WITH DFW TWR PROVIDING VISUAL SEPARATION TO 2 ACRS A TCASII RA WAS FLOWN BY ONE AND AN ABRUPT DIVE MADE BY THE OTHER AT LOW ALT TO AVOID CONFLICT.

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DEPARTED DFW RWY 36R WITH AN ASSIGNED HDG OF 345 DEGS. WE ESTIMATE THAT AT THE TIME OF THE INCIDENT WE WERE APPROX 1 MI N OF THE DEP END AND APPROX ON THE EXTENDED CTRLINE OF RWY 36L. AT 1100 FT AGL; CONCURRENT WITH THE ENABLING OF THE RA FUNCTION AND AURAL WARNINGS; WE RECEIVED A CLB RA. RECOGNIZING THAT COMING OUT OF THE RA SUPPRESSION MODE WE MIGHT NOT HAVE THE FULL 5 SECONDS TO REACT; I RESPONDED VERY QUICKLY. HOWEVER; IT WAS NECESSARY TO EXERCISE CARE TO NOT CLB EXCESSIVELY AS WE WERE SLIGHTLY BELOW MANEUVERING SPD FOR THE CONFIGN. IMMEDIATELY AFTER ESTABLISHING THE REQUIRED CLB; I CHKED THE TCASII AND NOTED A RED TARGET PERFECTLY CTRED ON THE DISPLAY (5 MI SCALE) INDICATING -01 AND CLBING. THE TARGET THEN CHANGED TO A DSCNT TREND AND A 'CLR OF CONFLICT' WAS QUICKLY GENERATED. A TWR SUPVR LATER TOLD ME THAT THE CONFLICTING TFC MADE AN ALARMINGLY STEEP AND ABRUPT DIVE. THE ENTIRE EVENT LASTED LESS THAN 5 SECONDS. IT WAS LATER LEARNED THAT THE CONFLICTING TFC WAS A SAAB 340 THAT DEPARTED FROM A DOWNFIELD INTXN OF RWY 36L WITH AN ASSIGNED 270 DEG HDG. THE TWR SUPVR TOLD ME THEY HAD PROVIDED SEPARATION ON A VISUAL BASIS WITH BOTH ACFT IN SIGHT. OUR FLT WAS NOT ADVISED OF THE SAAB. IT WAS NOT CLR WHETHER HE WAS ADVISED OF US; BUT IT IS UNLIKELY HE WOULD BE ABLE TO WATCH US ANYWAY AS WE WOULD COME FROM BEHIND. HIS TURN TO THE W WOULD ONLY MAKE IT MORE DIFFICULT FOR HIM TO SEE US. THE GEOMETRY OF OUR CLB MADE IT IMPOSSIBLE TO SEE THE SAAB AFTER OUR ROTATION. NOR DID I SEE HIM AFTER THE CONFLICT. HAD WE KNOWN OF HIM PRIOR TO TKOF WE WOULD HAVE MADE ADJUSTMENTS TO KEEP HIM IN SIGHT AND ENSURE SEPARATION. THOUGH WE NEVER SAW THE SAAB; THE RPTED ABRUPTNESS AND SEVERITY OF HIS MANEUVER COMBINED WITH THE ELECTRONIC INFO AVAILABLE TO US; STRONGLY SUGGESTS AN NMAC. RECOMMENDATION: ELIMINATE VISUAL SEPARATION PROVIDED TO IFR TFC BY TWR. IT IS EXTREMELY DIFFICULT; IF NOT IMPOSSIBLE TO ESTIMATE RELATIVE DOWN-RANGE DISTANCES FOR ACFT OF DIFFERING SIZES.