Slow-Down Collisions and Nonsequential Double Ionization in Classical Simulations

We use classical simulations to analyze the dynamics of nonsequential double-electron short-pulse photoionization. We utilize a microcanonical ensemble of ${10}^5$ two-electron “trajectories,” a number large enough to provide large subensembles and even sub-subensembles associated with double ionization. We focus on key events in the final doubly ionized subensemble and back-analyze the subensemble’s history, revealing a classical slow-down scenario for nonsequential double ionization. We analyze the dynamics of these slow-down collisions and find that a good phase match between the motions of the electrons can lead to very effective energy transfer, followed by escape over a suppressed barrier.

Figure 1

A typical laser field enclosed in a trapezoidal envelope with two-cycle turn-on $T$ and four-cycle plateau $\tau -2T$.

Figure 2

Left-hand plot: the path of the pilot atom during the first eight out of 100 000 time steps. The solid curve shows the boundary between the classical allowed and disallowed region. Right-hand plot: the distribution of trajectories of the initial ensemble.

Figure 3

Time evolution of the 4174 trajectories (from an original ensemble of ${10}^5$) which eventually participate in double ionization. The arrows show the direction and magnitude of the laser force [$F(t)=-E(t)$].

Figure 4

Time evolution of the 429 trajectories satisfying the conditions of double-ionization jets during this half-cycle. The arrows show the direction and magnitude of the laser force [$F(t)=-E(t)$].

Figure 5

Time evolution of one particular double-ionization trajectory. The horizontal axis shows position in atomic units while the vertical axis shows energy also in atomic units. The solid black and dashed gray curves show the combined potential of nucleus, electron-electron repulsion, and laser field each electron feels. The plots are drawn at equal time intervals, beginning at $t=3\mathrm{\text{cycle}}$, and extend over slightly more than a quarter-cycle.