A passive optical resonator is used to enhance the power of a pulsed $78\mathrm{MHz}$ repetition rate Yb laser providing $200\mathrm{fs}$ 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 $18\mathrm{kW}$ is generated with close to Fourier-limited pulses of $10\mathrm{W}$ 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 $2\mathrm{ps}$ , we could obtain $72\mathrm{kW}$ of intracavity circulating power with $50\mathrm{W}$ of input power.