Abstract: Ammonia (NH3) synthesis is crucial for the production of artificial fertilizer and is carried out through the Haber-Bosch process. With an energy consumption of 30 GJ/t-NH3 and the emission of 2 kg-CO2/kg-NH3, ammonia is the chemical with the largest environmental footprint. Haber-Bosch operates under high pressure and high temperature conditions. Plasma technology potentially allows greener ammonia production. Dielectric barrier discharges are a popular plasma source in which a catalyst is easily incorporated. The combination of plasma and catalyst can circumvent the harsh reaction conditions of the Haber-Bosch process. Plasma kinetics modelling is used to gain insight into the mechanisms of such plasma-catalytic systems. Special attention is given to the instantaneous power absorbed by the electrons, the relevant fraction of the microdischarges and the discharge volumes. The importance of vibrational excitation is investigated. Depending on the exact discharge conditions, it was found that both the strong microdischarges and vibrational excitation can be simultaneously important for the ammonia yield. The temporal behavior of filamentary dielectric barrier discharges was explicitly taken into account. Ammonia was found to decompose during the microdischarges due to electron impact dissociation. At the same time atomic nitrogen and other excited species are created. Those reactive species recombine to ammonia in the afterglow through various elementary Eley-Rideal and Langmuir-Hinshelwood surface reaction steps with a net ammonia gain. Finally, the concept of the fraction of microdischarges was generalized. It directly represents the efficiency with which the applied electric power is transferred to each individual particle in the plasma reactor. It is argued that any type of spatial or temporal non-uniformity of the plasma will cause unequal treatment of the gas molecules in the reactor, corresponding to a lower efficiency at which the power is transferred to the gas molecules. All of those insights aid in an increased understanding of plasma-catalytic ammonia synthesis as a potential green chemistry solution to the synthesis of ammonia on small scale.