Toroidal shaped Tesla Coil Since toroidal shaped transformers perform better than conventional E core transformers. Would a Tesla Coil that is shaped in a toroidal shape perform better than Tesla coils that is shaped cylindrical?
 A: Not likely, for several reasons:
First, the toroidal transformers are wound around some sort of magnetic material (iron, ferrite,...). Such materials enhance the magnetic field, and they work better if the field is fully contained inside the material. Sharp corners "leak" magnetic field, the toroid shape avoids that. But a Tesla coil is an air-core transformer. No core material is suitable, due to hysteresis or saturation. There is no material shaping or guiding the magnetic field. In that case, the straight shape works well.
Second, a Tesla coil deliberately has low coupling betweeen the primary and secondary winding. The point of a toroidal transformer is to improve the coupling, achieving lower losses and high efficiency as a transformer. That runs counter to the goals of a Tesla coil.
Last, but certainly not least: The point of the Tesla coil is to generate extremely high voltages utilizing resonance. Often, enough voltage to throw sparks a meter or so, for an entertaining display. These extreme voltages occur across the terminals of the secondary winding. These terminals therefore needs to be far away from each other, and distant from any other part of the apparatus as well. A straight coil achieves the longest distance between endpoints. A toroidal coil puts the endpoints close to each other, making for very short sparks.
