Study of microinstabilities in toroidal plasmas with negative magnetic shear

Abstract

The micreinstabilities driven by a pardel velocity shear, and a temperature gradient of ions are studied in toroidal plasmas with negative magnetic shear. Both the fluid and the gyrekinetic formulations are investigated. It is found that for a broad range of parameters, the linear growth rates of the modes are lower, and the threshold temperature gradient q k is higher €or plasmas with negative magnetic shear compared to plasmas with p'ositive magnetic shear of equal magnitude. The reduction in the growth rate (with negative shear), although not insigdicant , does not seem to be enough to account for the dramatic improvement in the confinement observed experimentally. Other possible physical mechanisms for the improved confinement are discussed.

Smoothness of turbulent transport across a minimum-q surface

“…There are numerous papers which discuss the linear theory of weak-shear ITG modes, 1,15,[17][18][19] but none that we are aware of analyze the s→0 limit of the toroidal ITG. In fact, for sϭ0, the toroidal ITG has a finite growth rate, and the corresponding eigenfunction is a complex Mathieu function.…”

“…Following the notation of Ref. 18, we write the eigenvalue equation as b͑ ͒ϭ ͩ qk ⑀ n ͪ 2 2⑀ n , ͑B3͒…”

Damping of toroidal ion temperature gradient modes

“…Comparing the growth rates at the same absolute value ͉ŝ͉, the negative shear ŝ Ͻ0 gives smaller growth rates than the positive shear ŝ Ͼ0 within the range ͉ŝ͉Ͻ1.7, which is the same tendency as found in other works. 18,19 However, the critical values of ŝ , which give ␥ϭ0, have almost the same absolute value ͉ŝ͉ϳ1.7. We should note that validity of the ballooning representation is lost in the limit ŝ˜0 although the growth rate and real frequency for ŝ ϭ0 is plotted in Fig.…”

“…The effects of negative magnetic shear on ITG modes have been theoretically investigated by several authors 18,19 relation to improvement of core plasma confinement observed in large tokamaks. [20][21][22] However, the results in these works only showed the dependence of positive growth rates on the magnetic shear.…”

Drift waves and transport

“…The growth rate is a maximum at sϭ 1 2 as can be understood from the small expansion of D i ( ,s). Dong et al (1996) re-investigate the somewhat subtle issue of the conditions for the existence of two distinct unstable drift modes: the eta-i (ITG) and the trapped electron (TE) mode. This is the standard case assumed for example in the Weiland transport model implemented in the Bateman-Kinsey transport codes (Kinsey et al, 1996).…”