In the interaction of laser pulses of extreme intensity ($>10^{23}~{rm W cm}^{-2}$) with high-density, thick plasma targets, simulations show significant radiation friction losses, in contrast to thin targets for which such losses are negligible. We present an analytical calculation, based on classical radiation friction modeling, of the conversion efficiency of the laser energy into incoherent radiation in the case when a circularly polarized pulse interacts with a thick plasma slab of overcritical initial density. By accounting for three effects including the influence of radiation losses on the single electron trajectory, the global `hole boring motion of the laser-plasma interaction region under the action of radiation pressure, and the inhomogeneity of the laser field in both longitudinal and transverse direction, we find a good agreement with the results of three-dimensional particle-in-cell simulations. Overall, the collective effects greatly reduce radiation losses with respect to electrons driven by the same laser pulse in vacuum, which also shift the reliability of classical calculations up to higher intensities.
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