A SAAB 340B AFTER LNDG AND TAXIING TO THE TERMINAL DECLARED AN EMER AND EVACED THE ACFT DUE TO THE L ENG AC ALTERNATOR CATCHING FIRE.

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NORMAL FLT FROM DFW TO LFT (VMC). WHEN APPROX 100 MI NW OF LFT; THE L AC GENERATOR LIGHT ILLUMINATED ON THE OVERHEAD PANEL. THE QRH WAS FOLLOWED (TRY TO RESET) AND THE GENERATOR WAS TURNED OFF. DISPATCH AND MOC WERE NOTIFIED AND THE L AC GENERATOR WAS DEFERRED PER THE MEL (IE; NO ICE CONDITIONS). NORMAL LNDG AND ROLLOUT AT LFT; BUT 20 SECONDS AFTER LEAVING THE RWY THE FLT ATTENDANT (FIRE WAS NOTICED BY PAX) NOTIFIED US (CREW) OF A L ENG FIRE. THERE WERE NO COCKPIT WARNINGS; BUT I COULD SEE FIRE COMING FROM THE ENG (IE; AC GENERATOR EXHAUST PORT). ENG FIRE/EMER EVAC MEMORY ITEMS WERE PERFORMED. PAX WERE ASSEMBLED AND TRANSPORTED TO THE TERMINAL. THERE WERE NO INJURIES TO PAX OR CREW NOTED OR RPTED TO CREW. LFT CFR WERE CALLED TO THE ACFT. DAMAGE TO ACFT IS MINOR; LIMITED TO AC GENERATOR AND EXHAUST PORT. AC GENERATOR WAS OVERHEATING IN AIR AND WHEN COOLING AIR WAS REMOVED AFTER LNDG; THE GENERATOR CAUGHT FIRE. FIRE WAS PUT OUT BY SHUTTING DOWN ENG AND FIRE BOTTLE WAS PULLED. EVAC TIME WAS APPROX 55 SECONDS. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE ACFT WAS A SAAB 340B PWRED WITH GE CT7-9B ENGS AND THE ALTERNATOR WAS A COX SYS 115 VOLT AC UNIT USED EXCLUSIVELY FOR ENG INLET; PROP; AOA; OUTSIDE AIR TEMP; AND PITOT DEICING. HE SAID THE UNIT HAD BEEN TURNED OFF PRIOR TO LNDG DUE TO FAILURE AND WAS DEFERRED DUE TO NO ICING CONDITIONS. HE ALSO RELATED ON LNDG AND TAXIING THE PROP RPM WAS ONLY 1000- 1400 RPM AND WAS PROBABLY NOT SUPPLYING ENOUGH COOLING AIR FOR THE OVERHEATED ALTERNATOR WHICH CAUGHT FIRE. RPTR STATED AT NO TIME DID HE EXPERIENCE AN ENG FIRE OR OVERHEAT WARNING. THE RPTR STATED THE ALTERNATOR IS DRIVEN DIRECTLY FROM THE ACCESSORY GEAR BOX AND THE COOLING AIR IS CONTAINED PASSING THROUGH THE ALTERNATOR THEN VENTED OVERBOARD. HE BELIEVES A CONNECTING OR COUPLING RING FAILED DIVERTING THE COOLING AIR CAUSING THE OVERHEATING. THE RPTR SAID THIS EVENT IS FAIRLY COMMON TO THIS ACFT BUT THIS WAS THE FIRST TIME HE HAS EXPERIENCED THIS TYPE OF FAILURE.