  We report on the optimization of discharge insensitive floating strip
Micromegas (MICRO-MEsh GASeous) detectors, fit for use in high-energy muon
spectrometers. The suitability of these detectors for particle tracking is
shown in high-background environments and at very high particle fluxes up to
60MHz/cm$^2$. Measurement and simulation of the microscopic discharge behavior
have demonstrated the excellent discharge tolerance. A floating strip
Micromegas with an active area of 48cm$\times$50cm with 1920 copper anode
strips exhibits in 120GeV pion beams a spatial resolution of 50$\mu$m at
detection efficiencies above 95%. Pulse height, spatial resolution and
detection efficiency are homogeneous over the detector. Reconstruction of
particle track inclination in a single detector plane is discussed, optimum
angular resolutions below $5^\circ$ are observed. Systematic deviations of this
$\mu$TPC-method are fully understood. The reconstruction capabilities for
minimum ionizing muons are investigated in a 6.4cm$\times$6.4cm floating strip
Micromegas under intense background irradiation of the whole active area with
20MeV protons at a rate of 550kHz. The spatial resolution for muons is not
distorted by space charge effects. A 6.4cm$\times$6.4cm floating strip
Micromegas doublet with low material budget is investigated in highly ionizing
proton and carbon ion beams at particle rates between 2MHz and 2GHz. Stable
operation up to the highest rates is observed, spatial resolution, detection
efficiencies, the multi-hit and high-rate capability are discussed.
