This might be me being too much of an amateur physicist - but I think it literally is a nuclear explosion, amplified by the power in investiture.
1: Harmonium acts like a heavy, possibly transuranic, element. Allik warns Wax not to store too much of it in one place, otherwise "odd things might happen". We know that the Axi of harmonium is likely composed of Lerasium and Atium, given that the reaction produced both. It seems likely to me that harmonium is literally a combination of those two elements, with the Intent+Investiture of Harmony providing the binding force sufficient to overcome their natural repulsion (both of Intent and electromagnetic).
2: We know that Bavadinium strongly repels Harmonium "more like it had the same charge".
3: We know that passing an electric current through Harmonium comes close to, but is not sufficient to separate Harmonium into Lerasium and Atium.
So I think what happens is when the current is passed through Harmonium and Bavadinium is brought close, that is sufficient to overcome the binding force of Harmonium - Lerasium and Atium subsequently separate and release energy, just like in nuclear fission. The atoms of Lerasium and Atium which split subsequently collide with other Harmonium atoms with enough energy to split them as well, in the classic chain reaction.
It's a very odd combination of physics and magic, and I'm sure the mathematics on it would be incredibly fuzzy, but it matches the description of Wax's experiment.
With a more powerful current or something like modern compression implosions they should be able to fission Harmonium even without Bavadinium.