Ponderomotive Acceleration Research Articles

Ponderomotive acceleration in the auroral region: A kinetic simulation

Alfvén waves with frequencies of the order of several Hertz have been observed in the auroral region. These waves are thought to be responsible for the acceleration of ionospheric particles out of the ionosphere and into the magnetosphere. As an Alfvén wave propagates into an inhomogeneous ionosphere, the amplitude of the wave decreases resulting in a gradient in the electric field and a ponderomotive force. The nature of the ponderomotive force is to accelerate ions out of the ionosphere, while accelerating electrons into the ionosphere decreasing the ambipolar electric field. Ponderomotive acceleration of ions can penetrate to low enough altitudes affecting the production regions for O+ and H+ ions. To understand the influences of ponderomotive acceleration on the lower ionosphere, a one‐dimensional hybrid particle code is used. The simulation model allows for multiple species, atmospheric chemistry and photoionization, tilted dipolar coordinate system, corotation, and convection. The electrons are treated as a charge neutralizing fluid where the parallel and perpendicular temperatures and heat flows are given by the 16‐moment transport equations. Coulomb, ion‐neutral, and electron‐neutral collisions are included in the hybrid simulation using newly developed collision techniques applicable to kinetic simulations. The altitude dependence of an Alfvén wave propagating from 6000 to 200 km in an inhomogeneous ionosphere is determined by solving Maxwell's equations. The parallel and perpendicular envelopes are determined and the resulting nonlinear, non‐resonant ponderomotive acceleration of ionospheric ions is calculated. The ponderomotive force is included in the kinetic simulation in the same fashion as gravity or the self‐consistent electric field. The acceleration event lasts for 10 min, by which time the density and flow speed profiles have reached equilibrium. The density and flow speed at 2500 km after 10 min of acceleration increase from 4.3 cm−3 and 1.6 km/s to 34 cm−3 and 6.0 km/s for H+, while the same quantities for O+ increase from 1670 cm−3 and −0.0009 km/s to 4795 cm−3 and 7.0 km/s. Collisional coupling between the H+ and O+ contributes to enhancing the outflow of H+. The net response of the ionosphere to the nonlinear ponderomotive force is an enhancement in ionospheric outflow of ions into the magnetosphere.

Energy distribution of photoelectrons generated from highly charged ions in a circularly polarized intense laser field

We observed the energy distribution of the photoelectrons generated from the highly charged ions in the tunneling regime by using a circularly polarized Ti:Sapphire laser (745 nm, 100 fs). The peaks for each successive charge state up to Ar3+, Kr4+, and Xe5+ were clearly resolved, and the peaks due to higher charge states were flattened in the high-energy region and deviated from those predicted by the quasistatic model. This deviation is explained by pondero-motive acceleration in the strong field gradient. In Xe, Xe8+ was generated at a peak intensity of 2.0 × 1016 W/cm2.

Ponderomotive effects on distributions of O+ ions in the auroral zone

Test particle calculations are used to compute the effects of gravity and ponderomotive acceleration by shear Alfvén wave oscillations on the distribution function of O+ ions along auroral field lines, assuming an ionospheric Maxwellian source of the ions at 2000 km altitude with ∼0.5 eV of thermal energy in the parallel component of velocity. The electric field model corresponds to a standing wave oscillation with a frequency ∼1 Hz in the azimuthal direction superimposed on the background dipole field, in which the wave amplitude is either increasing or decreasing in time. The electric field is taken to be primarily in the perpendicular direction. The time varying wave produces broad distributions with widths of 2 to 10 times the initial 0.5‐eV thermal energy of the Maxwellian source, and the density and flux of upward going O+ ions at one Earth radius are both enhanced in this model. The oxygen ion distribution functions at 1 RE altitude resulting from interaction with waves whose amplitudes are increasing in time have a more gradual lower energy cutoff than do the distribution functions resulting from decaying waves. The high‐energy part of the distribution functions in growing waves reflects the temperature of the Maxwellian source, while the high‐energy part of the distributions resulting from decaying waves steepens with time, independent of the source temperature.

Plasma energization by the ponderomotive force of magnetospheric standing Alfvén waves

The second‐order force generated by standing Alfvén waves in a dipolar magnetospheric geometry is rederived in a more straightforward and accurate way than previously done. The spatial structure of the resulting ponderomotive acceleration consists of regions in which plasma can be trapped between “diverging” nodes of the acceleration field (where the acceleration vector points away from the node). The “specific parallel energy” (parallel energy per proton mass) of accelerated plasma particles is derived. This quantity maximizes at “converging” nodes of the acceleration field (where the acceleration vector points toward the node). For the fundamental standing mode the converging node is at the equatorial plane, and the maximum specific energy there increases rapidly with L (where L is the McIlwain parameter), becoming significant above L = 5 for typical wave amplitudes. At L ∼ 10, H+ ions should reach energies of ∼ 100 eV and O+ ions energies of ∼ 2keV. Gravity has little effect on the energization, other than to define the magnetic latitude from which acceleration begins. At reasonably high L, almost all the energization occurs at magnetic latitudes above ±45°. For the second harmonic the converging nodes are situated away from the equatorial plane, and accelerated particles starting from rest do not reach that plane. The third harmonic has a converging node at the equatorial plane, and specific energies there are the same as for the fundamental mode. However, the accelerated particles originate from above the diverging nodes at latitudes of about ±18°, passing through a larger acceleration field than for the fundamental mode in that region. Particles having initial energies of a few electron volts near the ionosphere may be able to traverse the diverging nodes of the third harmonic and reach the equatorial plane.

Ponderomotive focusing in axisymmetric rf linacs.

In many present and planned compact electron sources and linacs, very large rf accelerating fields are present in the linac structures. A charged particle whose trajectory is parallel to the axis receives no net focusing from the periodic transverse forces arising from the axisymmetric rf wave. However, if the lowest-order periodic transverse motion of the particles is included, a net ponderomotive focusing force is obtained when the momentum transfer is averaged over a period of the motion. Since this force is second order in the electric-field amplitude, the resultant focusing can be non-negligible in high gradient structures. In order to produce and preserve high-brightness beams in rf linacs it is necessary to obtain a better understanding of all the forces acting on the beam and the subsequent beam dynamics. To this end we examine the lowest-order ponderomotive rf focusing of electrons in axisymmetric standing- and traveling-wave linac structures. We obtain a generalized paraxial envelope equation which includes the effects of the ponderomotive focusing and longitudinal acceleration to describe the transverse beam envelope evolution. The implications of our results on beam dynamics in electron linacs are examined, and extensions of the results to positron and proton linacs are discussed.

The ponderomotive force of standing Alfvén waves in a dipolar magnetosphere

Nonlinear effects associated with standing Alfvén waves may be significant in planetary magnetospheres. The field‐aligned second‐order force and acceleration generated by standing Alfvén waves in a dipolar magnetosphere are derived using previously published perturbation series for toroidal mode eigenfunctions and eigenvalues. The field‐aligned ponderomotive force and ponderomotive acceleration (PMA) are then derived by time integration. The second‐order acceleration and the PMA are independent of the plasma mass density distribution in the equatorial plane, and are only weakly dependent on the density structure along magnetic field lines. The second‐order acceleration has an oscillation at twice the standing wave frequency superimposed on the PMA at a given position. The amplitude and phase of this oscillation are dependent on ionospheric conductance and field‐aligned density structure. The PMA has an approximate L5 dependence, and can have relatively large values in the outer magnetosphere. For example a fundamental standing Alfvén wave with equatorial electric field amplitude 5 mV m−1 gives a maximum PMA of 12 g toward the equatorial plane at L = 9. An approximate upper limit on the energy of particles accelerated by this mechanism appears to be of the order of 1 keV, attained by O+ ions accelerated from the ionosphere to the equatorial plane at high L values.

Scattering-theoretical approaches to multiphoton ionization in strong fields.

The nonrelativistic version of the authors' theory of multiphoton ionization [Phys. Rev. 40, 4997 (1989)] is compared with other forms of scattering-theoretical approaches that employ different boundary conditions. These methods, which are expressed in terms of formal time-independent scattering theory, are shown to be equivalent in the large-photon-number limit to use of the semiclassical time-dependent S-matrix theory. In the authors' treatment it is assumed that the photoelectron has escaped from both the electromagnetic and atomic fields; a perturbation expansion in the photon-electron interaction is obtained that correctly accounts for the atomic final-state interactions of the photoelectron. The case of multiphoton detachment of ${\mathrm{I}}^{\mathrm{\ensuremath{-}}}$ is treated, for which the influence of the final-state atomic potential on the transition rate can be ignored. It is shown both analytically and numerically for the Nd--yttrium aluminum garnet wavelength that the transition rates obtained for this case from the various approaches are distinctly different. The present approach is shown to be consistent with an abrupt switching off of a spatially unlimited monomode field, in contrast with Keldysh-type approaches, which correspond to a long switch-off time if the ad hoc assumption of ponderomotive acceleration is made. Above-threshold-ionization spectra calculated from the present approach exhibit interference effects and are redshifted with respect to what is expected for slow switch-off. It is demonstrated, using the semiclassical time-dependent approach, that the corresponding final off-field scattering-state wave function only exists if the ponderomotive potential per unit photon energy is an integer, in accordance with our earlier time-independent analysis. The origin of this curious feature is made clear.

Ponderomotive force and AC Stark shift in multiphoton ionisation

A non-perturbative approach to the photoionisation of a model atom in arbitrarily strong fields is described. An explanation is given for the disappearance of the lowest energy electrons in a multiphoton ionisation experiment at very high intensities, in terms of the AC Stark shift of the ionisation potential of the atom, followed by ponderomotive acceleration of the photoelectrons.

Self-focusing of laser beams in a plasma by ponderomotive forces

Self-focusing of a laser beam in a plasma is treated in terms of the ponderomotive acceleration due to the gradient of the light intensity. The focusing of radiation within the first minima of diffraction sets a lower limit to the laser power which is of the order of 1 MW for the usual lasers if cut-off density and a plasma temperature of about 10 eV are assumed.