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The power handling and coupling of a poloidally and toroidally segmented antenna array recessed behind the first wall are analyzed numerically with a new three-dimensional code in the ion cyclotron range of frequencies for tokamak reactor plasma conditions. The fields inside the segments are approximated in the model of rectangular waveguides enclosing current straps and are matched through the shield to the outgoing plasma waves in the plasma column. Including the surface impedance for a hot reactor-sized plasma with account of misalignment between the ambient magnetic field and the screen bar directions and finding the selfconsistent current in the current straps allows one to investigate the input impedance, coupled power, and coupling between the segments. Reconstructing the field structure both inside the waveguides and in the plasma layer in front of the shield, the near field and the poloidal and toroidal spectra of the waves launched into the plasma are computed. At 55 MHz for a maximum 40-kV input voltage, an average RF power density in the range of 4-7 MW/m2 appears feasible in dipole phasing for a poloidally and toroidally stacked 4 × 4 strap antenna with the current strap-Faraday shield distance varying in the range 1-4 cm and with a reactor relevant high confinement (H-mode) edge density profile with a 12-cm separatrix-Faraday shield distance. Maximum sheath driven heat flux less than 1 MW/m2 on the protection limiters is guaranteed only in dipole phasing with well aligned Faraday screen bars (misalignment angle less than about 4°) for an RF power density 7 MW/m2 and electron density not higher than 1017 m-3 at the limiter.