Tearing mode saturation with finite pressure

Abstract

With finite pressure, the saturation of the current-driven tearing mode is obtained in threedimensional nonlinear resistive magnetohydrodynamic simulations for Tokamak plasmas. To effectively focus on the tearing modes, the perturbed pressure effects are excluded while the finite equilibrium pressure effects are retained. With this model, the linear growth rates of the tearing modes are found to be very insensitive to the equilibrium pressure increase. The nonlinear aspects of the tearing modes; however, are found to be very sensitive to the pressure increase in that the saturation level of the nonlinear harmonics of the tearing modes increases monotonically with the pressure rise. The increased level is associated with enhanced tearing island sizes or increased stochastic magnetic field region.

Global resistive MHD calculations for high beta divertor plasmas in the DIII-D tokamak

“…Here, the equilibrium profiles for a specific DIII-D discharge are obtained by inverting the exact Grad-Shafranov equation using the EFIT code [3], with external magnetic measurements and the total pressure profile used as input. The linear and nonlinear results are obtained from the initial value code CART [ 1 ], which employs the Cartesian co-ordinate system in the perpendicular plane (R, Z) and the spectral representation in the toroidal direction f. The first version [ 1 ] of CART has been extended using the finite aspect ratio version [4] of the high beta tokamak reduced MHD equations:…”

“…Here, R o stands for the major radius of the computational centre, n for viscosity and 17 for resistivity. The difference between the large aspect ratio version [ 1 ] and the finite aspect ratio version [5] comes from the terms involving R o and R in Eqs (1)(2)(3)(4)(5)(6)(7). The latter version, which is used throughout this Letter, has the advantage of supporting [4] the exact Grad-Shafranov equilibrium and of generating higher poloidal harmonics and shorter poloidal wavelength near the inboard edge region, in better agreement with experimental observations.…”

“…The saturation of the pressure driven modes is very difficult to achieve in the simulations [ 1 ] because of insufficient pressure damping mechanisms such as parallel heat conduction and compression, and because of the absence of the stabilizing finite Larmor radius effects in the reduced tokamak equations. Without these stabilizing effects, the n > 1 modes are more unstable linearly for high beta equilibria than the n = 1 mode, thus introducing uncertain parameters such as the starting amplitudes of various n modes for the nonlinear run.…”

“…Limited success in pursuing this goal has been achieved by employing three-dimensional (3-D) resistive nonlinear MHD simulations. As reported in this Letter, both linear and non-linear resistive MHD phenomena for finite beta (beta is the ratio of plasma pressure to toroidal magnetic field energy) non-circular tokamak equilibria have been studied using the 3-D initial value code CART [ 1]. This code, which employs a Cartesian co-ordinate mesh, is particularly suited for treating non-circular shapes, up-down asymmetry, open field lines and a magnetic separatrix, which characterize realistic DIII-D single-null divertor discharges with high pressure or high current.…”

“…Section 2 gives a brief description of our numerical procedure. In Section 3, the non-linear magnetic fluctuations calculated with CART [ 1 ] are compared with DIII-D Mirnov measurements of the magnitudes and phases of the magnetic probes at various poloidal locations. The role of the exact shape of the vacuum vessel is examined and found to be important.…”