We suggest a novel method for injection of electrons into the acceleration phase of particle accelerators, producing low emittance beams appropriate even for the demanding high energy Linear Collider specifications. In this paper we work out the injection into the acceleration phase of the wake field in a plasma behind a high intensity laser pulse, taking advantage of the laser polarization and focusing. With the aid of catastrophe theory we categorize the injection dynamics. The scheme uses the structurally stable regime of transverse wake wave breaking, when electron trajectory self-intersection leads to the formation of a flat electron bunch. As shown in three-dimensional particle-in-cell simulations of the interaction of a laser pulse in a line-focus with an underdense plasma, the electrons, injected via the transverse wake wave breaking and accelerated by the wake wave, perform betatron oscillations with different amplitudes and frequencies along the two transverse coordinates. The polarization and focusing geometry lead to a way to produce relativistic electron bunches with asymmetric emittance (flat beam). An approach for generating flat laser accelerated ion beams is briefly discussed.
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