Do a google search for flyback+tesla coil and you'll get loads of hits for a
very popular, very simple one or two transistor high voltage generator.
Here's one link...
http://www.aaroncake.net/circuits/hvgen.htm
With 12V input, you can get around 8KV output.
Add a diode to the outpu and you get 8KV DC.
Reduce input voltage accordingly to get 4KV.
There is also a cct diagram for a 4000volt DC supply in one of Robert
Ianinni's books (He of Information Unlimited fame.)
Cheers.
Mark H.

"Ed" wrote in message
...
Hello,

I would like to make a simple DC power supply capable of giving around
4KV.
The current only needs to be small. Is it possible to make such a power
supply that runs off a 9V battery? If it is, can anyone give me some
pointers on making one, links to schematics would be even better. I'm
hoping I could use an off the shelf transformer, rather than making my
own.

Thanks in advance,