Table of contents

There is no unique stationary scattering theory. We distinguish the main versions by analyzing the different idealizations (spatial or temporal boundary conditions - SBC and TBC, respectively) implied by different orders of taking the limits of infinite volume and of sharp initial conditions. The relations of the different representations are discussed in detail. The equivalence of the Schrödinger and Heisenberg dynamical pictures, as well as the hermiticity of the Hamiltonian fail for SBC but can be applied in TBC. However, when using TBC the scattering wave does not behave as an eigenfunction of the Hamiltonian. The evaluation of transition rates and rates of change of observables is described for the different approaches. We also distinguish the meaning of two types of invariants of the motion by resolving the temporal variation of the observables as an "internal" production rate plus a term representing the flux across the boundary of the scattering region.

Elastic scattering of antiprotons on even-even nuclei is calculated microscopically from the Dover-Richard and Paris potentials. The five different spin-dependent t-matrix elements are each parametrized in terms of simple functions. The fairly weak energy dependence is included by using an effective value of the relative energy obtained by averaging over the distribution in the nuclear tail. The first order optical potential reproduces reasonably well the differential cross section. The second order correction to the optical potential is then obtained in a perturbative treatment. Selfconsistency is only approximately satisfied, but we argue that the tremendous simplifications this entails are still sufficiently accurate for our purpose. Both the central and the spin-orbit optical potential, the differential cross section, the polarization and spin rotation functions are calculated. The spin dependence is significantly altered by the second order contribution. Simple analytical expressions are derived for medium effects and for the effect of various types of correlations. All experimentally available cases are investigated and very good agreement is found. We compare with previous work on this subject and discuss earlier conclusions in connection with our results.

It was believed that the value of the quadrupole moment of the deuteron Q is too large to be fitted by realistic local potential models. Two simple local potential models for the deuteron with large Q are considered.

Level-crossing experiments yielding Doppler-free signals are normally performed using a CW light source with a broad spectral distribution ("white" excitation), and the signals obtained are described by a well-known formula due to Breit. By using a single-mode dye laser or a pulsed laser for the excitation, strong modifications of level-crossing signals can be obtained. Profound changes in hyperfine structure crossing signals are demonstrated in experiments, performed in a cell, on the 9 ²D_3/2 state of ¹³³Cs. Practical utilisation of unconventional excitation in level-crossing and optical double resonance spectroscopy is discussed.

Doppler limited Optogalvanic Spectroscopic technique is employed to study the hyperfine structure of six transitions of ⁹³Nb. An externally stabilized single frequency ring dye laser and a commercial Nb/Ne hollow cathode lamp were used. From the observed well resolved hyperfine components of the spectra the magnetic dipole and the electric quadrupole coupling constants were evaluated. The hyperfine coupling constants for 12 levels are reported in this paper out of which values for four levels are reported for the first time. Our values are compared with the previous data wherever available.

The nonlinear mode coupling problem for a single resistive tearing mode as a possible explanation for the phenomenon of mode locking in Tokamaks is considered. The analysis is close to previous work by Nave and Wesson [1] and the purpose of this work is to clarify some of the issues brought forward by these authors. First a derivation of basic equations are given, based on first principles and without ad hoc assumptions. The role played by flux surfaces in the plasma region is discussed and the basic dynamic equations are derived in two ways: First by integrating over a "fixed" circular symmetric surface, and then over a nearby flux surface. The boundary conditions are stated in a general manner and the basic dynamic equation for the problem is derived. A consistent asymptotic expansion is attempted and qualitative results are presented which support the basic idea that this could give a possible explanation for mode locking.

Experiments on the propagation of an ion acoustic soliton from an isotropic plasma into a plasma region where a periodic magnetic field exists are described. The orientation of the magnetic field is transverse to the direction of the propagation of the soliton. A periodic focussing-defocussing of the soliton is detected which correlates with the location and dimension of the magnets

The transverse stability of solitary wave structures to the equation

iψ_t + ψ_xx + sψ_yy + p|ψ|²ψ = 0

is studied for the four cases; (p = 1, s = 1), (p = 1, s = −1), (p = −1, s = −1) and (p = −1, s = 1). Solitary waves in the x-direction are envelopes ψ = √2 sech(x) exp (it), for p = 1, and they are kinks; ψ = √2 tanh(x) exp (– 2it), for p = −1. For s = 1 an "energy principle" can be invoked, and instability for the envelope occurs in the range 0 < k² < 3, and for the kink in the range 0 < k² < 1. Here k is the wavenumber of the perturbation in the y-direction. Growth rates are estimated very simply by means of a Rayleigh-Ritz method. For s = −1, we review existing results for the envelope. It is unstable in a range 0 < k² ⩽ 1.17 where the upper limit must be determined numerically. For the kink, we find a continuum of unstable, non-local perturbations covering the whole range 0 < k² < ∞. On both sides of the kink structure (|x| ≫ 1) these perturbations are oblique, purely growing plane waves.

We conclude that both envelopes and kinks are transversely unstable for all signs of p and s.

We give a brief summary of an experimental observation of wave growth and saturation in a traveling wave tube modified so that a warm electron beam interacts with a single wave on the slow wave structure. This system has essentially the same physics as a weak warm beam plasma system but has a much lower inherent noise level. The growth rate and saturation level of the unstable wave are studied as a function of the beam parameters. We observe that, in the weak warm beam limit, the time-averaged beam distribution function develops a localized plateau. The electric field at saturation scales as the square of the linear growth rate of the wave. When the growth is stronger, the entire distribution function can become distorted.

We give a brief summary of an experimental test of the quasilinear theory of the bump on tail instability. Recent theoretical work has suggested that the quasilinear description of the weak warm beam plasma instability is incomplete. It has been suggested that beam mediated mode coupling effects neglected in standard quasilinear theory play an important role, and that their average effect is a zeroth order increase in the growth rate. We have experimentally observed strong mode coupling effects when a weak warm beam interacts with waves on a slow wave structure. However, when we average the effects of the mode coupling we do not observe the predicted zeroth order increase in the growth rate. This intriguing result suggests the action of some statistical or dynamical conservation law whose origin has not yet been theoretically identified.

The nonlinear behavior of the modulational instability of nearly constant amplitude, weakly dispersive, weakly nonlinear circularly polarized MHD waves with an initial periodic modulation is studied. The phenomena of recurrence is discussed by results from a multiple time scale development near marginal growth, a numerical study for moderate wavenumbers and finally a study of qualitative dynamics for nearly constant wavetrains. The conclusion is that the phenomena of recurrence and slow randomization of periodic wave motion of nonlinear MHD waves can only occur for large wavenumbers compared to the marginal one. For wavenumbers near the marginal one, it is expected that an initially constant amplitude wave will break irreversibly into a broad spectrum of waves.

The combined effect of modulational instability and nonlinear Landau damping on a circularly polarized MHD wave is studied. When the wave gets modulated, the magnetic mirror force as well as the parallel electric field associated with the modulations, transfer energy to the charged particles with velocity near the Alfvén velocity, to cause a nonlinear Landau damping. Our mathematical model is a DNLS equation extended with a nonlocal term representing the resonant particles. This irreversible model allows a conservation law which in a slowly varying wave train limit corresponds to conservation of wave action. In addition to the modulational instability already known from the DNLS model, the Landau damping term introduces a modulational instability in the wave number range where the wave would otherwise be stable. We present numerical studies of the development of the instabilities and the subsequent wave damping in both ranges. One of our principal findings is that the wave frequency decreases in the same proportion as the energy density. This can be understood in terms of the conservation of action law.

The DNLS equation describes weakly dispersive MHD waves propagating parallel as well as at a small angle to the magnetic field. For oblique propagation, the magnetosonic mode is described by the KdV equation, whereas certain aspects of the oblique Alfvén wave are described by the MKdV equation. The two latter equations possess one-parameter families of solitons. One-parameter families of oblique soliton solutions to the DNLS equation exist, which match to those of the KdV and MKdV in appropriate asymptotic limits. For parallel propagation, the DNLS equation possesses a well-known two-parameter family of soliton solutions. Such a family also exists in the oblique case (Kawata and Inoue, J. Phys. Soc. Japan 44, 1968 (1978)), but has so far been paid little attention. In the parallel case, soliton formation is known to result from modulational instability of circularly polarized wave trains. In the oblique case, a rich family of periodic wave train solutions exists which matches to the cnoidal solutions to MKdV and KdV in the appropriate limits. The modulational stability of these wave trains is studied by Whitman's method. A conjecture analogous to a result of Driscoll and O'Neil (Phys. Fluids 17, 1196 (1976)) is supported numerically.

Recent Bond-Charge-Model calculations of interplanar force constants for Si and Ge by A. Fleszar and R. Resta have provided an interesting comparison between ab initio and fitted force constants along [001] and [111] directions. Our extensions to polar GaAs and to the [110] direction provide a guideline for ab initio calculations and supply an helpful comparison between different directions for the study of semiconductor superlattice dynamics.

The results of DOS calculations for the s-d valence band of disordered paramagnetic Cu_0.50 Ni_0.50 alloy by the recursion method are presentef for total and partial densities of states. Use of the CPA for the continued fraction termination has allowed to reveal the fine structure of the DOS in the band, which is due to non mean field features of the recursion method, also to reduce required computer time. Results for different sets of LCAO parameters, comparison of the DOS calculations with the experiment and other calculations results are presented.

A computational technique of prediction of magnetising inrush current at various switching conditions is described. An improved modelling of B/H curve of electrical steel is presented. The effects of varying switching angles on the voltage wave, the energising circuit impedance and the remanent flux density are discussed. The effects of other parameters, such as the winding space factor and energising winding length, which have not been previously taken into consideration are also presented in this paper.

The magnetic properties of wound cores constructed from electrical steel strips have been found to be affected by their geometry, in particular the inner and outer diameters, the strip width and the build-up thickness of the toroids. Assessment of the effect of aspect ratio and winding ratio have been carried out in various sizes of toroid. An increase in aspect ratio resulted in better magnetic performance, whereas increase in winding ratio degraded the original magnetic properties. However, when the inner and outer diameters are varied with constant build-up and strip width, better performance is obtained by increasing the winding ratio.

The initial rate of rise of temperature technique using thermistors has been used to measured power loss on the inner and outer wraps of a wound toroid. The power loss of a 60 × 44 × 40mm toroid at 1.0 T before stress relief annealing was 0.88 and 0.52 W kg⁻¹ at the inner and outer layers respectively. After stress relief annealing, the power loss fell to 0.44 and 0.43 W kg⁻¹ at the inner and outer layers respectively. This indicates the higher stress produced by small diameter wrapping can be reduced by normal stress relief annealing.

Using refraction of neutrons passing through Bloch walls of a regular magnetic domain structure in the interior of a bulky ⟨110⟩-Fe (4 at.% Si) single crystal the thickness of the 90°-Bloch wall has been determined at T = 590°C to be d = 195 nm. Furthermore the decrease of the zig-zag angle ψ with increasing temperature has been measured and the critical neutron scattering in the neighborhood of the Curie point observed.