Impurity transport driven by kinetic ballooning mode in the strong gradient pedestal of tokamak plasmas - Shanni Huang; Weixin Guo; Lu Wang (Nuclear Fusion)
The impurity transport driven by kinetic ballooning mode (KBM) is theoretically studied in the DIII-D H-mode strong gradient pedestal plasmas. From the electromagnetic gyrokinetic equation, including the correction of the strong radial electric field, the dispersion relationship of KBM instability with non-trace impurity is firstly derived. Then, the turbulent impurity flux and ion heat flux, as well as the associated transport coefficients, are further calculated. Through the parametric dependence analysis of analytical results, it is found that dilution effects of light fully ionized impurities can reduce the drive of KBM by affecting the kinetic pressure gradient parameter $α $ and diamagnetic effects, thus leading to a decrease in both the absolute value of the real frequency $\left| {ω_\text{r}^{′}}\right|$ and the growth rate $γ_{\text{k}}^{′}$ of KBM instability. Stronger dilution effects by increasing the impurity charge number $Z$ or steepening the impurity density profile correspond to stronger effects. Moreover, the removal efficiency of light fully ionized impurities, quantified by the ratio between the impurity diffusivity and effective ion heat conductivity $\frac{{{D_{\text{z}}}}}{{χ _{\text{i}}^{{\text{eff}}}}}≈ \frac{{1 - {b_{\text{z}}}+ {{4{ω _{{\text{Dz}}}}}\mathord{\left/ {\vphantom {{4{ω _{{\text{Dz}}}}}{ω_\text{r}^{′}}}}\right. }{{{ω_\text{r}^{′}}}}}}}{{{{3\left({1+{1\mathord{\left/ {\vphantom {1 {{η _{\text{i}}}}}}\right. }{{η _{\text{i}}}}}}\right)}\mathord{\left/ {\vphantom {{3\left( {1 + {1 \mathord{\left/ {\vphantom {1 {{η _{\text{i}}}}}}\right. }{{η _{\text{i}}}}}}\right)}2}}\right. }2}}}$ , increases with an increase of $Z$ mainly due to the smaller impurity finite Larmor radius (FLR) effects reflected by ${b_{\text{z}}}\propto {1 \mathord{\left/ {\vphantom {1 Z}}\right. }Z}$ . Besides, the increase of the impurity density gradient can significantly enhance ${{{D_{\text{z}}}}\mathord{\left/ {\vphantom {{{D_{\text{z}}}}{χ _{\text{i}}^{{\text{eff}}}}}}\right. }{χ _{\text{i}}^{{\text{eff}}}}}$ , and this is because stronger impurity dilution effects make a larger magnetic drift term ${{\left| {{ω _{{\text{Dz}}}}}\right|}\mathord{\left/ {\vphantom {{\left| {{ω _{{\text{Dz}}}}}\right|}{\left| {ω_\text{r}^{′}}\right|}}}\right. }{\left|{ω_\text{r}^{′}}\right|}}$ ( ${ω _{{\text{Dz}}}}$ is the magnitude of impurity magnetic drift frequency) and ${η _{\text{i}}}$ (the ratio of ion density gradient scale length to ion temperature gradient scale length). For heavy metal impurities with a concentration of ${10^{ - 4}}$ , the peaking factor (PF) is positive, which means that its density profile is inwardly peaked, and the PF decreases with the enhancement of impurity FLR effects. These results may provide some theoretical reference on understanding the physical mechanism of impurity transport in the pedestal of H-mode plasmas.