| We study various aspects of the linear and 2D (helically symmetric) nonlinear development of m = 1 resistive instabilities in the cylindrical spheromak. The cylindrical spheromak is a fictitious configuration in which the toroidal spheromak has been cut and straightened out to become a circular cylinder of radius a, length 2(pi)R, and with periodic boundary conditions. It has proven to be a usefull model for studying spheromak instabilities in which toroidal effects are not important.;Our studies of the resistive interchange mode reveal that mode saturation can occur due to the quasilinear flattening of the pressure profile in the vicinity of the mode rational surface. However, this saturation process is defeated when the plasma overheats and in regions of the plasma where the shear is low. Also, we found that fluid compression plays a significant, and optomistic role in the long term nonlinear development of this mode. Finally, in a tearing mode stable cylindrical spheromak configuration with an axial beta value of 6%, complete overlap of the m = 1 islands occurs in about 3% of the resistive skin time for a magnetic Reynold's number of S = 10('5). For typical parameters of the S-1 device at Princeton, this time corresponds to nearly one millisecond.;We show that incorporation of the Hall terms into the resistive MHD model can stabilize the m = 1 resistive interchange mode provided ((omega)(,ci)t(,H))('-1)(TURN)15%. Here, (omega)(,ci) is the ion cyclotron frequency and t(,H) is the hydromagnetic time. The details of these and the above nonlinear results are presented.;In order to make feasible the calculation of accurate numerical solutions to the linear and nonlinear equations we present a formulation of the fully compressible, helically symmetric, resistive MHD equations which has the advantage of partially separating the ideal MHD characteristics. This formulation is based on Jardin's ideal MHD time scale splitting methods and on Park's formulation of the incompressible, helically symmetric equations.;The majority of interest in this area lies in attempting to understand the effect that the resistive interchange instability has on confinement in the spheromak, the reason being that finite pressure spheromak configurations are always unstable to this mode. Therefore, most of the results presented in this thesis pertain to the nonlinear development of the resistive interchange mode. Our goal is to understand the quasilinear modifications of the equilibrium profile due to the growth of this instability, and the subsequent effect that the equilibrium modification has on the growth rate and eigenfunctions. |
