Cessna Citation Mustang (C510)
Flight Crew Private; Flight Crew Multiengine; Flight Crew Instrument
Flight Crew Last 90 Days 60; Flight Crew Total 695; Flight Crew Type 52
Communication Breakdown
ATC Issue All Types; Conflict Airborne Conflict
Air Traffic Control Provided Assistance; Flight Crew Took Evasive Action
Procedure; Human Factors
I was climbing after takeoff VFR. I had filed an IFR flight plan direct at 13000. Radar services are unavailable under 3000 ft and I obtained contact with Center in the climb at approximately 4100. ATC instructed me to maintain 3500; due to traffic on approach. I began descending to 3500; when TCAS showed me a target at 5 miles; 12 o'clock and 4000. ATC advised me of the traffic as well; and I while I could hear ATC clear the oncoming traffic for the visual approach; I could not hear the oncoming traffic because I was on a different frequency. Both frequencies were operated by the same controller; who later switched me to the other frequency. He began descending on the straight in approach; converging with me (he was on a 160 heading and I was on a 340 heading; he was at 4000 descending and I was descending as well to 3500). TCAS counted down +5; +4; +3; +2 and I called ATC stating that I did not have the traffic in sight and it appeared to be converging. She misunderstood and thought I had the traffic in sight. When +1 became 0 almost a mile from me and the TCAS advisory called out and went yellow; I disconnected the autopilot; and banked hard right to avoid the traffic because I still did not have it in sight. ATC called back and said the traffic was no factor off my left side at 1 mile; and didn't appear concerned. Keep in mind; I'm traveling at 4 miles a minute; or one mile every 15 seconds. I felt this was too close.After landing I looked up both our tracks on flightaware; and it didn't appear either of us were in radar coverage at 3500. I am concerned that ATC had me descend into oncoming traffic rather than continue my climb where I would have been safely away from the traffic. What is a best practice at an uncontrolled airport that has poor radar coverage under 3000 ft and there is not an operative ground communication outlet to pick up a clearance in clear VFR conditions? Should I level off at 5000 (the MOA overlying ZZZ begins at 6000); then call ATC to prevent something like this from happening? The use of two frequencies in the area is also concerning because I could not know if the landing traffic had me in sight. I need to know what to do to prevent this from happening in the future.
Cessna 510 pilot reported an airborne conflict on departure.