results in a power converted in the lamp which is sufficient for preventing cooling of the plasma which would result in extinguishing of the lamp the surprising fact in relation to the solution according to the invention is the fact that actually an extension of the switch on duration of the second frequency must result in a further increase in the running voltage of the lamp in practice however this is surprisingly not the case as a result of the nonlinearity of the high pressure discharge lamp instead an extension of the switch on duration results in an increase in the lamp current therefore in heating of the plasma and therefore in a reduction in the running voltage in a preferred embodiment in addition to the extension of the switch on duration the second frequency is reduced this provides the advantage that the half bridge switches switch on when the current in the lamp inductor is equal to zero as a result the switching losses in the half bridge switches are reduced in preferred embodiments the second frequency is at least 15 khz while the first frequency is a maximum of 500 hz preferably the predeterminable period of time for the extension of the switch on duration is at least 30 u03bcs.