Capacitor (or condensor, same thing) Discharge Ignition.
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CDI stands for Capacitor Discharge Ignition and is an electronic ignition system particularly well suited to high-performance, high-rpm engines such as those commonly found in motorcycles.
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The capacitor can discharge over the connecting wires; i.e.,
outside the capacitor. Some discharge can also occur over the
dielectric, since it will not insulate completely.