We demonstrate a cryogenic buffer gas-cooled molecular beam source capable of producing bright, continuous beams of cold and slow free radicals via laser ablation over durations of up to 60~seconds. The source design uses a closed liquid helium reservoir as a large thermal mass to minimize heating and ensure reproducible beam properties during operation. Under typical conditions, the source produces beams of our test species SrF, containing molecules per steradian per second in the $X^{2}\Sigma(v=0, N=1)1.0(2)~$K and a forward velocity of m/s. The beam properties are robust and unchanged for multiple cell geometries but depend critically on the helium buffer gas flow rate, which must be standard cubic centimeters per minute to produce bright, continuous beams of molecules for an ablation repetition rate of Hz.

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