A loss of separation involving an airspace transition of a military aircraft without a transponder and two air carriers deviating around weather occurred during training of a developmental. The reporter faults himself for not taking over earlier.

Narrative

I was conducting on the job training on the BURBN RADAR position. We had a line of weather on the west side of the sector. Every east-west bound plane was deviating around it. We did not have a D-Side. The sector below us (FWA) called and asked for higher on an F18. They said he wanted to climb to FL410 to go over the weather then descend into GYY airport which was not far away. The trainee released FL410. As I leaned over to tell the trainee that it was a bad call; the FWA Controller suggested FL360 instead. The trainee approved FL360. After we approved FL360; the FWA D-Side yelled over that the F18 had no transponder. He then called to say that he was negative RVSM. I told the trainee to bring up our primaries. Since we are a super high altitude sector; we do not run with primaries on. We had another aircraft; Air Carrier Z that was deviating to the northeast and climbing to FL370; requesting FL380. Since Air Carrier Z was still climbing and I could not see the F18; I told the trainee to hurry Air Carrier Z to FL380. I still could not see the F18; I never saw the aircraft throughout the incident; and was yelling across the aisle asking for position and altitude reports. There was Air Carrier Y at FL380; westbound; that was in front of both Air Carrier Z and F18. Air Carrier Y asked to deviate right on a 295 heading for weather. Based on the position reports given to me off-line; I told the trainee to turn Air Carrier Z to a 290 heading until he was level at FL380 to avoid the F18. About the same time; Air Carrier Z asked to go direct BAE. The trainee approved this request. I am not sure that I heard that clearance because I was yelling for another position/altitude report on the F18. When I saw Air Carrier Z turn toward BAE; I realized that it did not look good with Air Carrier Y because Air Carrier Y appeared to be turning to the southwest. I took the frequency and turned Air Carrier Y first to a 310 heading then to a 360 heading. I also turned Air Carrier Z to a 250 heading. I told both aircraft that it was for traffic and conveyed urgency in my tone and language (using words like immediate and without delay). [I] asked Air Carrier Z if he had rolled out yet. He replied that hadn't but called Air Carrier Y in sight. It is my personal opinion that once the Air Carrier Z had the other aircraft in sight; he did not turn with the enthusiasm he could have. Once I received a report from the FWA Sector that F18 was below FL350; I cleared Air Carrier Z to FL370. All of this was not sufficient to save the error. During the incident the ZOB Controller to my east (GEA) was yelling across the lines that BURBN needs a hand off or D-Side increasing the noise level at the sector. After the incident started; the Supervisor called a D-Side over to the sector. Recommendation; first of all; the F18 flight created an unusual and difficult situation. Had that flight not been in the sector; I do not believe the error would have happened. We were trying to help out the fighter pilot because he was low on fuel and had weather in front of him. Unfortunately; I did not realize that he did not have a transponder until the altitude was released. Second; I should have taken the frequency sooner. Just before this happened; I had told the trainee to run the sector like I was not there so I could see what the trainee could handle. I was coaching but should have removed the trainee sooner. I do not think the trainee saw the error coming.