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This page is an attempt to show why there should be a connection between the junction between the diodes  in a MOT level shifter power supply for a tesla coil and the common point between the cores. Two models are used for this demonstration. The first is a model of the MOT level shifter circuit as normally used. The second is the same model with the connection between the common point between the diode stacks and the common point between the MOT cores removed.

Here is the model with the connection complete. It is highlighted in red. (fig.1)

Here is the model with the connection removed. (fig.2)

This is the voltage waveform for the circuit in figure 1.

Here is the current waveform for the current through the diodes for figure 1.

And now the current through the load resistor.

Now we will remove the connection between the midpoint of the MOTs and the midpoint of the diode strings. First the voltage waveform:

Now the diode current:

And now the output current:

As can be seen from this, the models do not show any difference whether the connection is there or not.