Plane Wave Perturbation Research Articles

Development of the MHD electrothermal instability with boundary effects

An analytic treatment of the linear development of the electrothermal instability with boundary effects is presented. The plasma is assumed to be bounded in one direction only, namely between two parallel walls of finite separation lying parallel to the applied magnetic field. The procedure of the calculation is to Laplace transform the linear electrothermal equations in time, solve the resulting spatial differential equations under the appropriate boundary conditions, and then transform back into real time to obtain the development of a given initial perturbation. Two cases are considered, viz., continuous insulator walls, and infinitely finely segmented electrode walls. In general, an initially plane wave perturbation in the electron density is split into an infinite number of modes, of which usually only a finite number are unstable. As the Hall parameter increases, more and more modes are successively destabilized. However, the critical Hall parameter for destabilization of a given mode usually increases as the wavelength parallel to the walls increases, so that, at least for some geometries, long wavelength perturbations are more stable. In the case of segmented electrodes it may be possible to achieve enhanced stability for a given wavelength by adjusting the external circuitry.

Excitation of Two-Phonon States by Inelasticα-Particle Scattering

Recent experiments on inelastic scattering of 40-MeV $\ensuremath{\alpha}$ particles have shown that the angular distributions from the excitation of some known ${4}^{+}$ states in medium weight nuclei are not in accord with the Blair phase rule. Calculations are reported which indicate that the anomaly arises as an interference effect between two possible mechanisms for exciting the first ${4}^{+}$ state, i.e., a direct transition and a multiple transition. This conclusion is contrary to previous interpretations based on plane-wave perturbation calculations. It is suggested that experiments of this type, and the analysis given here, promise to be a useful tool for the study of higher excited states.