A model for the ion-temperature-gradient-driven (ITG) instability is derived from the Braginskii magnetohydrodynamic equations of ions. The heat flow of electrons carried by the current density J|| in collision-dominant plasmas is introduced into the model. It is found that, in contrast to the finite Larmor radius effect, the current density suppresses the ITG instabilities with small wavenumber k⊥ as well as large wavenumber k||. In addition, the effects of J|| on the critical stability thresholds for the ITG mode are studied, and two critical values, ηic1 ⩽ ηic2, for the temperature gradient parameter ηi = d ln Ti/d ln n are identified. For typical tokamak parameters the stability condition ηi ⩽ ηic1 may be realized when the parameter εn = −(d ln n/dr)−1/R is large. However, the other stable regime ηi ⩾ ηic2 can only be reached when the safety factor is large enough. Similarly, there are two critical values for the safety factor, qc1 and qc2. It is shown that, under specific conditions, qc1 = qc2 so that the ITG modes are stable for any q value.
Ion-temperature-gradient modes in stellarator geometry