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In fusion negative ion sources, the negative ions are formed on the caesiated plasma grid predominantly by hydrogen atoms from the plasma. The space charge of the negative ions leaving the wall is not fully compensated by incoming positive ions and at high enough emission a virtual cathode is formed. This virtual cathode limits the flux of negative ions transported across the sheath to the plasma. A 1D collisionless model of the sheath is presented taking into account the virtual cathode. The model will be applied to examples of the ion source operation. Extension of the model to the bulk plasma shows good agreement with experimental data. A possible role for fast ions is discussed.