I was wondering about the collar as well. Other than the structural support which I too assumed was the primary function, it would short the ends of the cathodes together. Forcing equality in the electric potential of them all against any slight differences that build up due to feedback from the plasma interactions.
It would also allow the perpendicular components of the magnetic field around it to induce a current going round the collar.
These two interactions are just two ways of saying the same thing really since it is the current which will equalize the potential, but on different timescales, so you could have small current oscillations interacting at the frequencies of the order of the alfven, and magnetoacoustic waves in the surrounding plasma.