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The extreme properties of the gamma ray flares in the Crab Nebula present aclear challenge to our ideas on the nature of particle acceleration inrelativistic astrophysical plasma. It seems highly unlikely that standardmechanisms of stochastic type are at work here and hence the attention oftheorists has switched to linear acceleration in magnetic reconnection events.In this series of papers, we attempt to develop a theory of explosive magneticreconnection in highly-magnetized relativistic plasma which can explain theextreme parameters of the Crab flares. In the first paper, we focus on theproperties of the X-point collapse. Using analytical and numerical methods(fluid and particle-in-cell simulations) we extend Syrovatsky's classical modelof such collapse to the relativistic regime. We find that the collapse can leadto the reconnection rate approaching the speed of light on macroscopic scales.During the collapse, the plasma particles are accelerated by charge-starvedelectric fields, which can reach (and even exceed) values of the local magneticfield. The explosive stage of reconnection produces non-thermal power-law tailswith slopes that depend on the average magnetization $\sigma$. For sufficientlyhigh magnetizations and vanishing guide field, the non-thermal particlespectrum consists of two components: a low-energy population with softspectrum, that dominates the number census; and a high-energy population withhard spectrum, that possesses all the properties needed to explain the Crabflares.

Explosive X-point collapse in relativistic magnetically-dominated plasma