DC High Voltage Line Splitting Problem (Electrode "Tuning" Application)
I think this may do what you want:







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Electrode 2 positive-only with respect to Electrode 1.







simulate this circuit

Figure 2. Switchable polarity version.

Note that while the batteries, switches and potentiometer have a maximum of 18 V across them they are possibly all at high voltage (1,000 to 4,000 V) with respect to ground and you. All need to be properly insulated. The metal case of the potentiometer should not be grounded (as you're unlikely to find one with a 4,000 V rating between the carbon track and the case) but should be mounted totally inside the enclosure with only the plastic shaft protruding through the case with a knob on the outside.