Authorities say the suspect was not cooperating with TSA officers in the screening area. When airport police tried to assist TSA, the man ran.
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Officers caught up with the suspect at Gate 66, using a Taser to take the man into custody.
Passengers watched in shock, and one mother was seen shielding her child from the commotion.
"He had a really strange smile on his face the entire time," said witness Sean Dimond.
A number of witnesses recorded the confrontation on their cellphones, posting video and pictures on social media.
Paramedics responded and transported the suspect to a hospital for treatment.
An LAX spokesperson said the suspect was not armed.
Alaska Airlines confirmed to Eyewitness News the suspect was a ticketed passenger on Alaska, but for a flight that wasn't scheduled to leave until 8 p.m.
The suspect faces potential charges of trespassing and obstructing a peace officer.