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jim-frank,
I fail to follow your thinking. Once the spark is initiated, the impedance drops, a circuit component switches in a capacitor that delivers current to prolong the spark. The capacitor initial charge of 300-400V and 1uF provides the energy.
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The time constant of a 1 uF capacitor is one microsecond per ohm of spark gap resistance. If we assume an arc resistance of say 10 ohms, in fifty microseconds the capacitor will drop from 400 volts to nearly zero. That's not very long, and won't prolong the spark much, if at all.
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In the flyback case a circuit designed for 10-40KV at low current, at spark, sees a drop in impedance and a voltage less than 50V. Now what! There is a huge mismatch in the circuit impedance.
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The spark will dump whatever energy is stored in the secondary winding of the flyback, and when the voltage drops below what it takes to sustain the arc, it will extinguish. It will then restrike on the next cycle of the waveform.
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ConnClarke brings up a good point multiple sparks help.
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Multiple sparks in the time domain help as well, as the Mallory MSD shows.
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A long duration spark that erodes plugs is not necessary to keep the fire burning!
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It's really a series of short duration sparks. Plug erosion will not occur if the energy and power per spark is below what it takes to erode metal from the electrodes.