M. Wakatani

T. Unemura

National Institute for Fusion Science (NIFS-Repository)

§20. Role of Flow Shear and Magnetic Shear for Interchange Instabilities and Improved Confi nement Wakatani, M., Unemura, T. (Grad. School of Energy Sci., Kyoto Univ.) Even for the well-known MHD instability such as the interchange mode, there appears an in-teresting situation when both the flow shear and magnetic shear are included simultaneously in the stability analysis. Several years ago a sufficient stability criterion for the ideal interchange mode was derived for a cylindrical plasma with a mag-netic shear in the presence of a poloidal shear flow [1]. The radially localized mode in the neighbor-hood of the mode resonant surface r = ro is de-scribed by where keo = mjro: P~ = dPo j drlr=ro, Of dOjdrlr=ro: x = r - ro, kll = kllx, W - WE -wklr=rox and kll = mzflr=ro' Here z(r) is a pro-file of rotational transform and 0 is a potential function of average magnetic curvature in stel-larator j heliotron devices. The poloidal rota-tion frequency is given by WE = kevEjvpA = (mjr)(d<Pojdr) , where <Po is an equilibrium elec-tric potential function. Here VE(VpA) is an E x B drift (a poloidal Alfven) velocity. By assuming ¢ ex: XV for the solution of eq.(l), the necessary stability condition becomes, which corresponds to a non-oscillatory solution. From the stability criterion (2), the well-known Suydam criterion is obtained in the case of wk = 0 or by neglecting the poloidal shear flow. The stability criterion suggests several points for the interaction between the magnetic shear shown by kll and the poloidal velocity shear shown by wk. 1) When the magnetic shear is zero or very weak, (3) which means that the interchange mode is stable for Of > 0 (magnetic hill) since P~ < O. This is different from the speculation for the case of wk = o. 2) When Of < 0 (magnetic well), the inter-change mode becomes unstable particularly in the case of weak poloidal velocity shear. This is also different from the speculation for the case of wk = o. 3) It is also well-known that the Kelvin-Helmholtz mode is destabilized by the veloc-ity shear, and the magnetic shear has a stabi-lizing effect on the K-H mode. Thus, for the weak magnetic shear, it will be difficult to ob-tain the large velocity shear and the stability against the interchange mode becomes worse in the case of magnetic well. 4) For the finite magnetic shear case, the stabil-ity limit decreases compared to the Suydam limit given by the relation (3) in the case of Iklll > lWEI. The destabilizing mechanism is the same as for the K-H mode, and magnetic well has a stabilizing effect on the interchange mode. However, when Iklll < Iwkl, the mag-netic hill becomes favorable. Reference 1) \Vatanabe, K., Sugama, H. and \Vakatani, M., Nucl. Fusion 32 (1992) 1647 207 

Role of Flow Shear and Magnetic Shear for Interchange Instabilities and Improved Confinement

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