  Quasi-periodic oscillations (QPOs) are observed in the optical flux of some
polars with typical periods of 1 to 3 s but none have been observed yet in
X-rays where a significant part of the accreting energy is released. QPOs are
expected and predicted from shock oscillations. Most of the polars have been
observed by the XMM-Newton satellite. We made use of the homogeneous set of
observations of the polars by XMM-Newton to search for the presence of QPOs in
the (0.5-10 keV) energy range and to set significant upper limits for the
brightest X-ray polars. We extracted high time-resolution X-ray light curves by
taking advantage of the 0.07 sec resolution of the EPIC-PN camera. Among the 65
polars observed with XMM-Newton from 1998 to 2012, a sample of 24 sources was
selected on the basis of their counting rate in the PN instrument to secure
significant limits. We searched for QPOs using Fast Fourier Transform (FFT)
methods and defined limits of detection using statistical tools. Among the
sample surveyed, none shows QPOs at a significant level. Upper limits to the
fractional flux in QPOs range from 7% to 71%. These negative results are
compared to the detailed theoretical predictions of numerical simulations based
on a 2D hydrodynamical code presented in Paper II. Cooling instabilities in the
accretion column are expected to produce shock quasi-oscillations with a
maximum amplitude reaching ~ 40% in the bremsstrahlung (0.5-10 keV) X-ray
emission and ~ 20% in the optical cyclotron emission. The absence of X-ray QPOs
imposes an upper limit of ~ (5-10) g.cm-2.s-1 on the specific accretion rate
but this condition is found inconsistent with the value required to account for
the amplitudes and frequencies of the observed optical QPOs. This contradiction
outlines probable shortcomings with the shock instability model.
