  In this work, for the first time to our knowledge, stability and noise of a
thin-disk mode-locked Yb:YAG oscillator operating in both negative- (NDR) and
positive-dispersion (PDR) regimes have been analyzed systematically within a
broad range of oscillator parameters. It is found, that the scaling of output
pulse energy from 7 $\mu$J up to 55 $\mu$J in the NDR requires a dispersion
scaling from -0.013 ps$^{2}$ up to -0.31 ps$^{2}$ to provide the pulse
stability. Simultaneously, the energy scaling from 6 $\mu$J up to 90 $\mu$J in
the PDR requires a moderate dispersion scaling from 0.0023 ps$^{2}$ up to 0.011
ps$^{2}$. A chirped picosecond pulse in the PDR has a broader spectrum than
that of a chirp-free soliton in the NDR. As a result, a chirped picosecond
pulse can be compressed down to a few of hundreds of femtoseconds. A unique
property of the PDR has been found to be an extremely reduced timing jitter.
The numerical results agree with the analytical theory, when spectral
properties of the PDR and the negative feedback induced by spectral filtering
are taken into account.
