantly increased by shrinking the hole size.
