The authors consider a narrow divertor layer, on the assumption of anomalous (Bohm)coefficients of plasma transport across the magnetic field. It is established that the plasma parameters in sucha divertor are affected significantly by the re-cycling of matter from the wall in the form of neutral atoms and by the anomalous plasma viscosity. Account is taken of the cooling effect of the secondary processes occurringon the collector plates. The system of hydrodynamic equations describing the plasma is solved analyticallyand numerically, and the plasma density and temperature distributions in the divertor are found. The behaviour of impurities sputtered from the first wall is discussed. It is shown that at high specific thermal fluxes to the wall, which are necessary for the economic feasibility of a tokamak reactor, a narrow divertor iscapable of maintaining a sufficiently low impurity concentration in the working volume and would enable theunburnt fuel and helium to be removed from the reactor