FLC RESPONSE TO TCASII RA IS DELAYED IN EXECUTION; STARTING AN ODD CHAIN OF EVENTS.

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FLT DSNDING INTO PDX OUT OF NRT JAPAN. CAPT LINE CHK AIRMAN; GAVE IOE TO NEW FO. ATC CLRED US TO DSND TO 15000 FT AND SHORTLY AFTERWARD ASKED US TO MAINTAIN FL200 DUE TO CITATION TFC AT FL190. ATC ADVISED US OF HIS RELATIVE POS; BUT WE WERE UNABLE TO ACQUIRE HIM VISUALLY. THE TFC WAS A CESSNA CITATION WITH A CALL SIGN SIMILAR TO OURS. ATC AND THE CITATION HAD A DISCUSSION ABOUT RETURNING TO SOME POINT WITH A R TURN. THE CITATION SAID A L TURN MIGHT BE BETTER; SO WE COULD CONTINUE OUR DSCNT. I CALLED OUT OF 21 FOR FL200. SHORTLY AFTERWARD WE GOT A TA; 'TFC; TFC.' AN AMBER TARGET APPEARED ON OUR RADAR TCASII SCOPE. STILL NO CONTACT VISUALLY. AT ABOUT 20500 FT TCASII GAVE US CAUTION TO 'MONITOR VERT SPD' FOLLOWED IMMEDIATELY BY 'DSND; DSND.' AS WE LEVELED AT FL200. I IMMEDIATELY DISCONNECTED THE AUTOPLT AND PUSHED THE ACFT OVER TO DSND. I CHKED THE RA-VSI FOR VERT SPD GUIDANCE WHICH SHOWED RED DOWN TO GREEN ARC ABOUT 2500 FT VERT SPD. INITIAL PUSHOVER GAVE ABOUT 1500 FT PER MIN VERT SPD FOLLOWED BY TCASII WARNING 'CLB; CLB' WHICH I IMMEDIATELY DID. INITIAL PITCH OVER TOOK US DOWN TO 19600 FT AND CLB BACK TO 20500 FT; THEN FL200 WHEN 'CLR OF TFC.' ATC WAS ADVISED BY FO WHEN WE EXECUTED RA AND TFC WAS ACQUIRED VISUALLY WHEN THE CLB WAS EXECUTED. CITATION APPEARED TO BE APPROX 2 MILES AWAY AT OUR 1 TO 2 O'CLOCK POS. AT THAT RANGE HIS ALT RELATIVE TO OURS WAS DIFFICULT TO JUDGE. THE TCASII 'CLB; CLB' WARNING MAY HAVE SAID 'CLB; CLB; NOW;' BUT WITH ATC TALKING AND BOTH THE FO AND RELIEF PLT CALLING 'TFC IN SIGHT;' IT WAS DIFFICULT TO UNDERSTAND. THERE WAS CONFUSION SINCE THE TCASII HAD CHANGED ITS RA FROM 'DSND' TO 'CLB.' WE CALLED ATC IN PDX AND THEY ADVISED THE CITATION WAS AT 19200 FT AND CONFIRMED OUR DSCNT HAD TAKEN US DOWN TO 19600 FT. THE TCASII DIRECTED US INTO A PROB AND THEN DIRECTED US OUT OF IT. THIS SHOULD NOT HAVE HAPPENED! CONTRIBUTING TO THIS PROB IS THE LOCATION OF THE RADAR TCASII UNIT RELATIVE TO THE RA/IVSI. THE RADAR IS IN THE CTR CONSOLE AND THE VSI IS SMALL AND LOCATED OUTBOARD OF ALL THE FLT INSTRUMENTS. WHEN SECONDS COUNT; THE INTERPRETATION OF 2 INSTRUMENTS ACROSS SHIP IS CRITICAL. THE CORP JET DID NOT HAVE TCASII. HE SHOULD IF HE IS OPERATING AT THESE ALTS. THE RED DISPLAY ON THE RA-VSI OVERPOWERS THE DISPLAY. IT MAKES THE SMALL GREEN ARC DIFFICULT TO PICK OUT! AFTER BEING UP ALL NIGHT THE CREW PERFORMANCE WAS GOOD. OUR ACFT IS EQUIPPED WITH A REST FACILITY; WHICH HELPS WITH CREW ALERTNESS WHEN ON DUTY. 3 MAN CREWS ARE A MUST ON INTL OPS. SUPPLEMENTAL INFO FROM ACN 313967: WE WERE DSNDING INTO PDX AND PROCEEDING DIRECT TO THE BTG 275/25 FIX. WE WERE TOLD TO LEVEL OFF AT FL200 FOR XING TFC. THE OTHER ACFT WAS GIVEN A L TURN TO PASS BEHIND US SO WE COULD CONTINUE DOWN. BTWN FL210 AND FL200 WHILE IN DSCNT; THE TCASII COMMANDED TO 'MONITOR VERT SPD' FOLLOWED CLOSELY BY 'DSND; DSND.' SUPPLEMENTAL INFO FROM ACN 313565: APCHING FL200 (OUR CLRED TO DSND TO ALT) AT ABOUT 1000 FPM; TCASII ISSUED A TA 'MONITOR VERT SPD.' RED BAND ON VSI WAS 0 TO 1000 FPM DOWN. WE WERE AT ABOUT 1200 FPM DOWN. WE CONTINUED DSCNT WHILE LOOKING FOR TFC. AT ABOUT FL200; TCASII ISSUED A RA 'DSND; DSND' FOLLOWED IN 5 SECONDS BY 'CLB; CLB.' RADAR SCOPE SHOWED OUR TA TFC AT 1 TO 2 O'CLOCK 2 MI BELOW US; CLBING. IN RETROSPECT; I BELIEVE OUR TCASII WAS EXTRAPOLATING OUR VERT SPD VECTOR AND TRIED TO KEEP IT (THE VECTOR) BELOW THE CONFLICTING TFC. WHEN THE INTRUDER CROSSED SOME RANGE THRESHOLD; THE TCASII PROGRAM INITIATED OTHER EVASIVE MANEUVERS.