Second-order distorted wave calculation for electron impact ionization of hydrogen

The triple differential cross sections for ionization of atomic hydrogen by electron impact are analysed in the case of coplanar, asymmetric geometry within the framework of second- order distorted wave theory. Detailed calculations are performed without making any approximations (other than numerical) in the evaluation of the second-order amplitude. The present results are compared with experimental measurements and other theoretical calculations for incident energies of 250, 150 and 54.4 eV. It is found that the second-order calculations represent a marked improvement over the results obtained from first-order theories for impact energies of 150 eV and higher. The close agreement between the present second-order plane wave calculation and those of Byron et al calculated using the closure approximation at an incident energy of 250 eV implies that the closure approximation is valid for this energy. The large difference between the present second-order distorted wave calculations and experiment at an incident energy of 54.4 eV suggests that higher order effects are important for incident energies less than 100 eV.

A developed stage of Alfven wave phase mixing

Alfven wave phase mixing is an extensively studied mechanism for dissipating wave energy in an inhomogeneous medium. It is common in the vast majority of phase mixing papers to assume that even though short scale lengths and steep gradients develop as a result of phase mixing, nonlinear wave coupling does not occur. However, weakly nonlinear studies have shown that phase mixing generates magnetoacoustic modes. Numerical results are presented which show the nonlinear generation of magnetosonic waves by Alfven wave phase mixing. The efficiency of the effect is determined by the wave amplitude, the frequency of the Alfven waves and the gradient in the background Alfven speed. Weakly nonlinear theory has shown that the amplitude of the fast magnetosonic wave grows linearly in time. The simulations presented in this paper extend this result to later times and show saturation of the fast magnetosonic component at amplitudes much lower than that of the Alfven wave. For the case when Alfven waves are driven at the boundary, simulating photospheric footpoint motion, a clear modulation of the saturated amplitude is observed. All the results in this paper are for a low amplitude (less than or equal to 0.1), single frequency Alfven wave and a uniform background magnetic field in a two dimensional domain. For this simplified geometry, and with a monochromatic driver, we concluded that the nonlinear generation of fast modes has little effect on classical phase mixing.

Time signatures of impulsively generated coronal fast wave trains

Impulsively generated short-period fast magneto-acoustic wave trains, guided by solar and stellar coronal loops, are numerically modelled. In the developed stage of the evolution, the wave trains have a characteristic quasi-periodic signature. The quasi-periodicity results from the geometrical dispersion of the guided fast modes, determined by the transverse profile of the loop. A typical feature of the signature is a tadpole wavelet Spectrum: a narrow-spectrum tail precedes a broad-band head. The instantaneous period of the oscillations in the wave train decreases gradually with time. The period and the spectral amplitude evolution are shown to be determined by the steepness of the transverse density profile and the density contrast ratio in the loop. The propagating wave trains recently discovered with the Solar Eclipse Coronal Imaging System (SECIS) instrument are noted to have similar wavelet spectral features, which strengthens the interpretation of SECIS results as guided fast wave trains.

Total and single differential cross sections for simple resonant collisions using a fully orthonormal continuum-distorted-wave basis

Simple electron capture processes are studied using an orthonormal two state continuum-distorted-wave (CDW) basis. The suitability of the basis set is tested by comparing predictions for total and differential cross sections with available experimental data. Overall good agreement is obtained and the authors conclude that a relatively small CDW basis set may be suitable to model a wide variety of low-energy collisions if the members of this extended set are astutely chosen.

Plane wave and Coulomb asymptotics

A simple plane wave solution of the Schrodinger-Helmholtz equation is a quantum eigenfunction obeying both energy and linear momentum correspondence principles. Inclusion of the outgoing wave with scattering amplitude f asymptotic development of the plane wave, we show that there is a problem with angular momentum when we consider forward scattering at the point of closest approach and at large impact parameter given semiclassically by (l + 1/2)/k where l is the azimuthal quantum number and may be large (J. Leech et al., Phys. Rev. Lett. 88. 257901 (2002)). The problem is resolved via non- uniform, non-standard analysis involving the Heaviside step function, unifying classical, semiclassical and quantum mechanics, and the treatment is extended to the case of pure Coulomb scattering.

Magnetically quantized continuum distorted-wave theory in atomic and molecular collisions

The continuum distorted-wave eikonal initial-state (CDW-EIS) theory of Crothers and McCann (J Phys B 1983, 16, 3229) used to describe ionization in ion-atom collisions is generalized (G) to GCDW-EIS to incorporate the azimuthal angle dependence of each CDW in the final-state wave function. This is accomplished by the analytic continuation of hydrogenic-like wave functions from below to above threshold, using parabolic coordinates and quantum numbers including magnetic quantum numbers, thus providing a more complete set of states. At impact energies lower than 25 keVu(-1), the total ionization cross-section falls off, with decreasing energy, too quickly in comparison with experimental data. The idea behind and motivation for the GCDW-EIS model is to improve the theory with respect to experiment by including contributions from nonzero magnetic quantum numbers. We also therefore incidentally provide a new derivation of the theory of continuum distorted waves for zero magnetic quantum numbers while simultaneously generalizing it. (C) 2004 Wiley Periodicals, Inc.

The effect of water depth on the performance of a small surging wave energy converter

The effect of water depth on the performance of a small surging wave energy converter (WEC) is investigated analytically, numerically and experimentally. It is shown that although the average annual incident wave power is significantly reduced by water depth, a large proportion of this reduction is due to the dissipation of highly energetic, but largely unexploitable seas. It is also shown that the power capture is related more closely to incident wave force than incident wave power. Experimental results demonstrate that both the surge wave force and power capture of a flap-type WEC increase in shallow water.