Dissipative trapped electron modes in l=2 torsatrons

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Abstract
Trapped electron modes could play an important role in enhancing losses in a toroidal confinement device. However, no direct evidence of these instabilities has been found in such devices. The dissipative trapped electron modes [Sov. Phys. Dokl. 14, 470 (1969)] in l=2 torsatrons using the high‐n ballooning formalism and considering the full three‐dimensional geometry are studied. Using a perturbative analysis, it is found that there are toroidally localized as well as helically localized eigenfunctions in the ballooning space for these nonaxisymmetric devices. The helically localized eigenfunctions give the largest growth rates. It is shown that the helical symmetric limit gives a very good description of the helically induced modes for stellarators such as the Advanced Toroidal Facility [Fusion Technol. 10, 179 (1986)]. In this limit, the criteria for the density gradient and the temperature gradient for the existence of the dissipative trapped electron modes in l=2 stellarators are found. Also, it is found that the radial width of the unstable modes can be very broad, and therefore their effects could possibly be detected in future experimental studies with density control.