The effect of shaping on trapped electron mode stability: an analytical model

A reduced model for trapped electron mode stability has been developed, which incorporates the basic effects of magnetic surface shaping, in particular, elongation and triangularity. This model shows that while elongation is stabilising, though weakly, negative triangularity usually leads to a more unstable plasma. This is in marked contrast with the experimental evidence of a better confinement at negative triangularity, and with recent gyrokinetic linear simulations. This paradox is solved when finite orbit and/or finite mode extent along field lines (mode ballooning) effects are included. These effects give more weight to particles trapped at low bounce angles, which are those that exhibit lower precession frequencies at negative—compared to positive—triangularity. As a result, the interchange growth rate becomes lower at negative triangularity and large temperature gradients, so that negative triangularity appears to have an overall stabilising effect. Mode ballooning appears to play the most important role in this reversal of stability.