The trapped electron modes (TEMs) are numerically investigated in toroidal magnetized hydrogen, deuterium and tritium plasmas, taking into account the effects of impurity ions such as carbon, oxygen, helium, tungsten and others with positive and negative density gradients with the rigorous integral eigenmode equation. The effects of impurity ions on TEMs are investigated in detail. It is shown that impurity ions have substantially-destabilizing (stabilizing) effects on TEMs in isotope plasmas for (), opposite to the case of ion temperature gradient (ITG) driven modes. Detailed analyses of the isotope mass dependence for TEM turbulences in hydrogenic isotope plasmas with and without impurities are performed. The relations between the maximum growth rate of the TEMs with respect to the poloidal wave number and the ion mass number are given in the presence of the impurity ions. The results demonstrate that the maximum growth rates scale as in pure hydrogenic plasmas. The scale depends on the sign of its density gradient and charge number when there is a second species of (impurity) ions. When impurity ions have density profiles peaking inwardly (i.e. ), the scaling also depends on ITG parameter . The maximum growth rates scale as for the case without ITG () or the ITG parameter is positive () but the impurity ion charge number is low (). However, when and the impurity ion charge number is moderate (), the scaling law is found as . Here, Z is impurity ion charge number, and the effective mass number, , with and being the mass numbers of the hydrogenic and impurity ions, respectively, and being the charge concentration of impurity ions. In addition, with regard to the case of , the maximum growth rate scaling is . The possible relations of the results with experimental observations are discussed.
Impurity effects on quasi-linear particle transport induced by ubiquitous modes in tokamak plasmas