A passive optical resonator is used to enhance the power of a pulsed 78 MHz repetition rate Yb laser providing 200 fs pulses. We find limitations relating to the achievable time-averaged and peak power, which we distinguish by varying the duration of the input pulses. An intracavity average power of 18 kW is generated with close to Fourier-limited pulses of 10 W average power. Beyond this power level, intensity-related effects lead to resonator instabilities, which can be removed by chirping the seed laser pulses. By extending the pulse duration in this way to 2 ps, we could obtain 72 kW of intracavity circulating power with 50 W of input power.