We have measured electron impact ionization (EII) for Fe 7+ from the ionization threshold up to 1200 eV. The measurements were performed using the TSR heavy ion storage ring. The ions were stored long enough prior to measurement to remove most metast
ables, resulting in a beam of 94% ground state ions. Comparing with the previously recommended atomic data, we find that the Arnaud & Raymond (1992) cross section is up to about 40% larger than our measurement, with the largest discrepancies below about 400~eV. The cross section of Dere (2007) agrees to within 10%, which is about the magnitude of the experimental uncertainties. The remaining discrepancies between measurement and the most recent theory are likely due to shortcomings in the theoretical treatment of the excitation-autoionization contribution.
We report measurements of electron impact ionization (EII) for Fe^13+, Fe^16+, and Fe^17+ over collision energies from below threshold to above 3000 eV. The ions were recirculated using an ion storage ring. Data were collected after a sufficiently lo
ng time that essentially all the ions had relaxed radiatively to their ground state before data were collected. For single ionization of $fethirteen$ we find that previous single pass experiments are more than 40% larger than our results. Compared to our work, the theoretical cross section recommended by Arnaud & Raymond (1992) is more than 30% larger, while that of Dere (2007) is about 20% greater. Much of the discrepancy with Dere (2007) is due to the theory overestimating the contribution of excitation-autoionization via n=2 excitations. Double ionization of Fe^13+ is dominated by direct ionization of an inner shell electron accompanied by autoionization of a second electron. Our results for single ionization of Fe^16+ and Fe^17+ agree with theoretical calculations to within the experimental uncertainties.
The motion of self-propelled particles can be rectified by asymmetric or ratchet-like periodic patterns in space. Here we show that a non-zero average drift can already be induced in a periodic potential with symmetric barriers when the self-propulsi
on velocity is also symmetric and periodically modulated but phase-shifted against the potential. In the adiabatic limit of slow rotational diffusion we determine the mean drift analytically and discuss the influence of temperature. In the presence of asymmetric barriers modulating the self-propulsion can largely enhance the mean drift or even reverse it.
We report ionization cross section measurements for electron impact single ionization (EISI) of Fe^11+$ forming Fe^12+ and electron impact double ionization (EIDI) of Fe^11+ forming Fe^13+. The measurements cover the center-of-mass energy range from
approximately 230 eV to 2300 eV. The experiment was performed using the heavy ion storage ring TSR located at the Max-Planck-Institut fur Kernphysik in Heidelberg, Germany. The storage ring approach allows nearly all metastable levels to relax to the ground state before data collection begins. We find that the cross section for single ionization is 30% smaller than was previously measured in a single pass experiment using an ion beam with an unknown metastable fraction. We also find some significant differences between our experimental cross section for single ionization and recent distorted wave (DW) calculations. The DW Maxwellian EISI rate coefficient for Fe^11+ forming Fe^12+ may be underestimated by as much as 25% at temperatures for which Fe^11+ is abundant in collisional ionization equilibrium. This is likely due to the absence of 3s excitation-autoionization (EA) in the calculations. However, a precise measurement of the cross section due to this EA channel was not possible because this process is not distinguishable experimentally from electron impact excitation of an n=3 electron to levels of n > 44 followed by field ionization in the charge state analyzer after the interaction region. Our experimental results also indicate that the double ionization cross section is dominated by the indirect process in which direct single ionization of an inner shell 2l electron is followed by autoionization resulting in a net double ionization.
The Lagrange planetary equations are used to study to secular evolution of a small, eccentric satellite that orbits within a narrow gap in a broad, self-gravitating planetary ring. These equations show that the satellites secular perturbations of the
ring will excite a very long-wavelength spiral density wave that propagates away from the gaps outer edge. The amplitude of these waves, as well as their dispersion relation, are derived here. That dispersion relation reveals that a planetary ring can sustain two types of density waves: long waves that, in Saturns A ring, would have wavelengths of order 100 km, and short waves that tend to be very nonlinear and are expected to quickly damp. The excitation of these waves also transports angular momentum from the ring to the satellite in a way that damps the satellites eccentricity e, which also tends to reduce the amplitude of subsequent waves. The rate of eccentricity damping due to this wave action is then compared to the rates at which the satellites Lindblad and corotation resonances alter the satellites e. These results are then applied to the gap-embedded Saturnian satellites Pan and Daphnis, and the long-term stability of their eccentricities is assessed.
The secular perturbations exerted by an inclined satellite orbiting in a gap in a broad planetary ring tends to excite the inclinations of the nearby ring particles, and the rings self-gravity can allow that disturbance to propagate away in the form
of a spiral bending wave. The amplitude of this spiral bending wave is determined, as well as the wavelength, which shrinks as the waves propagate outwards due to the effects of the central planets oblateness. The excitation of these bending waves also damps the satellites inclination I. This secular I damping is also compared to the inclination excitation that is due to the satellites many other vertical resonances in the ring, and the condition for inclination damping is determined. The secular I damping is likely responsible for confining the orbits of Saturns two known gap-embedded moons, Pan and Daphnis, to the ring plane.
