Narrative:

Aircraft Y; departed an airport 5 miles northwest of ZZZ and requested a low approach on runway 10 with a left turn out back to ZZZ1. I gave him traffic to follow to the field and cleared him for a low approach to runway 10. I did not realize that the aircraft was so fast (approx. 150 kts on final) so I cleared an aircraft for departure off of runway 8. After realizing that the aircraft Y would overtake the departing aircraft; I instructed aircraft Y to do a right turn out to join the right downwind. He asked for another approach; so I cleared him for the low approach. I lined up an air carrier on runway 8 with the expectation of aircraft Y to turn out left to ZZZ1 after the low approach. At the same time; I had a C172 overhead the tower at 1500 feet eastbound and a helicopter 4 miles east of the field; westbound along the shoreline at 300 feet and an aircraft on a 5 mile final for runway 10. After aircraft Y completed the 2nd low approach I gave him instructions to turn left to join the shoreline westbound to ZZZ1 and to change to ZZZ1 frequency. After aircraft Y crossed over rwy 8; I cleared the departing air carrier for departure (left turn to a 350 degree heading) for takeoff off of rwy 8.I then remembered about the helicopter now 3 miles east of the field who probably would not have been a factor as the departing air carrier would have likely cleared him by more than 500 feet vertical; but to be sure; I told the helicopter to proceed direct to the tower and remain south of rwy 8. All of a sudden I got a call from aircraft X who was on the river transition (ZZZ1 had prior coordinated as a courtesy). I was talking for 2 minutes nonstop and did not realize aircraft X was already in my airspace. I looked at the scope and saw that aircraft X and aircraft Y (who I had already switched) were at the same altitude opposite direction to each other with a closing speed of probably almost 400 knots. I called the traffic to aircraft X; who did not see aircraft Y. I did not have a clear picture of the direction of their movement as there wasn't enough time before sweeps on the scope; so I was unable to give a proper safety alert. Aircraft X called traffic in sight when targets were less than .5 mile lateral separation at the same altitude. I called R5 sector to coordinate for higher for aircraft X; climbed the traffic VFR to 9500 ft; and switched him to approach airspace. During the confusion; I also mistook another aircraft; now for 4 miles east of the field; for the helicopter and gave incorrect instructions to the other aircraft accidentally that were meant for the helicopter. (The data block for the helicopter dropped automatically because he was over the airport at less than 500 feet; so I saw the other aircraft data block in around the same place as the helicopter was). I lost the picture momentarily with aircraft X and aircraft Y and it took a few seconds to get it back. I believe aircraft X was an airspace intrusion; having entered my airspace without my responding to him. He may have called once or twice; but I was busy and unable to respond. Pattern work is fairly uncommon here; as are jets on a VFR transition; so the combination of the two led to an increased workload and ultimately an unsafe situation. I was also overly eager to get out departures; leading to my misunderstanding of the picture with aircraft Y and the first departure initially followed by my departing air carrier with the helicopter. I unintentionally increased my workload to a level I was unable to handle with the offending VFR traffic added in. I went from being fairly slow; low workload; low complexity to high volume; high complexity in less than 2 minutes.coming off the quick turn with 6 hours of sleep led to slight fatigue that I believe was a contributing factor.it would be beneficial if ZZZ1 was able to coordinate high-performance VFR transitions directly with TRACON and then simply call us as a courtesy or for a point-out. The VFR transition was developed for and is utilized by mostly single and twin-engine prop aircraft cruising at less than 150 knots. Allowing an aircraft to fly the VFR transition at double the speed of other aircraft is a potential safety risk; and given that the courtesy call was 5 minutes in advance of when the aircraft X actually departed; it is difficult to pre-plan for it. I am all for giving pilots shortcuts to save them time; but not at the expense of safety margin.

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Original NASA ASRS Text

Title: During a busy arrival period a Tower Controller approved an aircraft for a low approach which resulted in a traffic conflict with a second aircraft transiting through the airspace. During the same time period the controller issued instructions to one aircraft that were meant for another as well as cleared an air carrier for takeoff into the crossing route of a VFR helicopter.

Narrative: Aircraft Y; departed an airport 5 miles northwest of ZZZ and requested a low approach on Runway 10 with a left turn out back to ZZZ1. I gave him traffic to follow to the field and cleared him for a Low Approach to Runway 10. I did not realize that the aircraft was so fast (approx. 150 kts on final) so I cleared an aircraft for departure off of Runway 8. After realizing that the Aircraft Y would overtake the departing aircraft; I instructed Aircraft Y to do a right turn out to join the right downwind. He asked for another approach; so I cleared him for the Low Approach. I lined up an air carrier on Runway 8 with the expectation of Aircraft Y to turn out left to ZZZ1 after the Low Approach. At the same time; I had a C172 overhead the tower at 1500 feet eastbound and a helicopter 4 miles east of the field; westbound along the shoreline at 300 feet and an aircraft on a 5 mile final for Runway 10. After Aircraft Y completed the 2nd low approach I gave him instructions to turn left to join the shoreline westbound to ZZZ1 and to change to ZZZ1 frequency. After Aircraft Y crossed over rwy 8; I cleared the departing air carrier for departure (left turn to a 350 degree heading) for takeoff off of rwy 8.I then remembered about the helicopter now 3 miles east of the field who probably would not have been a factor as the departing air carrier would have likely cleared him by more than 500 feet vertical; but to be sure; I told the helicopter to proceed direct to the tower and remain south of rwy 8. All of a sudden I got a call from Aircraft X who was on the River transition (ZZZ1 had prior coordinated as a courtesy). I was talking for 2 minutes nonstop and did not realize Aircraft X was already in my airspace. I looked at the scope and saw that Aircraft X and Aircraft Y (who I had already switched) were at the same altitude opposite direction to each other with a closing speed of probably almost 400 knots. I called the traffic to Aircraft X; who did not see Aircraft Y. I did not have a clear picture of the direction of their movement as there wasn't enough time before sweeps on the scope; so I was unable to give a proper Safety Alert. Aircraft X called traffic in sight when targets were less than .5 mile lateral separation at the same altitude. I called R5 sector to coordinate for higher for Aircraft X; climbed the traffic VFR to 9500 ft; and switched him to approach airspace. During the confusion; I also mistook another aircraft; now for 4 miles east of the field; for the helicopter and gave incorrect instructions to the other aircraft accidentally that were meant for the helicopter. (The data block for the helicopter dropped automatically because he was over the airport at less than 500 feet; so I saw the other aircraft data block in around the same place as the helicopter was). I lost the picture momentarily with Aircraft X and Aircraft Y and it took a few seconds to get it back. I believe Aircraft X was an airspace intrusion; having entered my airspace without my responding to him. He may have called once or twice; but I was busy and unable to respond. Pattern work is fairly uncommon here; as are jets on a VFR transition; so the combination of the two led to an increased workload and ultimately an unsafe situation. I was also overly eager to get out departures; leading to my misunderstanding of the picture with Aircraft Y and the first departure initially followed by my departing air carrier with the helicopter. I unintentionally increased my workload to a level I was unable to handle with the offending VFR traffic added in. I went from being fairly slow; low workload; low complexity to high volume; high complexity in less than 2 minutes.Coming off the quick turn with 6 hours of sleep led to slight fatigue that I believe was a contributing factor.It would be beneficial if ZZZ1 was able to coordinate high-performance VFR transitions directly with TRACON and then simply call us as a courtesy or for a point-out. The VFR transition was developed for and is utilized by mostly single and twin-engine prop aircraft cruising at less than 150 knots. Allowing an aircraft to fly the VFR transition at double the speed of other aircraft is a potential safety risk; and given that the courtesy call was 5 minutes in advance of when the Aircraft X actually departed; it is difficult to pre-plan for it. I am all for giving pilots shortcuts to save them time; but not at the expense of safety margin.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.