Measurement of the Inclusive Cross Section for Diffractive Deep Inelastic 
Scattering at High Q^2
-------------------------------------------------------------------------

A measurement is presented of inclusive diffractive deep inelastic scattering extending to the largest Q^2 values accessed to date. Data taken by the H1 experiment amounting to an integrated luminosity of 63 pb^-1 are used to investigate the process ep -> eXY in the kinematic range where diffractive exchanges are known to dominate. The Y system is a proton or proton remnant with M_Y < 1.6 GeV and |t| < 1.0 GeV^2 and it is separated from the X system by a large gap in pseudorapidity. The diffractive reduced cross-section sigma_r^D(beta, Q^2 x_pom) is extracted in the kinematic range 200 < Q^2 < 1600 GeV^2, 0.1 < (beta = x / xpom) < 0.9 and 0.0036 < xpom < 0.05.  The data are used together with other recent measurements at lower Q^2 to test various factorisation properties and models of diffractive DIS. Good agreement is found with predictions based on diffractive parton densities obtained from an NLO QCD fit to lower Q^2 data, evolved using the DGLAP equations, and with a model based on soft colour interactions.