It is a form of acoustic resonance inside the fill gas, what create (standing wave) bands with higher and lower pressure. As the emission strongly depend on the pressure, it create the light and dark bands. When you switch OFF the filament, the lamp voltage changes, what cause the inverter to change it's operating frequency, so it isn't in match with the tube resonance anymore. Moreover the lamp current start to have quite significant DC component, what tend to act against striations. That's why dimmable ballasts intentionally (usually by a resistor connected parallel to the DC blocking capacitor) give to the lamp a small DC current component. It is too small to cause electrolysis problem, but still large enough it effectively suppress the striations at low output settings.
By the way when electrodes are heated (either externally, or by the lamp's operation), even ballasts with asymmetric current waveform (e.g. ow voltage supplied blocking oscillators; all with single transistor output stage) do not cause DC component in the lamp, so the lamp operate on AC only (assume it is connected to a transformer secondary, so the voltage have no DC component). When electrodes are heated (so very small cathode fall), for fast current changes the arc behave as quite linear resistor. In fact what rectify high frequencies on lamps with not heated electrodes is the cathode fall, when the voltage is asymmetric. The current flow only in the polarity, when the circuit is able to generate high enough voltage, so when the transistor is OFF. As only cathode side is heated by the ion bombardment, what mean it would heat only the side, what is cathode during the transistor OFF phase. As a result most of single transistor ballasts without dedicated additional electrode heating stay in the rectification mode, with only the cathode side heated by the arc. This make it a bit easier to stabilize the power (during the ON state, when the voltage is given by the input and transformer ratio, so can not adopt to the lamp need, there flow no current anyway), but the lamp current have then high DC component, what could be problematic with some lamps.
When the ballast feed high enough power into the lamp, even the anode side eventually heat up, so it stop rectification. This is, why most simple battery ballasts start the lamp in two stages: First the lamp rectify, so work only on ~1/2 of the power, after some time the anode heat up, so allow the current to flow even during the transistor ON state, what mean the overall power and the light output nearly double.
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