Ponderomotive potential

Fig. 4.4. Distribution of / for P = 0 for He, Ne, and Ar, fko = 1.55 eV, and various intensities characterized by the corresponding ponderomotive potential Up. Because of symmetry, the distribution is only shown for P > 0. Each curve has been normalized to a maximum of unity the number given in parentheses for each curve specifies the respective normalization factor. The vertical arrows mark the position of 4y/Up cf. (4.12). From [15]...

Figure 1.7 Differential cross-section ( /r )(da /dQO against the harmonic order n for ponderomotive potential Up/(me2) = 1,2, 3,4 and a fixed observation angle 6 = 40°.

We now address the question how much atomic physics needs to be included in order to account for ATI In fig. 9.6, we show experimental data for ATI from [493], obtained at several laser intensities. One of the important properties of ATI peaks, referred to as peak suppression, is that the relative intensity of the first ATI peaks above threshold does not increase uniformly with laser field strength, but actually begins to decrease in intensity relative to higher energy peaks as the laser field strength increases. Such behaviour cannot be explained in a perturbative scheme, in which interactions must decrease monotonically order by order as the number of photons involved increases, but can be accounted for in terms of the AC Stark shift of the ionisation potential in the presence of the laser field. In ATI experiments, the ionisation potential appears to shift by an average amount nearly equal to the ponderomotive potential, so that prominent, discrete ATI peaks are seen despite the many different intensities present during the laser pulse. However, ATI peaks closest to the ionisation limit become suppressed as the amplitude of the laser field oscillations increases and the ionisation threshold sweeps past them (a different effect which also suppresses ionisation near threshold is discussed in section 9.24.1). 

This gives rise to a (harmonic) ponderomotive potential in the x-y direction which, for a single ion (or the center-of-mass (COM) motion of a group of ions), yields the motion... 

Integration of the tapered-wiggler pendulmn equation results in an equation similar to that foimd in the case of a uniform wiggler, with a ponderomotive potential... 

If the wiggler amplitude is a decreasing fimction of axial position, then sin fres < 0, and the average potential decreases linearly with the ponderomotive phase. The difference between the ponderomotive potential for a uniform and tapered wiggler is illustrated in Fig. 6. As a result, the motion is similar to that of a ball rolling down a bumpy hill that accelerates as it falls. 

The second term in the above equation describes the effective, or ponderomotive, potential of the electron in the light field. Noting that the intensity of the light beam is 7 = c/8-k)Eq, the ponderomotive potential can be written as... 

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