Arun Kumar Verma

Tokamak divertor maps

A mapping method is developed to investigate the problem of determination and control of heat-deposition patterns on the plates of a tokamak divertor. The deposition pattern is largely determined by the magnetic field lines, which are mathematically equivalent to the trajectories of a single-degree-of-freedom time-dependent Hamiltonian system. Maps are natural tools to study the generic features of such systems. The general theory of maps is presented, and methods for incorporating various features of the magnetic field and particle motion in divertor tokamaks are given. Features of the magnetic field include the profile of the rotational transform, single- versus double-null divertor, reverse map, the effects of naturally occurring low M and N , and externally imposed high- M , high- N perturbations. Particle motion includes radial diffusion, pitch angle and energy scattering, and the electric sheath at the plate. The method is illustrated by calculating the stochastic broadening in a single- null divertor tokamak. Maps provide an efficient, economic and elegant method to study the problem of motion of plasma particles in the stochastic scrape-off layer.

The simple map for a single-null divertor tokamak

We present the simple map for a single-null divertor tokamak. The simple map is an area-preserving map based on the idea that magnetic field lines are a single-degree- of-freedom time-dependent Hamiltonian system, and that the basic features of such systems near the X-point are generic. We obtain the properties of this map and the resulting footprints of field lines on the divertor plate. These include the width of the stochastic layer, the edge safety factor, the area of the footprint and the amount of magnetic flux diverted. We give the safety factor profile, the average and median values of strike angles, lengths and the Liapunov exponents. We describe how the effects of magnetic perturbations can be included in the simple map. We show how the map can be applied to the problem of the determination of heat flux on the divertor plate in tokamaks.

Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface

In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.

Existence of torsional surface wave in a porous crustal layer over an initially stressed inhomogeneous half-space

In this short communication, a mathematical model for torsional wave propagation in a porous crustal layer lying over an anisotropic inhomogeneous half-space has been studied. This study reveals that the inhomogeneity in the half-space is assumed to be present in the directional rigidities and density. The anisotropy nature of the half-space is due to the presence of initial stress. Bessels functions are taken to solve the problem and the frequency equations governing the propagation of torsional waves are derived. It has been observed that there are three sets of torsional wave fronts and one shear wave front. Each set of torsional wave front has a pronounced effect on phase velocity, whereas shear wave front remains un-affected. Numerical treatment is applied to seek these effects on phase velocity of the existing waves and presented graphically. Graphical user interface has been developed using MATLAB to generalize the effect of the various parameters discussed.

Love Wave Propagation in Prestressed Piezoelectric Layered Structure

In this paper, the effect of initial stress on the propagation of Love waves in a layered structure with a thin piezoelectric film bonded perfectly to an elastic substrate has been investigated. General dispersion equations, describing the properties of Love waves in both cases, electrically open case and electrically shorted case of the piezoelectric layer, have been obtained. The effects of inhomogeneity parameters in the substrate and the initial stress in both, the layer and the substrate on the phase velocity of Love waves, are analyzed and presented graphically. The analytical method and obtained results may find applications for designing the resonators and sensors.