Figure 1

(a) For hydrogen in parallel fields, with $B=4.5$, $E=-1.3$, the flux of electrons striking a detector (placed at $z=-4$) is plotted as a function of time $T$ after the excitation of the atom. The thin dark line models the outgoing electron wave packet by an ensemble of trajectories with precise energy and start time. The thick shaded line uses an ensemble given by a minimum uncertainty Gaussian wave packet with central energy corresponding to effective quantum number $N\equiv (-2\widehat{E}{)}^{-1/2}=80$. This implies physical parameters $\widehat{B}=0.49\mathrm{T}$, $\widehat{F}=19\mathrm{V}\mathrm{/}\mathrm{c}\mathrm{m}$, and one scaled unit of time $T$ equal to 52 ps. We used a wave packet of width $\Delta T=0.1$ scaled units (5.2 ps). (b) The time it takes a trajectory to strike the detector is plotted as a function of the initial angle $\theta$ at which the trajectory is launched. The dashed lines connect icicles to their corresponding pulses in (a). The lowest icicle, having only its upper portion visible in (b), corresponds to the direct trajectories. (c) The number of iterates required to escape the complex is plotted as a function of $\theta$. Each escape segment corresponds to an icicle in (b). (d) The epistrophic structure of the first several escape segments is shown. The dashed lines connect segments within one epistrophe. The solid arrows show the creation of new epistrophes according to the epistrophe start rule. The asterisk denotes a strophe segment which does not fit into the pattern of epistrophes.Reuse & Permissions

Figure 2

A contour plot of potential energy is shown ($B=4.5$; $E=-1.3$) with a prominent unstable periodic orbit (vertical curve) near the saddle point. Three ionizing trajectories are also plotted. The negative $z$ axis defines the surface of section.Reuse & Permissions

Figure 3

A surface-of-section plot ($B=4.5$; $E=-1.3$) showing the unstable fixed point ${\mathbf{z}}_{\mathsf{X}}$ with its homoclinic tangle of intersecting stable and unstable manifolds [the thin curve ($\mathcal{S}$) and the thick curve ($\mathcal{U}$), respectively]. The lobe $E_{-2}$ intersects the line of initial conditions ${\mathcal{L}}_0$, creating a segment that will escape (i.e., land in $E_0$) in two iterates.Reuse & Permissions