Finite Larmor radius magnetohydrodynamic analysis of the ballooning modes in tokamaks

In this paper, the effect of finite Larmor radius (FLR) on high n ballooning modes is studied on the basis of FLR magnetohydrodynamic (FLR-MHD) theory. A linear FLR ballooning mode equation is derived in an ‘ŝ — α’ type equilibrium of circular-flux-surfaces, which is reduced to the ideal ballooning mode equation when the FLR effect is neglected. The present model reproduces some basic features of FLR effects on ballooning mode obtained previously by kinetic ballooning mode theories. That is, the FLR introduces a real frequency into ballooning mode and has a stabilising effect on ballooning modes (e.g., in the case of high magnetic shear ŝ ≥ 0.8). In particular, some new properties of FLR effects on ballooning mode are discovered in the present research. Here it is found that in a high magnetic shear region (ŝ ≥ 0.8) the critical pressure gradient (α c,FLR ) of ballooning mode is larger than the ideal one (α c,IMHD ) and becomes larger and larger with the increase of FLR parameter b 0 . However, in a low magnetic shear region, the FLR ballooning mode is more unstable than the ideal one, and the α c,FLR is much lower than the α c,IMHD . Moreover, the present results indicate that there exist some new weaker instabilities near the second stability boundary (obtained from ideal MHD theory), which means that the second stable region becomes narrow.