  We propose a mechanism for the collective cooling of a large number N of
trapped particles to very low temperatures by applying red-detuned laser fields
and coupling them to the quantized field inside an optical resonator. The
dynamics is described by what appears to be rate equations, but where some of
the major quantities are coherences and not populations. The cooperative
behavior of the system provides cooling rates of the same order of magnitude as
the cavity decay rate kappa. This constitutes a significant speed-up compared
to other cooling mechanisms since kappa can, in principle, be as large as
square root of N times the single-particle cavity or laser coupling constant.
