This can't be anywhere near civilization, as a Tesla coil can fry any electronics. It also can't be in some forest wilderness, as a Tesla coil can easily ignite trees. As they say, they're making something that's more and more lightning like, which is also more unsafe. So building a 10' Tesla coil is probably not the hard problem.... the hard problem is operating it Safely, and actually being able to take experimental observations.... because, this is all very dangerous.
And also, will the FCC allow them to operate it, once they've built it?
Considering spark gap transmitters have long been banned due to the spectrum-wide interference they cause; and the earliest such radio transmitters were tesla coils... and EMI in particular can be generated across the spectrum as well, resulting in disruptions to communications, with such a large tesla coil, and such a large arc, especially if they are attempting to use frequencies associated with wireless transmissions; I wonder what will the RFI fallout will be.
; and any horizontally long metallic structure can get induced currents and also become antennae for further RFI emissions. Yes, lightning does show up on the radio spectrum as well, but a powered up Tesla coil emits many arcs not spread out by time, a much bigger footprint than lightning....