There’s no law that says that you have to have a ferrite toroid or any core material. Air core works, but the coil has to have many more turns, which makes it bigger and bulkier. But if the space is available, there’s nothing wrong with using a reasonably thick wire for the coils to keep the resistance low. I’ve made quite a few JTs with air core coils, all successfully lighting the LED.
To make a coil, take 16 feet or 5 meters of twisted pair telephone wire and wind it onto an AA cell, then remove the cell and tie the wires into a donut with wire ties, electrical tape or some short lengths of the same wire. It’s a good idea if the wire is twisted with the insulation on, so it does not make a shorted turn. You can also use cat5 cable, but it’s twisted much tighter and much harder to untwist. The white wire of one end connects to the colored wire of the other end, and both are connected to the positive of the AA cell. Of the remaining two wires, one goes to the collector, the other goes to one end of the 1000 ohm resistor.
Video This guy seems to have the right idea. Two hanks of insulated wire, each 10 meters or 39 feet long, tied together for the coil, and it puts out a reasonably bright light.