A continuous guided atomic beam of $^{88}\mathrm{Sr}$ with a phase-space density exceeding $10^{-4}$ in the moving frame and a flux of $3 \times 10^{7} \, \mathrm{at \, s^{-1}}$ is demonstrated. This phase-space density is around three orders of magnitude higher than previously reported for steady-state atomic beams. We detail the architecture necessary to produce this ultracold atom source and characterize its output after $\sim 4 \, \mathrm{cm}$ of propagation. With radial temperatures of less than $1 \,\mu \mathrm{K}$ and a velocity of $8.4 \, \mathrm{cm \, s^{-1}}$ this source is ideal for a range of applications. For example, it could be used to replenish the gain medium of an active optical superradiant clock or be employed to overcome the Dick effect that can limit the performance of pulsed-mode atom interferometers, atomic clocks and ultracold atom based sensors in general. Finally, this result represents a significant step towards the development of a steady-state atom laser.
Comment: 9 pages, 4 figures