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Polar magnetospheric gaps consume a fraction of the electric potential that develops accross open field lines. This effect modifies significantly the structure of the axisymmetric pulsar magnetosphere. We present numerical stead-state solutions for various values of the gap potential. We show that a charge starved magnetosphere contains significantly less electric current than one with freely available electric charges. As a result, electromagnetic neutron star braking becomes inefficient. We argue that the magnetosphere may spontaneously rearrange itself to a lower energy configuration through a dramatic release of electromagnetic field energy and magentic flux. Our results might be relevant in understanding the recent December 27, 2004 burst observed in SGR 1806-20.
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Ioannis Contopoulos (2005) studied this question.