SECOND DEPARTING ACFT CATCHES UP WITH THE FIRST DEPARTING ACFT AND CAUSES THE TCASII TO GO OFF.

Narrative

I WAS PIC OF ACR X; AN MDT LAX-SBA; PAX ACFT. AN IFR FLT PLAN WAS FILED AND WE OBTAINED THE IFR CLRNC FROM LAX ATC. WX WAS VMC; NO CEILING; GOOD VISIBILITY. LAX TWR CLRED OUR FLT FOR TKOF ON RWY 24R; HDG 270 DEGS AT THE SHORELINE; MAINTAIN 2000 FT. ON OUR TKOF ROLL WE HEARD LAX TWR CLR FOR TKOF 'ACR Y' FROM RWY 24L AND WAS TOLD TO MAINTAIN VISUAL SEPARATION WITH OUR ACFT. AFTER CONTACTING LAX DEP WE WERE CLRED TO 6000 FT; UPON REACHING 6000 FT; CLRED DIRECT VTU VOR. SHORTLY THEREAFTER; WE RECEIVED A TA ON OUR TCASII AND NOTED AN INTRUDER AT OUR 6 O'CLOCK POS. WE WERE OPERATING THE TCASII ON THE 5 NM RING. THE FO WAS PF SO MY ATTN WAS MORE FOCUSED TOWARDS THE TCASII INTRUDER AT THIS TIME. SHORTLY THEREAFTER THE TA TURNED TO AN RA CLB (1500 FPM) COMMAND. WE COMPLIED AND NOTICED THE INTRUDER NOW CLOSING VERY FAST ON US FROM THE 6 O'CLOCK POS. SHORTLY THEREAFTER WE RECEIVED A STRENGTHEN RA COMMAND 'INCREASE CLB' (2500 FPM). WE COMPLIED BUT NOW AT FULL PWR OUR AIRSPD WAS JUST ABOVE STICK SHAKER SPD. WE WERE ASTONISHED AT THE VERT CLOSURE RATE OF THE 6 O'CLOCK INTRUDER THROUGHOUT THE RA SERIES AND ESTIMATED IN NO WAY COULD WE OUT CLB THE INTRUDER AT THIS POINT. THE INTRUDER WAS NOW DIRECTLY BELOW THE PICTORIAL ACFT DEPICTED ON THE TCASII SCREEN AND OPERATING THE TCASII ON THE 'ALT' MODE INDICATED APPROX 3200 FT (OUR ALT APPROX 3400 FT). I ADVISED THE FO TO TAKE EVASIVE ACTION (R BANKED TURN) AND WE ENDED UP HDG 310 DEGS. SHORTLY THEREAFTER THE TCASII INDICATED CLR OF CONFLICT. WE ADVISED ATC THAT WE WERE RESPONDING TO AN RA AND THE CTLR TOLD US TO FLY A L TURN BACK TO APPROX 210 DEGS AND MAINTAIN 4000 FT. HE THEN CLRED US TO 6000 FT DIRECT VTU VOR. FROM THE FIRST TA THROUGH THE FINAL 'CLR OF CONFLICT' WE COULD NEVER ESTABLISH VISUAL CONTACT WITH THE INTRUDER. AFTER QUESTIONING THE DEP CTLR HE ADVISED 'I DON'T LIKE IT WHEN THE TWR RELEASES FASTER TFC TO MAINTAIN VISUAL SEPARATION.' AFTER PHONING LAX TWR AND SPEAKING WITH A SUPVR HE ADVISED ME IN AN ARROGANT; CAVALIER ATTITUDE 'WE DID EVERYTHING CORRECT; BY THE BOOK; AND YOUR PROB IS NOT WITH US BUT WITH THE PLT OF THE INTRUDER ACFT.