Trapped-Particle Effect on Drift-Wave Instability in Toroidal Systems

We analyze the effects of the radial drift of the trapped particles on the drift-wave instability in toroidal systems. These effects appear as $O\left(\sqrt{\epsilon }\right)$ corrections to the dispersion relation, $\epsilon$ being the toroidicity. Instabilities due to the drift orbit are found in the following limits: (a) $a_e\gg \frac{\omega }{k_{\parallel }}\gg a_i$, ${\epsilon }^{\frac{1}{2}}{a}_e$, (b) ${\epsilon }^{\frac{1}{2}}{a}_e$, $a_i\gg \frac{\omega }{k_{\parallel }}>{\epsilon }^{\frac{1}{2}}{a}_i$, where $a_e$ and $a_i$ are the thermal speeds of the electrons and ions, respectively.