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

Abstract

Tokamak experiments show that the plasma empirical energy confinement scaling law varies with plasma ion mass (Ai) 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 (fz) 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 Mi-0.48 -0.12, whilst that of impurity mode scales as Mi-0.46 -0.3. Here, Mi is the mass number of primary ion in the plasma. In both cases the fitting index with Mi deviates further away from -0.5 when impurity charge concentration fz increases. The isotope mass dependence of ITG turbulence gradually weakens when the effective charge number Zeff increases. The isotope mass dependence of impurity mode turbulence also weakens with Zeff increasing for the same impurity ion charge number (Z). In contrast, the isotope mass dependence gradually strengthens with effective charge number Zeff increasing for the same impurity charge concentration (fz). On average, the maximum growth rates of impurity mode scale roughly as max~Mi-0.35Zeff1.5 and max~Mi-0.4Zeff1, respectively, for Zeff 3 and Zeff 3. 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.

Tungsten impurity effects on the coupling of TEM and ITG mode in reversed magnetic shear tokamak plasmas

“…Although the physical properties of W, such as high melting point, low tritium retention, and high sputtering energy threshold, are outstanding compared with other candidates, once sputtered into the plasma region, it will threaten the steady-state operation by diluting the background particles and exciting instabilities. On the other hand, when the hydrogen isotopes are used as fusion fuel, the W impurity will enhance and weaken the isotope effect on ITG and W impurity modes, respectively [44,45]. Therefore, it is worth considering the W impurity effects.…”

Exact solution of a topological spin ring with an impurity*

“…[27] The effects of impurity scattering on the surface of topological insulators have been investigated extensively. [28][29][30] A key issue is to determine the conditions for the stability of the current-carrying states at the edge of the sample, [31,32] as this is the feature that most directly impacts prospect for future applications in electronics and spintronics. [33] Therefore, it is worthwhile to investigate the effects of impurity when the impurity locates at the twisted boundary.…”