High beam quality laser accelerations in vacuum

In order to be useful, any acceleration scheme must produce an accelerated bunch with small angular divergence and single energy distribution (high beam quality). It is difficult to realize such a high beam quality acceleration by using one laser beam, because there is a transverse ponderomotive force existing in the focused laser pulse. Here, we give a way to get a bunch accelerated axially by using two laser beams. Then we give another way to realize ultracold, almost no angular divergence laser vacuum acceleration. It is well known that a laser beam of a finite transverse extent will generate a transverse ponderomotive force to expel the electron from the beam axis. So, if an electron is initially between two parallel laser beams, each beam will push the electron to the axis of symmetry of the two parallel beams. And the electron will remain near the axis. In our scheme, we use two non-parallel beams to accelerate the electrons.