Question) Simple model for electron motion following tunneling ionization. (a) Intensity scaling. In tunneling ionization, the electric field strength can be large enough to suppress the Coulomb field that binds an electron to the ion. Although tunneling ionization can take place at lower intensities, to get a sense of scale for what intensity is required, estimate what laser intensity will have an electric field approximately equal to the atomic field. To do this, calculate the force on an electron due to a proton when the two are separated by a Bohr radius. Set this force equal to eE, where here, the E is the electric field strength of the laser beam. Now this laser field strength can be associated with the binding field in the H-atom. Next calculate an expression for the laser intensity and the ponderomotive potential at which the peak laser electric field strength equals that of the atom. Get a numerical estimate: Suppose the laser wavelength is 800nm, the pulse duration is 100fs, and the beam is focused to a diameter of 50um. Calculate the pulse energy required to reach the intensity you calculated above, and the ponderomotive energy (in eV) at this intensity. The ionization potential for an isolated hydrogen atom is one Rydberg = 13.6eV. We can get a field strength by dividing by the Bohr radius do = 0.53 A. (b) Equation of motion for the electron. Calculate the non-relativistic equation of motion for an electron that is released from the ion at a phase o relative to the peak E-field of the wave. You will be doing a non-relativistic calculation that ignores the effect of the B-field in the wave. Assume the initial velocity = 0. You should find that the electron oscillates, but there is also a drift term (linearly proportional to t). Depending on the emission time relative to the peak of the laser electric field, that drift can send the electron back to the ion. Plot several trajectories for different values of o. You should find that there is a range of where the electron will return to the ion before drifting away