What is the purpose of transistor and zener in this circuit?
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Redrawn circuit with negative rail at bottom.

I'd say your circuit analysis is pretty good and your explanation of circuit use is a great help. Convention on circuit schematics is that current generally flows from top to bottom and since most of us reads left to right we generally put inputs (logic, analog, power) on the left and outputs on the right. What that in mind, I've redrawn your schematic.

What you have described is a "shunt regulator". If the voltage across the regulator rises above the preset voltage the regulator turns on and "shunts" current away from the power source to hold the voltage in control. They are not all that common because they waste power in the shunt circuit - hence the large heatsink and ceramic resistor in your circuit. Also, the shunt circuit relies on the source power-supply having some internal resistance otherwise a huge current would flow through the shunt as the power supplies try to keep the voltage up and the shunt tries to keep it down.

This circuit is a rather unusual, however, because there is no complete power circuit through the shunt circuit. Based on your Hall thruster link (page 338) your circuit schematic regarding the non-closed loop is correct. 

So, if all the above is correct, what's happening is as follows:


The circuit is designed to maintain the V1, 2 and 3 negative terminals \$V_{CLAMP}\$ somewhere between 0 V (actually + 0.7 allowing for the diode forward-voltage drop) and -50 V DC.
C1 is a local bypass capacitor and will shunt any high-frequency noise away from the regulator. It won't have any effect on the DC.
If \$V_{CLAMP}\$ rises above GND then D1 will be forward biased and prevent it from rising any futher.
If \$V_{CLAMP}\$ falls below -50 V then D2 Zener diode will break down feeding current into the base of Q1. This will allow current to flow through R3 and Q1 to "pull \$V_{CLAMP}\$ back up" to -50 V.
If the voltage is between 0 and -50 V the shunt circuit will take no action.


Please let me know if you think this is inconsistent with any other information you have. I know nothing about thrusters.