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It's a boost converter. The two transistors are arranged to increase gain (similar to a darlington or sziklai pair). The capacitor charge and discharges, causing voltage variations at the left-hand transistor. It creates hysteretic action turning the right hand transistor On and Off.
The joule thief is a cousin of this circuit. The joule thief has a coupled inductor, where this has several components which make up the biasing network.
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