  We present the results of a search for galaxy clusters in the first 36
XMM-Newton pointings on the COSMOS field. We reach a depth for a total cluster
flux in the 0.5-2 keV band of 3x10-15 ergs cm-2 s-1, having one of the widest
XMM-Newton contiguous raster surveys, covering an area of 2.1 square degrees.
Cluster candidates are identified through a wavelet detection of extended X-ray
emission. Verification of the cluster candidates is done based on a galaxy
concentration analysis in redshift slices of thickness of 0.1-0.2 in redshift,
using the multi-band photometric catalog of the COSMOS field and restricting
the search to z<1.3 and i_AB < 25. We identify 72 clusters and derive their
properties based on the X-ray cluster scaling relations. A statistical
description of the survey in terms of the cumulative log(N>S)-lg(S)
distribution compares well with previous results, although yielding a somewhat
higher number of clusters at similar fluxes. The X-ray luminosity function of
COSMOS clusters matches well the results of nearby surveys, providing a
comparably tight constraint on the faint end slope of alpha=1.93+/-0.04. For
the probed luminosity range of 8x10+42 - 2x10+44 ergs s-1, our survey is in
agreement with and adds significantly to the existing data on the cluster
luminosity function at high redshifts and implies no substantial evolution at
these luminosities to z=1.3.
