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The observation of Hα-radiation extending along the magnetic field lines during pellet injection in ASDEX suggests a renewed discussion of ablation models and, in particular, an investigation of the additional shielding of the pellet by the high-density, medium-temperature plasma generated by the ablated material. In the present paper the authors have simulated the frozen-in gas flowing along the field lines with a 1-D hydrodynamic code, coupled to the neutral-gas shielding model describing the ablation. To take into account long-mean-free-path effects on the electron heat transport in the plasma, it was necessary to replace the classical Spitzer-Harm conductivity by a non-local transport model. – A plasma hose with a density of up to several hundred times that of the background plasma and extending over several metres was found to form along the field lines. As the temperature of this plasma is much lower than that of the background one (in a computation for ASDEX it dropped from 500 to approximately 40 eV), this effect should lead to a distinct decrease in the resulting ablation rate.