Theoretical Review of m/n=1/1 Sawtooth Instability and Comparison with Experimental Observations in KSTAR

Abstract

One of the main problems in nuclear fusion is plasma instability. This instability causes the loss of energy in tokamak, and results in shorter confinement time. By studying plasma instability, it can be predicted in more detail, and therefore, better controlled. In this thesis, sawtooth instability at the core of the tokamak is discussed.

At the core of tokamak, the plasma density and temperature shows periodic temporal behavior. When the plasma is heated, the temperature increases linearly. As the core temperature increases and reaches a critical value, the core density and temperature rapidly drop and start to increase again. The periodic relaxation of the core plasma is observed as the sawtooth-like signals of the density and temperature.

In this thesis, two famous models by Kadomtsev and Wesson to explain the “sawtooth instability” are introduced. Kadomtsev’s model explains that the fast crash is due to the magnetic reconnection. This model is called ‘the fast reconnection model’. Due to the internal kink instability, the plasma is concentrated near q=1 surface, and pressure increases in this region. Then the magnetic reconnection takes place near q=1 surface, and the core heat and temperature collapses through this region. Wesson’s model explains the sawtooth instability assuming a flat q-profile inside the q=1 surface. Due to the flat q-profile, magnetic shear near the core is very small, and that results in the formation of ‘hot crescent, cold bubble’ inside the q=1 surface. This model is called ‘the quasi-interchange’ model. In order to explain both models theoretically, the change of potential energy, δW for a finite plasma displacement ξ, is derived to determine stability. When δW>0, the plasma equilibrium is determined to be stable whereas when δW<0, the plasma equilibrium is determined to be unstable. In m/n=1/1 internal kink mode, δW is composed of a second order term, δW_2, and a fourth order term, δW_4. Kadomtsev’s model assumes dξ/δr→0 except q=1 surface, and Wesson’s model assumes q ~ 1 inside the q=1 surface. These models have different approaches for explaining the fast disruption in the core. To validate the theoretical models, experimental observation is conducted by measuring several parameters such as temperature or density.

In tokamak, it is impossible to measure the temperature, because there is no material to measure the plasma temperature at that high temperature. To measure the temperature, an indirect method by measuring radiation intensity emitted by gyrating electrons is used in which the radiation is proportional to electron temperature. The ECEI system is a diagnostic system which can directly visualize the MHD instabilities by measuring electron temperature fluctuation. The KSTAR ECEI system measures 2-D/quasi 3-D electron temperature fluctuation which is proportional to the intensity of radiation emitted by electrons. According to Rayleigh-Jean’s law, the optical depth of the plasma is thick enough, the plasma temperature is proportional to the intensity of radiation.

Sawtooth oscillations were observed in this study using ECEI system by measuring electron temperature fluctuations in 3D. The sawtooth period was observed as τ_sawtooth ~ 10 ms and collapse time was observed as τ_c ~ 100 μs. The observed spatial structure at the core of the sawtoothing plasma resembles the m/n=1/1 internal kink mode, which concludes that the Kadomtsev’s model gives a more relevant explanation of the sawtooth instability in the experiment than Wesson’s model.