Classical threshold behaviour in a 1+1-dimensional model for double   ionization in strong fields
  Building on insights about the classical pathways to double ionization in strong laser fields we here propose a 1+1-dimensional model that captures essentials of the 3-d potential landscape and allows efficient studies of the process in reduced dimensions. The reduction to one degree of freedom for each electron is obtained by confining their motion to lines at an angle of pi/6 with respect to the field axis; the justification for this choice is that upon variation of the electric field the Stark saddles move along the same lines. In this way we obtain a low-dimensional representation in which symmetric electron escape is possible. As a demonstration of the advantages of this model we confirm numerically the equivalent of the Wannier threshold behaviour for constant electric field and identify several classes of trajectories that can contribute to the ionization process. 
Bruno Eckhardt and Krzysztof Sacha