The plasma is the resistive coil. Microwaves are used to carry energy to it because wires would melt.

How about tungsten coils?

I think those would burn, since these engines are meant to breath air (with oxygen in it.) Tungsten filaments work in lightbulbs because those are filled with an inert gas, or vacuum. The filaments burn quick when the bulb is broken.

There's really no solid that can handle thermal plasma. We're talking 10,000K to 100,000K temperatures here.