Extended instability of kinetic ballooning modes induced by ion temperature gradient and impurity in tokamaks

Abstract

Kinetic ballooning mode (KBM) instability in tokamak plasmas is studied with gyrokinetic theory. It is extended and improved of the theory of higher order kinetic ballooning mode which is not subject to second stabilization [Hirose A, et al. 1994 Phys. Rev. Lett. 72 3993]. It is verified that increasing ion temperature gradient ($\eta_i$) significantly enhances the instability of KBMs, and causes extended instability in the second MHD stable regime. Especially when $\eta_i\gtrsim 1$, the mode is unstable almost in the whole $\beta$ space from an experimental point of view, here $\beta$ is the ratio of kinetic pressure to magnetic pressure. It is found that for the case with relatively low safety factor ($1\lesssim q \lesssim 2$) and $\eta_i\approx 0$, which is generally in central regions of a tokamak plasma, the KBM instability can also be extended to the region of $\beta$ or $\alpha$ far beyond the second MHD stability boundary due only to impurity effect, here $\alpha=-Rq^2 (d\beta/dr)$. It has characteristics similar to the extended instability induced by $\eta_i$, while its instability window is narrower than the latter. From the observations, the unstable window of extended instability is finite. As the safety factor $q$ and magnetic shear $\hat {s}$ ($\equiv rdq/qdr$) increases, the “theoretical” critical $\beta$ of the second stable regime decreases and the $\alpha$ threshold increases. When the impurity effect is combined with the $\eta_i$ effect, the unstable window of the extended instability induced by $\eta_i$ can be greatly reduced by the former. In some cases, for instance as $\eta_i\gtrsim 1$ and $q$ is larger, and in the presence of impurity with mediate mass number, the impurity effect can even make the second stable regime of “experimental significance” re-appear in KBMs. The influence of $\eta_i$ and impurity effects on broadening mode structure of KBMs are smaller than $q$ and $\hat {s}$. The stability boundary based on $\hat {s}-\alpha$ plane conforms the above results.

Gyrokinetic Simulation of Kinetic Ballooning Mode and its Parametric Stabilization in Tokamak Plasmas With Impurities

“…It is demonstrated that with the increase of magnetic shear ŝ, the critical α for the ideal MHD stable regimes increase. Moreover, when the q value is changed from 2 (the black solid line) to 4 (the green solid line), or when the ŝ value is changed from 1 (the green solid line) to 2 (the blue dasheddotted line) and the other parameters remain unchanged, there is no occurrence of extended instability [25] in both β e and α spaces, but only from one MHD-like ballooning mode to another similar one. That is, from Fig.…”

“…2(b) and (d). In a word, the occurrence of extended instability mainly depends on ion inverse Lamdau damping (when η i ≳ 1 is active) or other causes (e.g., impurity effect (also see [25]).…”

“…The extended instability [25], which refers to the KBM instability in the second stable regime of ideal MHD ballooning mode, is shown to be a plausible candidate for the low-k broadband fluctuation recently observed in the wide-pedestal quiescent-H (QH) mode of DIII-D [26]. The study [25] shows that this extended instability is caused by two parametric effects, say, the effects of ITG (η i ) and impurity. In fact, the multiple parametric effects on KBM in tokamaks are an enduring topic, which is often closely related to the destabilization and stabilization of ballooning mode instability.…”

Ideal conductive wall and magnetohydrodynamic instability in Tokamak

“…为了实现聚变点火目标，建成一个经济、小巧的的受控聚变反应堆，第一步 工作需要实现高𝛽托卡马克稳态运行 [1][2][3][4] 。 这里， 定义 𝛽 = 不稳定性作用，托卡马克所能达到的最大  值是受限的。因此，研究 MHD 不稳定 性成为一个重要课题 [5,6] 。内、外扭曲模是托卡马克中最危险的理想磁流体不稳 定扰动，与先进托卡马克运行的关系非常密切 [7][8][9][10] 。因为与气球模 [11,12] 、撕裂模 [13] 等比较起来，扭曲模对等离子体运行  极限施加了更加严格的限制 [14] 。 一般用归一化等离子体电流来对最大稳定𝛽进行定标，称为 Troyon 定标 [15,16] ，…”

Gyrokinetic simulation of electromagnetic instabilities in the high β p scenario on EAST

“…It is well known that the electrostatic ion temperature gradient (ITG) mode is stabilized by the electromagnetic effects [9,10]. The growth rate of TEM remains unchanged with increasing β e while the electromagnetic kinetic ballooning mode (KBM) becomes unstable when β e exceeds a critical, the growth rate of KBM keeps increasing until β e reaches the second stability region [11,12]. Previous research on KBM mainly focus on those situations with T i ⩾ T e .…”