[en] A time dependent two-dimensional MHD calculation for pinch experiments, previously developed at Columbia, is improved and modified so that very long calculations (until the plasma reaches a quasi-equilibrium state) are possible. The calculation method is presented, and the simulation results of the Jutphaas screw pinch SP-1 and the Los Alamos reverse-field pinches ZT-I, ZT-S and ZT-40 are studied

[en] A time dependent two-dimensional MHD calculation for pinch experiments, previously developed at Columbia, is improved and modified so that very long calculations (until the plasma reaches a quasi-equilibrium state) are possible. The calculation method is presented, and the simulation results of the Jutphaas screw pinch SP-1 and the Los Alamos reverse-field pinches ZT-I, ZT-S, and ZT-40 are studied. A set of single fluid resistive MHD equations are solved using standard alternate direction implicit method in an Eulerian difference scheme. Initial conditions correspond to the start of the main discharge in the experiment, with a homogeneous fully ionized plasma at rest. The equations are driven by time dependent boundary conditions: the toroidal magnetic field and the poloidal flux at the wall

[en] Pregnant mice of the day 10 + 2 have been irradiated with X-rays, the doses being 50, 100, and 200 R. The embroys have been taken 2, 4, 6, 8, 12, 24 or 48 hours after the irradiation, as well as on the 18th day, for subsequent examination by electron microscopy and optical microscopy. Characteristical areas of necrosis have been detected by optical microscopy as soon as 2 hours after the irradiation and could be well defined up to 48 hours post irradiation. The examination by electron microscopy revealed these pathological changes to be due to shrinkage. The necrotic areas have been found at various places of the embryonic organisms, with the strongest evidences of necrosis having been found in the primordial extremeties and in the brain and spinal cord anlage. Taking into account these findings and the results obtained, the development of typical radiation-induced malformations can be explained in terms of embryology. Analogous to other teratogeneous substances known to induce necrosis already 2 hours after application, a radiation-induced effect on the cell cycle during the S-phase can be expected. (orig./MG)

[en] Results are summarized of two-dimensional MHD simulations of the reversed field pinches Eta-Beta, ZT-1, ZT-S, and ZT-40. The model used is the single-fluid, time-dependent, axisymmetric (i.e., no toroidal variation) magnetohydrodynamic equations with dissipation. Initial conditions assume a fully ionized cold (approximately 1 eV) plasma-at-rest, with appropriate bias toroidal field. The equations are driven by time-dependent boundary conditions: the toroidal field B/sub z/(t), and the poloidal flux chi (t), prescribed as functions of time in agreement with the experimental conditions. The poloidal flux is indirectly extrapolated from the prescribed toroidal current I/sub z/

[en] A reduced set of two-dimensional MHD equations have been derived describing the axisymmetric time evolution of a MHD stable plasma evolving slowly due to resistive diffusion and changing boundary conditions. The equations are restricted to low β but allow changing topology. They are integrated in time to demonstrate a possible spheromak formation method. External circuit equations are integrated simultaneously with the plasma equations to determine the electromagnetic boundary conditions self consistently. The effects of a finite conductivity vacuum chamber are included

[en] A three-dimensional nonlinear toroidal full MHD code, MH3D, has been used to study sawtooth oscillations in tokamaks. The profile evolution during the sawtooth crash phase compares well with experiment, but only if neoclassical resistivity is used in the rise phase. (Classical resistivity has been used in most of the previous theoretical sawtooth studies.) With neoclassical resistivity, the q value at the axis drops from 1 to about 0.8 before the crash phase, and then resets to 1 through a Kadomtsev-type complete reconnection process. This Δq₀ ≅ 0.2 is much larger than Δq/sub o/ ≅ 0.01, which is obtained if classical resistivity is used. The current profile is strongly peaked at the axis with a flat region around the singular surface, and is similar to the Textor profile. To understand this behavior, approximate formulas for the time behavior of current and q values are derived. A functional dependence of sawtooth period scaling is also derived. A semi-empirical scaling is found which fits the experimental data from various tokamaks. Some evidence is presented which indicates that the fast crash time is due to enhanced effective resistivity inside the singular current sheet, generated by, e.g., microinstability and electron parallel viscosity with stochastic fields at the x-point. 16 refs., 5 figs

[en] Gyrokinetic/Magnetohydrodynamics hybrid simulations have been carried out using MH3D-K code to study the nonlinear saturation of the toroidicity-induced Alfven eigenmode driven by energetic particles in a tokamak plasma. It is shown that the wave particle trapping is the nonlinear saturation mechanism for the parameters considered. The corresponding density profile flattening of hot particles is observed. The saturation amplitude is proportional to the square of linear growth rate. In addition to TAE modes, a new n = 1, m = 0 global Alfven eigenmode is shown to be excited by the energetic particles

[en] We describe work on a full MHD code using an unstructured mesh. MH3D++ is an extension of the PPPL MH3D resistive full MHD code. MH3D++ replaces the structured mesh and finite difference / fourier discretization of MH3D with an unstructured mesh and finite element / fourier discretization. Low level routines which perform differential operations, solution of PDEs such as Poisson's equation, and graphics, are encapsulated in C++ objects to isolate the finite element operations from the higher level code. The high level code is the same, whether it is run in structured or unstructured mesh versions. This allows the unstructured mesh version to be benchmarked against the structured mesh version. As a preliminary example, disruptions in DIIID reverse shear equilibria are studied numerically with the MH3D++ code. Numerical equilibria were first produced starting with an EQDSK file containing equilibrium data of a DIII-D L-mode negative central shear discharge. Using these equilibria, the linearized equations are time advanced to get the toroidal mode number n = 1 linear growth rate and eigenmode, which is resistively unstable. The equilibrium and linear mode are used to initialize 3D nonlinear runs. An example shows poloidal slices of 3D pressure surfaces: initially, on the left, and at an intermediate time, on the right

[en] An initial value numerical solution of the time dependent nonlinear ideal magnetohydrodynamic equations demonstrates that spheromak equilibria which are linearly unstable to nonresonant helical internal perturbations saturate at low amplitude without developing singularities. These instabilities thus represent the transition from an axisymmetric to a non-axisymmetric equilibrium state, caused by a peaking of the current density

[en] The eddy current induced on the TFTR vacuum vessel during compression experiments is estimated based on a cylindrical model. It produces an error magnetic field that generates magnetic islands at the rational magnetic surfaces. The widths of these islands are calculated and found to have some effect on electron energy confinement. However, resistive MHD simulation results indicate that the island formation process can be slowed down by plasma rotation