![]() The application of this type of force to low frequencies above the aurora was investigated by Li et al. This force is often referred to as the “Miller force” ( Miller, 1958). For example, averaging the force acting on an ion over the course of its gyration in a wave field with a spatial gradient yields a force oppositely directed to the spatial gradient in the wave amplitude. Ponderomotive forces are obtained by considering the net force by the electric and magnetic fields of an Alfvén wave acting on a particle over its gyration. Both of these mechanisms are nonresonant but can significantly accelerate ions as will be described in the following paragraphs. The second case deals with the case of scattering of ions by DAW, which are obliquely propagating with perpendicular wavelength comparable to the ion gyroradius. First, when the Alfvén waves have a perpendicular wavelength much larger than the ion gyroradius, a number of so-called “ponderomotive” forces can be exerted on the plasma that can lift charged particles to higher altitudes. There are multiple pathways through which Alfvén waves can exert influence on plasmas, but here we group them into two general categories. Low-frequency Alfvén waves, whose frequency is much less than the ion gyrofrequency, have also been argued to play an important role in the acceleration of plasma in the cusp and auroral regions. In Cross-Scale Coupling and Energy Transfer in the Magnetosphere-Ionosphere-Thermosphere System, 2022 1.4.1.3 Acceleration by interactions with low-frequency Alfvén waves We may thus proceed to use these data as a test of theories such as the KFR model, which treat the ATI process as scattering between the ground state and Volkov states in the continuum. In any case, the absence of sharp resonances in the 140 fsec electron spectra is very good evidence that bound states play a minimal role in ATI with circular polarization. This argument is explained in more detail in reference 14, and gives very similar results to the KFR calculations for circular polarization, as in reference 13. Evidently, transitions to continuum states is favored over transitions to these bound states, since even though high lying continuum states must have absorbed more photons and thus carry still more angular momentum, they can penetrate close to the ground state more easily because of their high energy. have their angular momentum L approaching their principal quantum number n. Essentially, these are high lying states that are relatively circular, i.e. ![]() ![]() A similar argument may be made for the bound states that come into resonance during ionization. There we found that the centrifugal barrier was an effective means of reducing the overlap, and hence the transition rate, between the ground state and continuum states of high angular momentum but low energy. Why have the resonances gone away? We speculate that the situation is essentially the same as for long pulses with circular polarization. The main difference is the absence of resonances in the circularly polarized case. The bottom trace in figure 3 the xenon ati spectrum for spectrum for 140 fsec 616 nm pulses with circular polarization. It now appears that at least one such system has been found: sub-picosecond photoionization of rare gases with circularly polarized light. We would like know if systems exist for which high order multiphoton ionization is truly nonresonant. The dominance of intermediate resonances complicates the business of calculating ATI. This fine structure has been associated with excited atomic states that are temporarily Stark shifted into resonance by the intense radiation. Reiss ( reference 13), integrated over the measured temporal and spatial profile of the laser pulse.Ħ16nm pulses, which reveal that each ATI peak really consists of a “fine structure” of electrons with different energies, ionized when the laser intensity was at different values. Bottom: A computer simulation of the experiment, using ionization rates from the Keldysh theory of H. Top: ATI spectrum for circularly polarized 1064 nm light in xenon (from reference 14).
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