This is a good question. Theoretically, each tube is individual, but collectively, I think the static field passes through the glass and the path to the nearest anode may be *through* the glass, causing a gating effect.
So you would need 3 x 15Kv PSU, separately decoupled or powered by different batteries, so that you can connect the tubes in series- That is to say something like this.
A<--C|A<--C|A<--C
45K-30K|30K-15K|15K-0K
So the total voltage potential is 45K, but is experienced as 15K between tubes, with the Anode (Screen) of one tube connected electrically to the (Photo)Cathode of the tube next to it.
Or 15K per tube, but not electrically coupled, so that they are floating, eg, 3 x PSU, 3 x Batteries, All disconnected from each other - So no connection between tubes - Though if the tubes charge up, they could cause their own fields to drift, which could be bad, so you'd still want to couple the Cathodes to the Anodes next to them.
Does the above make sense?
Regards
David