Kurdish fighters who defeated Islamic State across much of Syria with U.S. help will struggle to fend off the Turkish army and its Syrian rebel allies who thrust across the border on Wednesday in a long-threatened offensive.Under Turkish attack after their U.S. allies withdrew from part of the border, the Syrian Democratic Forces (SDF) - which the Kurdish YPG militia spearheads - is heavily outgunned by NATO's second-largest military. While the United States has armed and trained the SDF through years of fighting IS, Washington held back from supplying its Kurdish allies with a more sophisticated arsenal, reflecting the needs of the battle but also Turkish concerns."The YPG don't have heavy weapons (from the U.S.) that would be useful against Turkish aircraft or tanks," a YPG source told Reuters."The heaviest weapons we got from the U.S. are some mortar shells, nothing heavier. No missiles, no anti-aircraft weapons, no anti-tank," added the source, speaking on condition of anonymity to discuss military affairs.Washington's policy towards the YPG has underscored the broader complexities of its role in the Syrian conflict that developed from protests against President Bashar al-Assad into a multi-sided war and sucked in Russia, Turkey and Iran.Though the SDF proved an effective ally against IS, U.S. support for it infuriated Turkey. Ankara views the YPG as terrorists because of links to the Kurdish PKK movement which has waged a long insurgency inside Turkey.Syrian opposition sources said some of the Turkey-backed Syrians now facing the SDF benefited from U.S. military support in an earlier phase of the war, when the Central Intelligence Agency oversaw a program to arm and train anti-Assad rebels.U.S. President Donald Trump shut down that program in 2017, part of an effort at the time to improve U.S. relations with Russia, Assad's most powerful ally. The program was criticized because some of the rebels switched to jihadist groups.'ROJAVA' AT RISKThe SDF currently numbers around 40,000 fighters, a second YPG source said. On top of this, Kurdish authorities had long established other security forces such as the Asayish numbering in the tens of thousands.Though the United States did not provide heavy or advanced weapons, Kurdish fighters have sourced anti-tank missiles on their own, the second YPG source said."Our duty is to resist. This is the Middle East and the black market is in full swing," the source said.A Syrian rebel source familiar with Turkey's position said Ankara has long been monitoring the weapons delivered to the YPG, a point of friction with Washington. "They were constantly in discussion with the Americans about the type of weapons being given to the (YPG)/PKK," the source said.The part of the border that U.S. forces vacated this week, a nearly 100-km (62-mile) stretch between the Syrian towns of Tel Abyad and Ras al-Ain, is now under attack. Turkey began pounding the region with air strikes and artillery on Wednesday.The area is mainly flatland, making it a tough battlefield for hardened YPG fighters who have gained years of experience in urban warfare fighting jihadists but are left almost defenseless against Turkish warplanes.That border strip, part of which historically had a strong Arab presence, is important to Syrian Kurdish fighters because it links the mainly Kurdish swathes of the Northeast with the Kurdish town of Kobani, where U.S. and allied troops still have a base.Depending on how deep Turkey pushes into Syria, the territorial contiguity of the SDF region in northern Syria, known as Rojava in Kurdish, could be endangered.The SDF, which controls around a quarter of Syria across the North and East, has said the U.S. move amounted to a "stab in the back."Washington has opposed the emergence of autonomous regions that Kurdish leaders and their allies carved out in Syria, even as it has militarily backed the SDF - which includes Arabs and other ethnicities.'BITING LIKE A MOSQUITO'To roll back Kurdish gains, Turkey has already staged two major incursions into the North. The last of these, "Olive Branch," drove the YPG and many Kurdish civilians from the Afrin region of the Northwest.Kurdish fighters have been waging an insurgency in Afrin ever since.The first YPG military source said the border strip between the two towns, which is Ankara's current focus, may ultimately be lost. But YPG forces were bent on making the battle as difficult and long as possible for Turkey, relying in part on fortifications at the border and fighters ready to die for the Kurdish cause, he said.If they face defeat there, "there would be a never-ending insurgency" against Turkish forces there."They will pay for this. Ultimately we may lose (that) area, which seems like it will be the case, but that doesn't mean we will just give up and retreat."The former head of U.S. Central Command said the Kurdish fighters would be unable to stop a Turkish invasion."I think Kurds will, first of all, defend themselves to the best that they can. When it becomes apparent to them that they cannot deal with this very modernized army and the capabilities that Turkey has, then I think they will leave the area," Joseph Votel, who retired earlier this year, said on Tuesday."Not only will the fighters leave, but I would expect that their citizens would leave as well, with the feeling that they would not be secure remaining in that area," Votel added.Nihat Ali Ozcan, security analyst at TEPAV, a Turkish think-tank, said the SDF would use guerrilla tactics, hit-and-runs, mines, roadside bombs or perhaps anti-tank missiles in its possession. "They will keep biting, like a mosquito," he said.