Glass is a great insulator at low temperatures, but quickly becomes conductive at temperatures above 800 Deg. C. Upon first switching on power to the Tesla Coil, the electric field around the top of the coil is shaped in such a way that the plasma of the air completely ignores the flake of glass. However, the 1-atmosphere plasma in the arc is quite dense, and extremely hot - hot enough to heat the glass near it by simple convection. As the temperature of the glass rises, the electric field begins distorting in such a way that the current begins to pass through the hot glass itself. Eventually, the arc cuts a path through the glass at it heats up a "trail" of more and more material.
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