Abstract.  The technology of high power ultra-short laser beams has greatly evolved in the last 30 years. Terawatt lasers shorter than 50 fs has been operating from late 90's, allowing the flourishing of the laser-plasma acceleration field. The advances in the experimental techniques and in the basic knowledge of the interaction have permitted the production of high quality ultra-short electron bunches with energies approaching the GeV. The power of these sub-50 fs lasers has been continuously growing, attaining values as large as few hundred TW but with a limited repetition rate in the 10 Hz level in the best case. On the other hand, a new generation of ultra-short laser beams able to reach relativistic intensities with durations shorter than 10 fs is being developed. The first laser beams composed of few optical cycles with mJ energies and repetition rates of kHz are already operational. We explore here the possibility of using such beams to perform laser-wakefield electron acceleration.

We present simulations of the laser-wakefield electron acceleration using sub-5 fs lasers performed with the Particle-in-Cell code Calder Circ. The particular features of the transport of these ultra-short beams in an under-dense plasma is discussed in the first part of this work. In the second part we show the feasibility of the injection and the acceleration of electrons in the laser wakefield created by these pulses, as well as the high qualities of electron bunches produced.