Tensor transformation technique for the transport equation

A step-wise tensor transformation technique is presented for the transformation of the single energy group transport equation to an arbitrary spatial coordinate system. Both gradient and divergence forms of the equation are given and the same method is applied to the derivation of the diffusion approximation. It is demonstrated that using an orthogonal representation of the propagation vector will simplify the divergence form of the equation. The application of this technique is in the representation of the transport equation in coordinate systems other than the usual rectangular, cylindrical and spherical ones. Its use is demonstrated by transforming the transport equation to a toroidal coordinate system consisting of nested circular toroids. (auth

Transformation of the single energy group transport, equation to axissymmetric toroidal coordinates

The streaming term of the single energy group transport equation was derived for a general class of axisymmetric toroidal geometries using a tensor transformation formalism. The particular case of nested circular toroids treated previously by Pomraning and Stevens may be obtained by direct substitution into the equation. Other, more complicated geometries of interest to plasma physics and fusion reactor research are obtainable in the same manner. The cylindrical limit in which the azimuthal curvature is neglected may be obtained by taking the ratio of the poloidal curvature to X$sup 1$, the toroidal curvature, to zero. Similarly the planar limit results when both curvatures are small compared to the inverse of the physical dimension measured normal to the toroidal surface. (auth

MHD equilibrium properties of tokamak fusion reactor designs

The equilibrium properties of several Tokamak Reactor Designs are analyzed and compared for varying pressure and current profiles using the Princeton Equilibrium Code. It is found that the UWMAK configuration has a broader range of equilibria than the Princeton Reference Design configuration, but that the safety factor on axis is less than unity for peaked current distributions. The Argonne Experimental Power Reactor has a satisfactory range of equilibria, but a means of limiting or diverting the plasma has not yet been proposed, and this may substantially change the results obtained. (auth

Blister divertor for tokamaks

The results of model calculations that demonstrate the feasibility of producing the required blister region and a preliminary evaluation of the divertor collection efficiency are presented. (MOW

Transport equations in axisymmetric toroidal coordinates

A derivation is presented of the conservation law form of the single energy group transport equation in an axisymmetric toroidal coordinate system formed by rotating a nest of smooth, simply closed, plane curves of arbitrary parametric description about an axis which does not intersect the nest. This general equation may be used for generating equations specific to particular cross section geometries, or as the basis of a finite difference equation for the general case. The effect of both the toroidal and poloidal curvatures of the system are investigated, and criteria for the validity of cylindrical and planar approximations are established. The diffusion equation for this geometry is derived, and it is shown to be formally homologous to the ''r-theta'' cylindrical diffusion equation if the coordinate system is orthogonal and if the azimuthal coordinate, phi, is ignorable. (auth

Analytical solution of the toroidal constant tension solenoid

The coil shape is determined by requiring that the curvature of the flexible conductor be proportional to the distance from the toroidal axis. The resulting second order differential equation for the coil coordinates can be integrated once but for the second and final integration no closed form has been found and the integration has been done numerically. This solution of this differential equation is analytical in terms of an absolutely and uniformly convergent infinite series. The series converges quite rapidly and in practice ignoring all but the first five terms of the series introduces an error of less than 2 percent. (MOW

Vacuum vessel design for a tokamak ignition test reactor

The conceptual design of a double walled titanium vaccum vessel is presented. The following details of this semi-monocoque construction are analyzed: vessel-plasma-coils electrodynamic interaction, tritium containment, structural requirements and thermal requirements. In the electrodynamic analysis, consideration is given to the characteristic magnetic diffusion time and vessel overpressure during a major disruption. In the structural analysis, membrane stresses and poloidal and toroidal static buckling are considered. In the thermal analysis both surface boiling and liquid turbulent heat transfer are found to be adequate. The coolant quantity and distribution is determined