Effects of parallel ion motion on zonal flow generation in ion-temperature-gradient mode turbulence

The role of parallel ion motion for zonal flow generation in ion-temperature-gradient (ITG) mode turbulence is investigated with focus on the effects of acoustic modes and toroidicity on the zonal flow. One possible reason for the weak suppression of ITG turbulence by zonal flows found in experiments in the Columbia Linear Machine (CLM) [Phys. Plasmas {\bf 13} 055905 (2006)] might be due to the small toroidicity ($\epsilon_n = 2L_n/R$) in the experiment. The zonal flow is often directly dependent on the ITG mode and the coupling of zonal flow to acoustic modes and hence is directly affected by any change of the relevant parameters. The model consists of the continuity, temperature and parallel ion momentum equations for the ITG turbulence. The zonal flow time evolution is described by a Hasegawa-Mima like equation and a fifth order zonal flow dispersion relation is derived. The results are interpreted in terms of quality of zonal flows, i.e., the ratio of growth rate and real frequency ($Q = \Omega^{IM}/\Omega^{RE}$). It is found that the quality of the zonal flow rapidly decreases with decreasing toroidicity.