  In this work, a part of the Research and Development effort of the PICOSEC
detector is presented. The PICOSEC detector is a novel gas-filled detector,
based on the Micromegas detector, which has been developed by the RD-51 PICOSEC
collaboration. Instead of relying on traditional direct ionization, the PICOSEC
detector takes advantage of the prompt timing characteristics of Cherenkov
radiation by converting the Cherenkov photons into electrons through the use of
a photocathode. The detector has been put into two type of tests where
experimental data are collected. One involves a laser beam and a single
photoelectron response at CEA-SACLAY, while the other involves a test beam of
150 GeV muons at the CERN SPS H4 secondary beamline, with multiple
photoelectrons. The methods employed in the statistical analysis of the
detector's timing properties are summarized and in their application an optimal
time resolution of 76 ps is achieved for single photoelectrons. A strange
dependence of the mean timing on the size of the electron peak is observed,
which mimics the behaviour of the "time walk" effect. A simulation of the
detector is developed to study the timing properties, which is also the main
scope of the thesis. After a detailed investigation, it is found that the
electrons in the gaseous mixture move with a different drift velocity before
and after the first multiplication, introducing this "time walk" effect, and a
phenomenological explanation of this effect is provided. Finally, a maximum
likelihood statistical method for the estimation of the mean number of
photoelectron extracted per particle is developed and an optimal time
resolution of 24 ps is achieved with a mean number of photoelectrons per
particle equal to 10.4. In this work, a deep understanding is acquired on a new
detector which has brought upon unprecedented results in the field of
gas-filled detectors.
