AIN ISSA, Syria: In a muddy camp in northern Syria, civilians who fled Raqqa said fear of an expected U.S.-backed assault on Daesh (ISIS) bastion was reaching a fever pitch. This week, hundreds of civilians escaped Raqqa and headed north to the camp in Ain Issa, in territory controlled by the Syrian Democratic Forces, a U.S.-backed Arab-Kurdish alliance.

As part of their campaign to capture Raqqa, the Syrian heart of the militants’ so-called “caliphate,” the SDF have been bearing down on the Daesh-held Tabqa Dam over the past 10 days.

Rumors that Syria’s biggest dam would collapse and flood Raqqa, 55 kilometers downstream, have sparked panic in the city.

“The hisbah [religious police] announced over the megaphones ‘the land of Muslims will be flooded, the Tabqa dam has collapsed,’” said Mohammad Mahmoud, 38.

Mahmoud, his brother and both their families paid $1,000 to a smuggler and fled Raqa on foot earlier this week.

“I was so afraid, I couldn’t think straight,” he said.

The camp where he has found shelter is home to several thousand Syrians displaced by war, including 400 families who arrived this week from Raqqa.

Children waddled through makeshift pathways between tents emblazoned with the logo of the U.N. refugee agency (UNHCR), clutching sandwiches and water bottles.

Inside tents, men waited for their turn to have their Daesh-mandated beards shaved then examined their bare chins in a small mirror.

Mahmoud’s face was weighed down by exhaustion, his clothes covered in dust.

He hovered protectively around his elderly mother who sat in a wheelchair, its wheels caked in mud after their arduous 14-hour trek out of Raqqa.

“It’s hell there. Fear rules over everything,” he said as he took apparent pleasure puffing on a cigarette, a vice which Daesh banned when they captured Raqqa in 2014.

“Daesh is finished now. Most of its fighters fled to Mayadeen or Albukamal,” two towns in the oil-rich eastern province of Deir al-Zor, most of which is under Daesh control.

At the entrance to the camp, Kurdish police units – known as Asayesh – searched visibly shaken new arrivals.

Ahmad, a Raqqa native in his 50s, said residents seized the opportunity to flee when they saw Daesh fighters leave. “We were no longer afraid to flee Raqqa like before, because Daesh fighters were less and less visible,” he said, his six children perched atop suitcases packed with their belongings.

Ahmad said the militants “abandoned most of the checkpoints, built tunnels around the city” and protected their positions with sand bags.

He said the journey to Ain Issa was traumatic.

“We were so terribly afraid of the airstrikes, that the coalition might think we are Daesh fighters,” he said.

“Daesh is afraid of the assault on Raqqa,” a 25-year-old man who asked to use the pseudonym of Zuhair for security reasons, said.

“Many of their fighters fled with their families on motorbikes and there are fewer and fewer checkpoints,” he said.

But even as the militants left, “they warned residents ‘not to go to the infidels,’” said Zuhair, who still has relatives trapped in Raqqa, a city of 300,000 residents.

“I don’t know what happened to them,” he said, tearing up.

Daesh applies an ultraconservative interpretation of Islamic law in territory under its control, torturing or executing law-breakers.

Zuhair said he was jailed and lashed by militants several times for selling tobacco in defiance of a Daesh ban.

“But if I hadn’t taken the risk, I couldn’t have fed my family,” he said, crouched near his 1-year-old daughter Qamar.

Syria’s conflict began in 2011 with anti-government protests, but has since turned into a multifront war that has killed hundreds of thousands of people and forced millions to flee their homes.

Since March 21, the battle for Tabqa Dam and the adjacent town has killed at least 110 civilians and 68 militants, according to the Britain-based Syrian Observatory for Human Rights. It said SDF fighters were around 2 kilometers from Tabqa.

Jilal al-Ayyaf, who runs the camp in Ain Issa, said he was bracing for an influx of displaced people as the SDF press their advance.

“The more the noose tightens [around Daesh], the more displaced people we’ll get,” he said.