Currents and fields of a magnetron

I can't make heads or tails of the descriptions of magnetrons (i.e. microwave) I'm reading online. Hyperphysics does the best job of illustrating fields and currents, but the story of its operation seems to contradict in some ways.

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/magnetron.html

The description goes that electrons radiate outward from the central cathode, and then the magnetic field (created by permanent magnets not seen in the image) causes them to circle back. Other sources seemed to imply that these electrons are reabsorbed in the cathode. I have trouble with this, among other details:

1. Where do the electrons end up? Do they make it back to the central cathode to be reabsorbed there, or are they absorbed in the outer ring? (the latter seems implausible considering the high efficiency)
2. How is current flowing in the material around the cavity - it would seem it has nowhere to go. Does the current go all the way around the outer ring? No description seems to be clear on this.
3. How does charge accumulate in the the + and - regions in the image? If thermoelectric emission is happening, it should happen at all angles around the central cathode. This would distribute the charge and lessen the $E$ field in the area where the electrons reach, but it doesn't, by itself, predict any angular non-uniformity of charge like this.
4. Supposedly, the magnetron doesn't require AC electrical input, only DC. The LC comparison is nice, but with a DC battery, inductor, and capacitor you can't make oscillations. You need switching circuitry (like transistors) or an AC input. So how can this explain the emergence of oscillations?
-