Present interest in tokamaks with noncircular cross sections motivates study of the magnetohydrodynamic stability properties of general axisymmetric configurations. Here we report on such a program and present some of the results. We divide the problem into two parts -(1) the determination of equilibrium configurations and evaluation of stability criteria for localized modes, and (2) the study of the complete normal mode spectrum of the configuration.Determination of an equilibrium configuration is carried out either analytically or numeri-ally.. It is always useful to study simplified configurations where analytic solutions exist. These models provide a means for checking numerical techniques and give an understanding of the mode structure to be expected in more general configurations. For more realistic systems we have developed an efficient numerical program which determines the equilibrium magnetic fields, given the distribution of the current in external conductors and a prescription of the pressure distribution and the net current inside each magnetic surface in the plasma.Two localized instability criteria are evaluated by integrating over each magnetic line in the plasma. Ideal interchange modes are studied by means of the Mercier criterion which implies stability if1
The Cerenkov interaction of a weak electron beam with a plasma is studied numerically. Three parts of the nonlinear evolution of the convective instability are discussed. In the first part the understanding of the saturation amplitude of the initial wave and its harmonics is extended. In the second part it is shown that a quasi-linear-like cascade process is responsible for the simutaneous appearance of beam particles and waves which move slower than the original beam velocity. These modes destroy the trapped particle oscillations of the initial wave. The third part of the instability is the development of fast waves whose phase velocities are greater than the original velocity of the beam. It is shown that these waves arise due to a mode coupling mechanism.
A Wigner function representation of multi-band quantum transport theory is developed in this paper. The equations are derived using non-equilibrium Green's function formulation with the generalized Kadanoff-Baym ansatz and the multi-band k.p Hamiltonian including spin. The results are applied to a two-band resonant inter-band tunneling structure.
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