Role of impurities in modifying isotope scaling law of ion temperature gradient turbulence driven transport in tokamak

Tokamak experiments show that the plasma empirical energy confinement scaling law varies with plasma ion mass (A(i)) in a certain range under conditions of different plasma parameters or different devices. In order to understand such a modification of the empirical energy confinement scaling law, the isotope mass dependence of ion temperature gradient (ITG, including impurity modes) turbulence driven transport in the presence of tungsten impurity ions in tokamak plasma is studied by employing the gyrokinetic theory. The effect of heavy (tungsten) impurity ions on ITG and impurity mode is revealed to modify significantly the isotope mass dependence and effective charge effect. As the charge number of impurity ions (Z) or impurity charge concentration (f(z)) changes, the theoretical scaling law of ITG turbulence transport varies substantially in a relatively large range. The maximum growth rate of ITG mode scales as M-i(-0.48 -> -0.12), whilst that of impurity mode scales as M-i(-0.46 -> -0.3).Here M-i is the mass number of primary ion in the plasma. In both cases the fitting index with M-i deviates further away from -0.5 when impurity charge concentration f(z) increases. The isotope mass dependence of ITG turbulence gradually weakens when the effective charge number Z(eff) increases. The isotope mass dependence of impurity mode turbulence also weakens with Z(eff) increasing for the same impurity ion charge number (Z). In contrast, the isotope mass dependence gradually strengthens with effective charge number Z(eff) increasing for the same impurity charge concentration (f(z)). On average, the maximum growth rates of impurity mode scale roughly as gamma(max)similar to M(i)(-0.35)Z(eff)(and)(1.5 ) gamma(max)similar to M(1)(-0.4)Z(eff)(1 )respectively, for Z(eff) <= 3 and Z(eff) >= 33. The reason for the deviation of isotope scaling law from the normal case is investigated deliberately, and it is demonstrated that the isotope scaling index deviates from -0.5 more or less due to the fact that the impurity species, charge number and impurity concentrations vary in a certain range. These results demonstrate that it is impossible to deduce a unique isotope scaling law due to the variety of micro- instabilities and various plasma parameter regimes in tokamak plasma, which is consistent with the experimental observations. These results may contribute to the transport study involving heavy (tungsten) impurity ions in ITER discharge scenario investigation.