Reduction of chemical networks. II. Analysis of the fractional ionisation in protoplanetary discs

(abridged) We analyse the evolution of the fractional ionisation in a steady-state protoplanetary disc with a vertical temperature gradient and with gas-grain chemistry including surface reactions. The ionisation due to stellar X-rays, stellar and interstellar UV radiation, cosmic rays and radionuclide decay is taken into account. Using our reduction schemes as a tool for the analysis, we isolate small sets of chemical reactions that reproduce the evolution of the ionisation degree at representative disc locations with an accuracy of 50%-100%. Column densities of key molecules are calculated and compared to the results of other recent studies and observational data.