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A simple model is introduced for the fields of a chirped laser pulse. Dynamics of laser-acceleration of a single electron by the fields of a pulse, with a $\sin^4$ envelope, is investigated. Multi-GeV energy gains from interaction with pulses of peak intensity $I_0\sim10^{20}$ W/cm$^2$, are reported.

A Simple Model for the Fields of a Chirped Laser Pulse With Application to Electron Laser Acceleration