R. Storer

Monte-Carlo solution of Schrödinger's equation☆

Abstract A new Monte-Carlo method is presented for the calculation of the ground-state wavefunction and energy value of the many-body Schrodinger equation. Several refinements to the iterative scheme, including the use of variational wavefunctions to improve the energy estimate and a variance reducing technique, are also discussed. The method allows for a straightforward treatment of repulsive potentials. It is applied to several problems including the three-nucleon problem with simple two-body forces.

Glial cell and fibroblast cytotoxicity study on plasma-deposited diamond-like carbon coatings

Diamond-like carbon films have been evaluated as coatings to improve biocompatibility of orthopedic and cardiovascular implants. This study initiates a series of investigations that will evaluate diamond-like carbon (DLC) as a coating for improved biocompatibility in chronic neuroprosthetic implants. Studies in this report assess the cytotoxicity and cell adhesion behavior of DLC coatings exposed to glial and fibroblast cell lines in vitro. It can be concluded from these studies that DLC coatings do not adversely affect 3T3 fibroblast and T98-G glial cell function in vitro. We also successfully rendered DLC coatings non-adhesive (no significant fibroblast or glial cell adhesion) with surface immobilized dextran using methods developed for other biomaterials and applications. Future work will further develop DLC coatings on prototype microelectrode devices for chronic neural implant applications.

A new method for the numerical solution of the Schrödinger equation

Abstract A new method for the numerical solution of the diffusion-type equation Hψ = − ∂ψ / ∂β is presented for both infinite and bounded regions. When H is the Hamiltonian for a system of particles, a method closely related to the path integral technique is used to find an approximate form for the Greens function of this equation for small β. Iteration, using this Greens function as an integral operator, gives the solution for any β. Alternatively, the eigenvalues and eigenvectors of the corresponding integral equation are directly related to those of the Schrodinger equation. The technique is illustrated by its application to several one-dimensional problems including the hydrogen atom.

Stability and transport of parallel velocity shear driven mode with negative magnetic shear

The linear and quasilinear behavior of the drift-like perturbation with a parallel velocity shear is studied in a sheared slab geometry. Full analytic studies show that when the magnetic shear has the same sign as the second derivative of the parallel velocity with respect to the radial coordinate, the linear mode may become unstable and turbulent momentum transport increases. On the other hand, when the magnetic shear has opposite sign to the second derivative of the parallel velocity, the linear mode is completely stabilized and turbulent momentum transport reduces.

Suppression of Rayleigh–Taylor instability by flow curvature

The question of whether it is the shear [V(r)′] or the curvature [V(r)″] in the flow profile [V(r)] which plays the dominant role in suppressing the low-frequency (ω<ωi, where ωi is the ion gyrofrequency) instabilities and fluctuations is investigated. Rayleigh–Taylor (RT) instability is considered in this work. The role of flow curvature is found to have a robust effect on the stability and on the radial structure of the mode. For a positive value in the flow curvature RT is suppressed whereas a negative flow curvature excites the mode. Flow shear, on the other hand, plays an insignificant role in this matter. These theoretical findings are in agreement with the recent experimental results.

Numerical studies of toroidal resistive magnetohydrodynamic instabilities

A time-stepping code has been constructed to study the dominant resistive magnetohydrodynamic (MHD) instability of an axisymmetric toroidal plasma. The model used is based on the linearized, incompressible MHD equations with constant density and includes the toroidal ideal model if the resistivity is taken to be zero. The equations are solved fully implicitly using a coordinate system for which one set of coordinate surfaces coincides with a set of surfaces of constant poloidal flux. This is crucial for the accurate representation of modes for which the perturbed quantities vary rapidly near surfaces with rational values of the safety factor. The code is checked by comparison with an exactly soluble model, cylindrical resistive MHD codes and a toroidal ideal MHD code (ERATO). Results are presented showing the effect of resistivity on the unstable internal modes near nq0 = 1 for an INTOR-like numerically generated equilibrium.

The anomalous skin effect in cylindrical plasmas

A theoretical analysis of the anomalous skin effect in cylindrical plasma is carried out for a model where the radial electron-density distribution is of Gaussian form. It is shown that there are major qualitative differences between the results for cylindrical and those for plane geometry. Calculations of the electromagnetic field distribution over the plasma cross-section show that the present theory is in satisfactory agreement with experiment.

A plasma resistive diffusion model

Abstract A self-consistent study of the slow resistive evolution of an axisymmetric toroidal plasma gives rise to a set of transport equations involving one space variable which require input from the solution of a generalized differential equation obtained from the time-differentiated Grad-Shafranov equation. An iterative scheme is presented for the numerical solution of this generalized differential equation which overcomes the problems of the non-standard boundary conditions. As an illustration this method is used to compute the instantaneous diffusion velocity of a class of model toroidal equilibria. A more detailed study is presented of the time evolution of this model in the cylindrical limit in order to illustrate techniques which can be used in a more complete toroidal simulation.

Improvements on a new method for the numerical solution of the Schrödinger equation

Abstract Two procedures are described for improving the accuracy and efficiency of a method recently proposed for the numerical solution of the bound state Schrodinger equation. Firstly, an analysis of the errors in the method dictates the most efficient way for obtaining accurate results and also allows for the use of extrapolation techniques. Secondly, an expansion around the solution for a harmonic oscillator potential yields a more rapidly convergent procedure. Illustrations for a simple one-dimensional potential are given.

A computer model for resistive MHD analysis

Abstract This paper describes the formulation of a linear MHD stability code in toroidal geometry. The only assumption involved is that the perturbations are incompressible. The emphasis is to construct a code capable of calculating the effects of finite plasma resistivity. Thus, a magnetic flux coordinate system is employed since resistivity is known to be important in narrow regions in the vicinity of resonant magnetic surfaces. The code is constructed as an initial value problem, using fully implicit temporal differencing to eliminate shortest timescales. This permits “timesteps” comparable to the mode growth times of interest. Illustrative examples of both ideal and resistive instabilities are presented.