What was found
AT APPROX. 1000 AGL THE LEFT AFT LAV SMOKE DETECTOR WENT OFF AND THERE WAS AN ENVIRONMENTAL SMOKE SMELL NOTICED BY BOTH PILOTS AND BOTH REAR FLT ATTENTANTS. NO VISIBLE SMOKE OR FIRE. LAV & TRASH COMPARTMENT WAS CHECKED. SMELL DISSIPATED RAPIDLY AND WAS GONE WHEN WE CLEARED RUNWAY. SMOKE DETECTOR STOPPED SOUNDING AFTER CLEARING RUNWAY. ACCOMPLISHED NO GO ODI PREVENTION FORM . HIGH POWER RUN AND DUCT BURN OUT. NO ODOR NOTED. REPLACED COALESCER SOCKS. REF AMM 21-20. CREW SMOKE AND FUME QUESTIONNAIRE COMPLETED AND ATL MC ADVISED. SEE LOG 5529160 FOR CORRECTIVE ACTION OF LAV LIGHT BALLAST AND SMOKE DETECTOR ACTIVATION. (LP5529158)