ASTRA IAI-1125 FLT CREW HAS A TCAS RA DURING APCH TO MHR.

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I WAS THE PNF IN THE R SEAT. MY CO-CAPT WAS FLYING THE EMPTY LEG IN THE L SEAT AS PF ON OUR REPOS FLT TO MHR. WE WERE EXPECTING A VISUAL APCH INTO MHR ARPT AND WERE UNDER RADAR VECTORS FROM NORCAL APCH. SMOKE FROM A NEARBY WILDFIRE REDUCED VISIBILITY TO APPROX 7 MI AT OUR LOCATION. WE WERE GIVEN A R TURN TO FACILITATE TFC AND COMPLIED. ALMOST IMMEDIATELY I NOTICED A POTENTIAL CONFLICT VIA TCAS AT 1 O'CLOCK POS; 3 MI AND 1100 FT BELOW US AS WE PASSED THROUGH ABOUT 5200 FT MSL DURING OUR DSCNT TO 4000 FT. I BEGAN TO VISUALLY SCAN FOR THE TFC AND CONCURRENTLY MADE A CALL TO NORCAL TO STATE THAT WE WERE PROBABLY GOING TO HAVE AN IMMINENT TFC CONFLICT. WE REDUCED OUR RATE OF DSCNT AND IMMEDIATELY BEGAN TO SCAN FOR TFC. I SPOTTED THE TFC; A SINGLE ENG CESSNA; AT 12 O'CLOCK POS AND BELOW US AT APPROX 3 MI; BUT HE WAS CLBING AND WE WERE OVERTAKING HIM. I CALLED THE TFC TO THE PF; BUT HE DID NOT SEE IT; AND WE CONCURRENTLY RECEIVED A TA VIA TCAS. WE COORD AND EXCHANGED CTL; AND I TOOK THE PF ROLE AS I SAW THE TFC. I IMMEDIATELY ADDED PWR TO LEVEL OFF AT 4400 FT AND BEGAN AN IMMEDIATE TURN TO THE L SO AS TO KEEP THE TFC IN SIGHT BELOW US AND TO THE R. HOWEVER; I NOTICED THE ACFT MAKING A 30 DEG BANKED TURN TO THE L; IN OUR DIRECTION AND ALSO CLBING IN WHAT APPEARED TO BE A MAX PERFORMANCE CLB. I LEVELED OUR BANK TO MAKE A RAPID EVALUATION OF HIS TRACK AND DETERMINED WE NEEDED TO CLB AND CONTINUE OUR L TURN. CONCURRENTLY; WE RECEIVED AN RA VIA TCAS; BUT I KEPT THE TFC IN SIGHT AND COMPLIED WITH THE TA FOR ALT GUIDANCE AS THE CESSNA THEN; BY NOW; HAD REVERSED HDG AND PASSED BELOW US IN A L TURN; NEARLY GOING IN THE OPPOSITE DIRECTION THAT WHEN ORIGINALLY SPOTTED. HE PASSED APPROX 500 FT BELOW US AS WE WERE AT 4800 FT NOW. IT ALMOST SEEMED THAT THE SINGLE ENG CESSNA WAS PERFORMING A 'CHANDELLE' OR A 'LAZY EIGHT' VISUAL MANEUVER; WITH HDG AND ALT CHANGES. IT WAS DIFFICULT TO PREDICT HIS INTENDED PATH AS IT APPEARED TO CHANGE EVERY TIME I WAS ABLE TO MAKE A PREDICTION TO EVADE HIS PATH. OR; HE MAY HAVE SIMPLY BEEN MANEUVERING WITHOUT KNOWLEDGE TO OUR POS OR TFC FLOW INTO MHR AIRSPACE. AFTER WE WERE CLR OF THE TFC CONFLICT; WE TOLD ATC WE COULD ACCEPT A VISUAL APCH. IN THE HEAT OF EVADING THE TFC; I BELIEVE ATC WAS ATTEMPTING TO GIVE HELPFUL GUIDANCE TO AVOID THE TFC; BUT WE HAD THE TFC IN SIGHT AND WERE ABLE TO ADEQUATELY AVOID THE CONFLICT AND WERE VERY BUSY DOING SO.