NUMERICAL STUDIES ON THE SUSTAINMENT OF THE AXIAL MAGNETIC FIELD IN A REVERSED FIELD PINCH USING A SQUARE CROSS SECTION
Abstract
A computational study of the three dimensional non-linear resistive magnetohydrodynamic equations for a straight cylinder is presented. The studies are applied to self-production of the an axial magnetic field, the so called the alpha effect in the Reversed Field Pinch. The resistive MHD equations are solved by potentials that allow the poloidal and toroidal symmetry of the magnetic and velocity fields to be exploted. The MHD steady state is allowed to change on a resistive time scale and solved numerically. This state is independent on z and allows the introduction of a flux function as independent variable. The resistive MHD equations are Fourier analyzed along the ignorable coordinate of the equilibrium. Two different codes are developed. The first code is for an incompressible plasma with a specific mode number along the z axis as an approximation. Finite difference methods are employed on the x and y variables. For the incompressible case, the calculation is carried out for two spatial variations of the resistivity. The first spatial variation of the resistivity is uniform, while the second case is characterized by a sharp increase towards the wall. The second code is for three dimensional compressible MHD of constant resistivity. The pseudospectral method is used for the x,y and z coordinates. Diffusion terms are used for both codes. A time centered implicit method is developed for the temporal advancement of the resistive MHD equations. The simulation of the incompressible case of variable resistivity shows the production of the alpha effect, while the constant resistivity case shows the absence of the alpha effect. The simulation of the three dimensional case shows the production of the axial field. The comparison of the cartesian approximation with the previous cylindrical approximation shows that the ratio of the axial current density to the axial magnetic field is 3.145 which gives the Taylor state a slight reversal in the cylindrical configuration, gives a very large reversal in the cartesian configuration.
Degree
Ph.D.
Subject Area
Fluid dynamics|Gases
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