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If you want complete insulation, you should use opt isolation.
V/F F/V converter(such as AD650) is useful. Changing analog signals into frequency, and send logic pulses with opt fiber.
Frequency data can be re-converted with F/V converter into analog signals.
If you can use resistor divider(it doesn't complete isolation), it's easy to use isolation amp or differential amp.
Many isolation amp don't have isolation such as 5kV, so use R divider, reduce voltage to under 1kV.
But both methods don't have good frequency responce.
It's very difficult to get good frequency responce with isolation.
4kV thats a lot of turns for the secondary. I would look at a small black and white domestic TV Line output transformer + HV rectifier. 1mA is quite a lot of current, so it might not work. I would build the line output circuit and use one of the unused windings for feed back. You will need something of the order of a 100V DC supply to power it.
I have a TV HV transformer and cascade for my 25 kV tester. For 4kV 4W, the solution seems somewhat oversized in my opinion. I rather suggest a reversed off-mains SMPS transformr driving a Cockcroft Walton multiplier.
I had tried to run a domestic B/W 14" FBT with drive at 100VDC switching at 15,625KHz .
However , isolation, current limits , controls on feedback , ripples and damping were affecting perfomance.
The same was true for minor variations at input voltage of 95VDC or 110VDC .
I was considering fifth harmonic ocscillations which I shall try now and revert .
I was thinking of using four doublers in series but currents are a problem..
Long ago , some 80`s i have designed and build circuit board
breakdown tester devices.
I used neon transformer connected to adjustable 230V supply transformer.
You can find neon transformers secondary voltages 2....20kV
and neon transformers are usually short circuit proof.
Only add HV-cascade and filter capacitor.
If you protect cascade with series resistance, your whole device is
capable to handle short circuits too.