An analysis is made of the basic physical conditions under which a small local microwave-induced breakdown region in a gas may develop to extended 'global' breakdown. The analysis describes the different nonlinear stages of the microwave breakdown process. In the first stage, the increasing breakdown plasma density suppresses the electric field in the breakdown region to reach a quasi-stationary state with constant electron density. The subsequent heating of the gas due to absorption of microwave power in the breakdown plasma is then analysed and the corresponding steady state for the thermal evolution is found including the temperature dependence of the breakdown electric field. The stability properties of the stationary state are examined and it is found that there exists a critical (unstable) radius of the initial breakdown plasma region such that initial regions smaller than this critical dimension will shrink to ultimately vanish whereas plasma regions larger than the critical dimension will grow indefinitely and transform the local breakdown region into full scale 'global' breakdown. The practical implication of this model is to give an order of magnitude estimate for the critical size of hot spots, regions of enhanced field and intensified heating in rf systems.
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