Pressure driven instabilities in the reversed-field pinch : numerical and theoretical studies

Abstract: According to classical linearized resistive magnetohydrodynamics theory, pressuredriven modes are unstable in the reversed-field pinch (RFP) due to unfavorable magnetic field line curvature. The result is based on the assumption of an adiabatic energy equation where anisotropic thermal conduction effects are ignored as compared to convection and compression. In this thesis the effects of heat conduction in the energy equation have been studied. We have examined these effects on the linear stability of pressure-driven resistive modes using boundary value theory (Δ´ ) and a novel initial-value full resistive MHD code employing the Generalized Weighted Residual Method (GWRM). In the Δ´ method, a shooting technique is employed by integrating from the resistive layer to boundaries. The GWRM method, on the other hand, is a time-spectral Galerkin method in which the fully linearized MHD equations are solved. For detailed computations, efficiency requires the temporal and spatial domains to be divided into subdomains. For this purpose, a number of challenging test cases including linearized ideal MHD equations are treated.Numerical and analytical investigations of equilibria reveal that thermal conduction effects are not stabilizing for reactor relevant values of Lundquist number, S0, and normalized pressure, βθ, for tearing-stable plasmas. These studies show that growth rate scales as  γ~_ S0−1/5 , which is weaker than for the adiabatic case, γ~_ S0−1/3.A numerical study of optimized confinement for an advanced RFP scenario including ohmic heating and heat conduction, is also part of this thesis. The fully nonlinear resistive MHD code DEBSP has been employed. We have identified, using both Δ´ and GWRM methods, that the observed crash of the high confinement is caused by resistive, pressure-driven modes.