I made a few promises to post schematics but I got involved in a few projects both at home and at work, unfortunately this slipped my mind.
I have here a very simple power supply schematic from a Wentgate EB welder we used to have a long time ago. It was a low power, small chamber machine. I believe the maximum power was around 1kW - 2kW might have been lower or higher.
The bias method uses the transformer bias method. Basically a small high voltage power supply which consists of transformer whose output is rectified and filtered. The output is wired in series with the filament in reverse polarity relative to the high voltage power supply. The "Gun Cable Plug" has three pins, L and E are the filament and N connects the negative of the high voltage power supply directly to the Wehnelt cap.
I have seen a few X-ray power supplies on eBay which use the exact same bias method. So this is a very simple yet tried and true method to regulate beam current. The only problem is how to digitally control the beam current bias transformer. Building a variable AC power supply is no small task but the AC transformer could be substituted for a switching transformer which can be PWM regulated from a microcontroller. The 400Hz system I described before simply used a power op-amp to drive the bias transformer using a sine wave. The 400Hz was constant and the amplitude was varied to change the voltage. The reason for 400Hz was simple, it reduces ripple in the bias supply.
As you can see, in the second picture, the curve shows you how the bias voltage affects the beam current for a given voltage from the power supply. the higher the voltage the more bias voltage you need to cut off the beam.
This schematic is a great starting point and is very similar to the system in one of our EB machines.