MHD Stability

Abstract

Ideal, resistive and kinetic MHD instabilities are described. Since the birth of steady state tokamak research in 1990, there are number of important understandings of MHD modes related to steady state tokamak. In Sect. 8.1, we introduce the spectral property of MHD operator such as continuous spectrum and spectral gap, in brief. Marginal stability is discussed using the Newcomb equation in Sect. 8.2. Section 8.3 deals with flow effect on ideal MHD based on the Frieman-Rotenberg equation briefly. Localized MHD instabilities such as ELM, peeling/ballooning modes, infernal and barrier localized modes are discussed in Sect. 8.4. In Sect. 8.5, we introduce progress of resistive MHD such as the classical tearing mode (TM), the neoclassical tearing mode (NTM), the double tearing mode (DTM). Kinetic MHD equation is introduced in Sect. 8.6. In Sect. 8.7, Alfven eigenmode (AE) is introduced extensively. An important resistive/kinetic instability called the resistive wall mode (RWM) is introduced in Sect. 8.8. Control of ideal, resistive and kinetic MHD is essential element of fusion research. For three types of advanced tokamak operation (WS, NS, CH) to realize efficient steady state operation, ideal MHD modes such as peeling/ballooning modes for edge plasma, infernal modes for core plasma and BLM for ITB, resistive MHD modes such as NTM, DTM, RWM, kinetic MHD modes such as TAE, RSAE are understood well including control knob, while some kinetic MHD are still in progress in understanding. Key issue is that plasma profile does not match optimum profile for high beta advanced tokamak operation since profile is determined by the turbulent transport. Hence, combined understanding of MHD and turbulent transport is essential to optimize operation scenario for steady state tokamak operation.