The performance of spherical tokamak reactors depends on plasma β, and an upper limit is set by long-wavelength kinetic ballooning modes (KBMs). We examine how these modes become unstable in spherical-tokamak reactor relevant plasmas, which may contain significant fast-ion pressure. In a series of numerically generated equilibria of increasing β, the KBM becomes unstable at sufficiently high plasma β, and for such cases, it is also significantly unstable even in the long-wavelength limit. The β threshold for the KBMs is similar to the ideal Magnetohydrodynamics (MHD) threshold, and in cases without fast ions, their frequencies are as predicted by diamagnetic-drift stabilised MHD. To isolate and explore the KBMs, simulations are performed where the pressure gradient is entirely due to the density profile, or entirely due to the temperature profile; the resulting KBMs have similar properties in the long-wavelength regime. The introduction of energetic ions restricts the KBMs to longer wavelengths, and reduces the β threshold somewhat; for parameter regimes of current-day devices, this is such long wavelength that a global analysis would become necessary. Mode frequencies in plasmas with a significant fast particle population are seen to be controlled by fast particle precession frequencies.

球形托卡马克反应器的性能取决于等离子体β，上限由长波长动力学气球模 (KBM) 设定。我们研究了这些模式如何在球形托卡马克反应堆相关等离子体中变得不稳定，这些等离子体可能包含显着的快离子压力。在一系列增加β的数值生成的平衡中，KBM 在足够高的等离子体β下变得不稳定，对于这种情况，即使在长波长极限下也非常不稳定。该βKBM 的阈值类似于理想的磁流体动力学 (MHD) 阈值，并且在没有快离子的情况下，它们的频率与抗磁漂移稳定的 MHD 预测的一样。为了隔离和探索 KBM，在压力梯度完全由密度分布或完全由温度分布引起的情况下进行了模拟；由此产生的 KBM 在长波长范围内具有相似的特性。高能离子的引入将 KBM 限制在更长的波长上，并在一定程度上降低了β阈值；对于当今设备的参数制度，这是如此长的波长，以至于需要进行全局分析。具有显着快速粒子群的等离子体中的模式频率被认为是由快速粒子进动频率控制的。