Effect of Triangularity on Ion-Temperature-Gradient-Driven Turbulence

The linear and nonlinear properties of ion-temperature-gradient-driven (ITG) turbulence with adiabatic electrons are modeled for axisymmetric configurations for a broad range of triangularities δ, both negative and positive. Peak linear growth rates decrease with negative δ but increase and shift toward a finite radial wavenumber kx with positive δ. The growth-rate spectrum broadens as a function of kx with negative δ and significantly narrows with positive δ. The effect of triangularity on linear instability properties can be explained through its impact on magnetic polarization and curvature. Nonlinear heat flux is weakly dependent on triangularity for |δ| ≤ 0.5, decreasing significantly with extreme δ, regardless of sign. Zonal modes play an important role in nonlinear saturation in the configurations studied, and artificially suppressing zonal modes increased nonlinear heat flux by a factor of about four for negative δ, increasing with positive δ by almost a factor of 20. Proxies for zonal-flow damping and drive suggest that zonal flows are enhanced with increasing positive δ.</p

Observations of sustained phase shifted magnetic islands from externally imposed m/n = 1/1 RMP in LHD

New observations in the Large Helical Device (LHD) show that the magnetic islands externally imposed by m/n = 1/1 resonant magnetic perturbation (RMP) can be maintained in an intermediate state with a finite phase shift away from the value present in vacuum. Given the previous experimental observation that the saturated magnetic islands show either growth or healing, the intermediate states are realized in the “healing region” in the beta and collisionality space, which implies that a parameter other than beta and collisionality should exist in order to determine the island state. Theories based on the competition between electromagnetic torques and poloidal flow-induced viscous torques provide a prediction for the intermediate state. These two types of torques might be balanced to realize the steadily maintained intermediate state whereas the islands are placed in the growth state or healing state in the case in which the balance is broken. The experimental observation shows that there is a possibility for the magnetic island phase to deviate from its designed position. If the parameters are controlled properly, it is possible to control the phase of the magnetic island, which may permit continued utilization of the island divertor concept

Nonlinear tearing mode interactions and mode locking in reversed field pinches

The nonlinear interaction of a set of tearing instabilities and plasma flow is studied in a cylindrical plasma. An analytic theory of mode locking is developed which includes the effects of the localized electromagnetic torques, plasma inertia and cross-field viscosity. The calculation is specialized for the case of mode locking on the Madison Symmetric Torus (MST) reversed field pinch. In MST plasmas, a set of m = 1 tearing instabilities become phase locked and form a toroidally localized, rotating magnetic disturbance. An evolution equation for the phase velocity of this magnetic disturbance is derived which accounts for two types of electromagnetic torques. The external torques describe the interaction of the tearing modes with static magnetic perturbations located outside the plasma region. The interior torques describe the nonlinear interaction of three tearing modes which satisfy a wave number resonance condition. For conditions typical of MST, the internal torques dominate the external torques, which suggest the nonlinear interaction of tearing instabilities play a prominent role in the momentum degradation and mode locking

Ideal ballooning stability near an equilibrium magnetic island

The stability properties of ideal ballooning modes on toroidal flux surfaces near a quasistatic magnetic island is examined. On these surfaces, magnetic field-line trajectories tend to bunch on that part of the magnetic surface closet to the X-point of the magnetic island. Because of this preferential bunching, the stabilizing effect of field-line bending due to magnetic shear can be reduced. Eigenfunctions localized in helical angle near the X-point and in poloidal angle on the bad curvature side of the tokamak are more susceptible to ballooning instability than are modes in corresponding equilibria without the magnetic island. For a slowly growing island, a growing number of flux surfaces located near the separatrix become ballooning unstable. Secondary ballooning instabilities may play a part in the crash phase of sawteeth or macroscopic island dynamics

Pressure profiles, resonant Pfirsch-Schlueter currents, thermal instabilities and magnetic island formation

A prescription for constructing the plasma pressure profile in the vicinity of an equilibrium magnetic island is derived by solving a sourced pressure diffusion equation near the island region. For pressure sources and sinks that are relatively constant in space, it is found that the plasma pressure profile is insensitive to pressure sources; thus the pressure profile can be constructed by assuming that the net pressure flux across any topologically toroidal magnetic surface is constant. This construction of the pressure profile is also valid for magnetic islands that are slowly evolving in time. By coupling the pressure evolution equation with the magnetostatic equilibrium equations, the theory is applied to the case of self-consistent construction of pressure-gradient-driven magnetic islands. In particular, we address the question of resonant Pfirsch-Schlueter current induced magnetic islands and the role of thermal effects on nonlinear magnetic islands