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The Bubble regime of electron acceleration in ultra-relativistic laser plasmais considered. It has been shown that the bubble can produce ultra-short densebunches of electrons with quasi-monoenergetic energy spectra. The firstexperiment in this regime done at LOA has confirmed the peaked electronspectrum (J. Faure, et al., {\it submitted}, 2004). The generated electronbunch may have density an order of magnitude higher than that of the backgroundplasma. The bubble is able to guide the laser pulse over many Rayleigh lengths,thus no preformed plasma channel is needed for high-energy particleacceleration in the bubble regime. In the present work we discuss a simpleanalytical model for the bubble fields as well as the scaling laws.Comment: accepted for publication in Plasma Physics and Controlled Fusion,  200

The bubble regime of laser–plasma acceleration: monoenergetic electrons and the scalability