The stimulated Brillouin scattering (SBS) threshold enhancement factor in a pure white noise linewidth broadening Yb-doped fiber amplifier (YDFA) with a short large mode area fiber is theoretically and experimentally studied. We demonstrate a 1064.08 nm, 11.6 GHz linewidth, 1.5 kW output power YDFA with an SBS threshold enhancement of ∼57 (26 W SBS threshold with single frequency seed). The output beam is near-diffraction limited with a beam quality factor of 𝑀 2 = 1.15 and a slope efficiency of up to 87%. No SBS or stimulated Raman scattering effects are observed in the whole power range. Further power scaling is limited by the available pump power in our system.