  This thesis discusses the search for supersymmetry at the future Large Hadron
Collider (LHC) and the ongoing construction of one of the four large LHC
experiments, the Compact Muon Solenoid (CMS), and focuses on the detection of
signals from the annihilation of supersymmetric dark matter in the spectra of
cosmic rays.
  Measurements of cosmic ray antiparticles, such as positrons, can impose
strong constraints on the nature of new physics beyond the Standard Model.
However, cosmic ray positron measurements are experimentally very challenging
due to the vast proton background. A novel approach of positron identification
with the space-borne AMS-01 experiment, namely through the detection of
bremsstrahlung conversion in a silicon microstrip detector, is introduced.
Bremsstrahlung from protons is suppressed by a factor of more than 3*10^6 with
respect to positrons. The results of the positron measurement show that the
bremsstrahlung approach extends the sensitivity range of AMS-01 to positron
momenta up to 50 GeV/c, which is far beyond the original scope of the
experiment. At momenta above 8 GeV/c there is indication for a positron
overabundance with respect to model predictions for purely secondary positron
production. Therefore, the AMS-01 data lend further weight to the hints of a
positron overabundance seen in the data from earlier experiments.
  The positron fraction measurements from the most recent experiments are
combined with the results of this analysis, giving the most precise positron
fraction data yet available.
