B737 FLT CREW RPTS TCAS RA AT 17000 FT E OF FLUNK ON THE ARR TO SMF COMMANDING A DSCNT. INTRUDER ALSO TRIED TO DSND WITH B737 PASSING 300 FT BELOW INTRUDER AT CPA.

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WE FLEW FLT TO SMF. DSCNT CLRNC WAS GIVEN TO 16000 FT. SHORTLY THEREAFTER; ATC CHANGED ALT TO 17000 FT DUE TO OTHER TFC. AFTER LEVELING OFF; WE SAW ONCOMING TFC ON THE TCAS DISPLAY 500 FT LOWER AND CLBING. THE CAPT STATED THAT THERE WILL BE A DEFINITE CHANCE FOR A TCAS RA. THE ONCOMING TFC LEVELED AT 17000 FT AND I ADVISED ATC OF THE SITUATION. WE HEARD ATC 'SUGGEST' TO THE OTHER TFC TO DSND AGAIN TO 16500 FT. WE NEVER HEARD A REPLY AND WE DID NOT KNOW IF ATC WAS WORKING MULTIPLE FREQUENCIES AT THE TIME. WHILE REACTING TO THE INITIAL TCAS RA; WE WERE DSNDING AT ABOUT 2500 FT/MINUTE; THE CAPT'S HEADSET FAILED. HE WAS NOT ABLE TO HEAR ANY ATC COMS. HE TRANSFERRED ACFT CTL TO ME. WHILE REACTING TO THE TCAS RA; I INFORMED ATC OF OUR DSCNT DUE TO THE RA. ATC REQUESTED A LEVELOFF AT 16000 FT TO WHICH I REPLIED THAT WE WILL LEVEL ONCE WE ARE OUT OF THE RA. DURING THIS TIME WE INCREASED OUR DSCNT TO OVER 3700 FT/MINUTE DUE TO A SECOND RA ('INCREASE DESCENT/MONITOR VERTICAL SPEED'). THE ONCOMING TFC WAS STILL CLOSING AND DSNDING AS WELL. WHILE DSNDING AT CLOSE TO 4000 FT/MINUTE WE RECEIVED A THIRD RA; THIS TIME DEMANDING A CLB. THE GREEN BAND WAS AT ABOUT 3000 FT/MINUTE CLIMB. ACCORDING TO THE TCAS SCREEN; THE TFC WAS NOW LESS THAN 1/2 MILE AND 300 FT ABOVE US. WE WERE SURE THAT REVERSING OUR DSCNT FROM -4000 FT TO +3000 FT WOULD HAVE PUT US RIGHT INTO THE OTHER TFC. THE CLIMB RA LASTED FOR 2 SECONDS AFTER WHICH THE 'CLEAR OF CONFLICT' COULD BE HEARD. I CLIMBED BACK UP TO 15000 FT AND INFORMED ATC OF OUR NEW ALT. THE ONLY RESPONSE WE RECEIVED WAS TO MAINTAIN 15000 FT AND A FREQUENCY CHANGE. ATC SHOULD HAVE BEEN MORE INFORMATIVE ABOUT OUR TFC; MORE AGGRESSIVE TO RESOLVE THE SITUATION. ATC CANNOT DEMAND A LEVELOFF DURING A TCAS RA MANEUVER. THERE WAS NO QUESTIONING HOW WE RESOLVED THE SITUATION OR AN UPDATE ABOUT THE OTHER TFC. WE WERE TOO BAFFLED AT THE TIME TO QUESTION THE SITUATION. WE INFORMED ATC ON THE NEXT FREQUENCY ABOUT THE NEAR-MISS.SUPPLEMENTAL INFO FROM ACN 740049: WE WERE ARRIVING/DESCENDING ON THE FLUNK ARR INTO SMF; EAST OF FLUNK WITH DSCNT CLRNC TO 16000 FT. ATC AMENDED CLRNC TO 17000 FT; REFERENCING VFR TFC TO N AT 16500 FT. WE LOCATED TFC ON OUR DISPLAYS AND OBSERVED HIM TO BE CLBING TO OUR ALT OF 17000 FT. I WAS PLT FLYING AND ADVISED FO THAT WE WERE PROBABLY GOING TO GET AN RA AND TO PREPARE FOR THAT. THE FO RPTED TO ATC THAT WE OBSERVED TFC NOW CO-ALTITUDE WITH US. ATC 'RECOMMENDED' TO TFC THAT THEY DSND TO 16500 FT (NOT ON SAME FREQUENCY AS US). WE THEN RECEIVED AN RA (DON'T RECALL IF WE EVER GOT A TA) WITH A DSND COMMAND OF APPROX 3500 FPM. WE COMPLIED WITH THAT; ADVISING ATC; SUBSEQUENTLY RECEIVING A 'DEEPER' RA. WHILE COMPLYING WITH THAT; I LOST ALL COMS; ADVISED THE FO; AND GAVE HIM THE ACFT. HE IMMEDIATELY TOOK THE ACFT AND CONTINUED THE DSCNT. OUR ACFT SYMBOLS ALMOST TOUCHED; ON THE SMALLEST SCALE; WITH TFC 2-300 FT ABOVE US. AT THIS POINT; WE RECEIVED A CLB RA OF APPROX 3500 FPM. I INSTRUCTED THE FO TO CONTINUE DSCNT; WHICH HE DID; AS HE TURNED THE ACFT AWAY FROM THE TFC (A GOOD DECISION; I THOUGHT). UPON RECEIVING OUR 'CLEAR OF CONFLICT;' WE COORDINATED WITH ATC AND THEY SHIPPED US IMMEDIATELY TO NEW FREQ. WE RPTED THAT WE WOULD BE 'WRITING IT UP;' AND TO INFORM PREVIOUS CTLR. AS AN ASIDE; WE LATER FIGURED OUT THAT I LOST COM AS A RESULT OF AN ACFT PROBLEM; NOT MY HEADSET; WHICH I HAD INITIALLY SUSPECTED. IT TOOK US A COUPLE OF LEGS; BUT WE WERE ABLE TO DUPLICATE THE SITUATION; WITH DIFFERENT HEADSETS; AND TO WRITE UP THE DISCREPANCY WHEN WE LANDED AND HAVE MAINT ADDRESS THE ISSUE. I WOULD LIKE TO SEE ATC TAKE A MORE AGGRESSIVE RESPONSE TO TFC CONFLICTS LIKE THIS ONE. THIS SITUATION WAS MONITORED CLOSELY BY US AND AT LEAST BY ATC; BUT NO TURNS WERE ISSUED EVEN THOUGH WE RPTED CO-ALTITUDE.CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE TCAS WAS APPARENTLY TRYING TO OUT DSND THE INTRUDER ACFT WHICH WAS TRYING TO DO THE SAME TO THE B737. AS THE ACFT CAME TOGETHER THE TCAS COMMANDED A CLBWHICH WOULD HAVE BROUGHT THEM CLOSER TOGETHER. THE OTHER ACFT WAS A SINGLE ENGINE PROPELLER ACFT.