[en] Kicker magnets are required for all ring-to-ring transfers in the 5 rings of the proposed KAON factory synchrotron. The kick must rise/fall from 1% to 99% of full strength during the time interval of gaps created in the beam (80 ns to 160 ns) so that the beam can be extracted with minimum losses. Approximately one-third of the injection and extraction kicker magnets will operate continuously at a rate of 50 pulses per second: the others operate at 10 pulses per second. The kicker magnet PFN voltages will be in the range 50kV to 80kV, hence multi-gap thyratrons will be used for the injection and extraction kicker systems. Displacement current arising from turn-on of a multi-gap thyratron flows in the external circuit and can thus increase the effective rise-time of the kick. A mathematical model of a three-gap thyratron, which includes the drift spaces, has been developed for simulating turn-on, and is described in this paper. The thyratron model has been used to investigate ways to suppress the effects of displacement current on the kick, and to reduce thyratron switching loss. A ferrite saturating inductor may be connected adjacent to each thyratron to reduce switching loss, so that thyratron life can be extended and the kick rise-time improved. This inductor can also be used to reduce the effect of anode displacement current during turn-on of a multi-gap thyratron. The research has culminated in a predicted kick rise time (1% to 99%) of less than 50 ns for a TRIUMF 10 cell prototype kicker magnet. The proposed improvements are currently being implemented on our prototype kicker system. (author). 15 refs., 11 figs