Sawteeth In Tokamaks Research Articles

Supersaturation and nonlinear crash of tokamak sawtooth oscillations.

A full-torus, compressible, resistive MHD simulation reveals that in the slow ramp phase of tokamak sawtooth oscillations an ideal kink mode slowly emerges at the magnetic axis as a result of current peaking and gradually expands radially outwards, forming a crescent-shaped poloidal magnetic structure that allows the central /ital q/ value to go substantially below 1. Its converging return flows drive nonlinear reconnection to make two magnetic islands. The kink mode turns into a resistive convection type with a slow but larger growth rate. As the flow grows substantially, a large-scale rigid flow arises and suddenly crashes the plasma structure, forming a crescent-shaped pressure distribution.

Numerical simulations of sawteeth in tokamaks

Numerical simulations of sawteeth in tokamaks have been carried out using reduced magnetohydrodynamics and a simple transport model. The electron temperature is evolved self-consistently, including Ohmic heating and a highly anisotropic thermal diffusivity. The sawtooth period and collapse time found in the simulations for Lundquist numbers S below 107 compare favourably with experimental results from small and medium size ohmically heated tokamaks. The sawtoothing is found to be sensitive to the values of the transport coefficients. In particular, the perpendicular viscosity must be comparable to, or larger than, the perpendicular thermal diffusivity for distinct relaxation oscillations to occur. To study the scaling with S, the viscosity and perpendicular thermal conductivity have been scaled as 1/S, and S has been varied. Modifications of the equilibrium, caused by the sawteeth, play an important role in the scaling of the collapse time and period with the Lundquist numnber. The self-consistently computed q-profiles are very flat in the central region where q ≈ 1. Outside the low-shear region, the shear rises sharply. This q-profile allows a resistive mode to be turned on quickly with a high growth rate. The deviation of the central q from unity over the sawtooth cycle decreases with increasing S, and the collapse time shows a weaker dependence than the S½ scaling of Sweet and Parker.

Toroidal studies of sawtooth oscillations in tokamaks

Tokamak sawtooth oscillations are studied with a nonreduced, fully toroidal, resistive magnetohydrodynamic (MHD) model that includes Ohmic heating, and parallel and perpendicular thermal conductions. Effects of perpendicular transport in producing different types of sawteeth, varying from simple, periodic oscillations to giant sawteeth with temperature modulations of order unity, and compound sawteeth with multiple relaxations, are demonstrated. Some of the recent experimental observations from large tokamaks, such as the fast crash times and a presumed topological anomaly in the x-ray tomography pictures, thought to be inconsistent with the Kadomtsev reconnection model, are examined and possible explanations are offered.

Global and local relaxations in magnetohydrodynamic plasmas

Based on theoretical and computational considerations, it is confirmed that magnetic reconnection driven nonlinearly by a kink instability plays a key role in the magnetohydrodynamic relaxation. An important finding is that the relaxation takes the form of either global relaxation (e.g., the reversed field pinch relaxation) or local relaxation (e.g., the tokamak sawtooth relaxation), depending on whether the driven reconnection is total (antiparallel) or partial (partially antiparallel).

The fast crash of the central temperature during sawteeth in tokamaks

A simple model of the crash phase of sawteeth in tokamaks is presented, which explains many of the significant experimental observations: small oscillations in the electron temperature prior to the crash (precursor), a short crash time, and large long-lived oscillations in the electron temperature following the crash (successor). In tokamak discharges with good central confinement the temperature profile across the center of the discharge remains rather flat. In such profiles skin currents form that cause the safety factor q to fall below one at a finite radius rs while q(r=0)≂1. The sawtooth crash is caused by the m=n=1 tearing mode growing on such a profile. For a profile in which q falls below one by an amount Δq, the crash time is given by the helical Alfvén time τA/Δq, independent of the resisitivity. The size of the magnetic island of the precursor can be a small fraction of rs. In contrast, a remnant magnetic island of the order of rs survives the crash and causes the successor oscillation. Estimates of the decay time of the successor are given.

The m=1 convection cell and sawteeth in tokamaks

Resistive magnetohydrodynamic (MHD) simulations of sawtooth activity in tokamaks are presented. An m=1 convection cell driven by the resistivity gradient forms in the center of the column and causes the sawteeth to die away. The nonlinear properties of this convection cell are calculated analytically. Periodic sawteeth are obtained when the parallel thermal conduction is sufficiently large.

Skin currents and compound sawteeth in tokamaks.

Two-dimensional MHD simulations are carried out which demonstrate that the cross-field thermal conduction near the magnetic axis controls the structure of sawteeth in tokamaks. In simulations of discharges with good central confinement, skin currents form at a finite radius causing the safety factor $q$ to fall below 1 away from the magnetic axis. Both normal and compound sawteeth are produced which have many features consistent with experimental observations.