Barbour, a native of Van Nuys, California, was the aircrew flight equipment flight commander with the 47th Operations Support Squadron and an instructor pilot with the 87th Flying Training Squadron.
Injured in the accident was Capt. Joshua Hammervold, an instructor pilot for the 87th FTS. He was transported to Val Verde Regional Medical Center, where he was treated for his injuries and released in good condition.
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The trainer jet went down at approximately 4 p.m. local time Monday. The next day, the base temporarily suspended all flying operations through the Thanksgiving weekend.
"After extensive reflection, we decided to suspend flying for today and tomorrow, leading into a previously-scheduled holiday break," Col. Charlie Velino, 47th Flying Training Wing commander, said in a post on Laughlin's Facebook page Tuesday. "The Air Force is a close-knit family, and the loss of one of our own affects all of us."
In the statement Wednesday, Velino said, "Every day, our pilots take a risk as they step into the cockpit, and every day they operate with the utmost skill, professionalism and dedication to train the next generation of flying Airmen and to ensure the safety of this great nation."
He added, "Rest assured, we are doing everything we can to support the investigation and prevent future incidents."
Air Force Chief of Staff Gen David Goldfein expressed his condolences on Twitter following the incident.
"Our hearts go out to the community & all the friends and families of these Airmen. We are keeping them all in our thoughts," he said Monday.
The cause of the accident is under investigation.
The twin-engine, high-altitude T-38 is used to train pilots to fly in fighter and attack aircraft such as the F-15 Eagle, F-16 Fighting Falcon, A-10 Thunderbolt and F-22 Raptor, as well as the B-1B Lancer.
The service plans to replace the Northrop Grumman Corp.-made, two-seater T-38 over the next few years, with hopes of buying 350 new aircraft at a time when the service needs to replenish its fighter pilot ranks.
In December, the service launched a potential $16 billion competition to build a replacement T-38, which entered service in 1961. Firms publicly competing for the contract -- known as the T-X program -- include Boeing Co., Lockheed Martin Corp. and Leonardo S.p.A.