A gang of youths set a woman's hair on fire with a lighter in an unprovoked attack on a train.
CCTV images captured the moment the Swedish tourist was set alight on the service from Hastings to London's Charing Cross.
The woman, a teacher on a school trip, was walking through the carriage when one of the youths held out a lighter and touched her hair.
She only realised she was on fire when her students started screaming and she was able to pat out the flames.
British Transport Police (BTP) Inspector Gary Ancell, who is leading the inquiry, said the woman escaped injury but was "extremely distressed".
He said police are hunting four youths, two of whom were thrown off the train by a conductor who found them hiding in a toilet.
Mr Ancell said: "The victim was walking through the carriage around 6.30pm when a youth held out a lighter as she passed by him.
"Her hair immediately caught alight and she only realised what had happened when she walked towards her students and saw them screaming and pointing to her hair. She was then able to pat the fire out.
"The victim was incredibly lucky because within a few more seconds the majority of her hair could have been on fire, causing her serious harm.
"Assaults of this nature are extremely rare on the railway system but I am treating this incident very seriously and urge the youths pictured in the CCTV images or anyone who recognises them to come forward to police."
* Anyone with information about the incident, on Sunday July 19, or who recognises the youths, should call 0800 40 50 40.