Small Transport; Low Wing; 2 Turbojet Eng
Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine; Flight Crew Private
Flight Crew Last 90 Days 27; Flight Crew Total 3585; Flight Crew Type 867
Communication Breakdown; Confusion; Situational Awareness
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Procedure; Human Factors
Enroute to ZZZ descending and cleared for visual approach to ZZZ airport Runway XXR. The Tower Controller said 'Execute a 360 right turn' (believed to be for traffic but that information was not provided pursuant to the FAA Manual (JO 7110.65X) no reason for the turn was provided). After I turned my aircraft and completed approximately 150 degrees of the 360 degree turn my TAS (Traffic Advisory Sensor instrument) displayed approaching traffic from the south. The altitude of the approaching traffic was lower than my altitude by a few hundred feet; therefore; to avoid the traffic I chose to climb because there was high terrain below me and I could not see the aircraft while in a 30 degree banked turn. The TAS showed the target aircraft climbing. The more I climbed higher the target aircraft climbed higher as well. When the target aircraft passed under my aircraft TAS showed the target was on a collision course and the altitude showed 00 as it passed underneath me. I have never had such a frightening experience thinking we were going to be killed as this aircraft was within the Class B and not talking to Approach or Tower and I was relying on the controller who appeared to be creating the unsafe near-miss condition as it would not have happened had he not turned me. Once the aircraft passed; the controller issued me a new clearance to enter a right downwind while it is believed that the near-miss aircraft was landing at ZZZ and now talking and cleared for a left base to the same runway. The jet aircraft believed involved in the near-miss was told by ZZZ Tower that he needed to call in due to a possible pilot deviation and was given a telephone number.Someone needs to determine if the controller turned me into this traffic which gave me no way out in the turn; and not calling the traffic was also troubling without a traffic advisory. This near-miss was terrifying for us. The copilot's seat was occupied by my wife who is also a pilot but was not flying and is not type rated in the [aircraft] but she has had level D simulator training and has about 700 hours in the right seat of this [aircraft]. I hope someone can determine what the controller was doing and why he was turning me and why did he take such actions that nearly killed us all?
Pilot flying a small jet aircraft reported a near mid air collision with another small jet aircraft.