Determination of alpha_S at 500 GeV from Event Shapes and Jet Rates

The potential of the TESLA linear e+e- collider to determine the strong coupling constant, alpha_S, at 500 GeV is investigated. Experimental complications due to background from W- and Z-pairs, top-production, initial state photon radiation and from beamstrahlung are considered. The hadronic event selection procedures used by the experiments at LEP II are reviewed for the applicability at TESLA. An estimate of the various error contributions to the total uncertainty of an $\alpha_S$ determination is presented. It confirms that hadronisation effects are diminished while the uncertainty from the choice of the renormalisation scale will dominate. Fits of the ln(R)-matched second order (O(alpha_S^2)) and resummed calculation (NLLA) to six observables are used to estimate the error contributions. This yields the expectation of the precision for alpha_S(500 GeV) of +-0.0025.