Magnetohydrodynamic (MHD) n=1 kink mode with n the toroidal mode number is studied and the operational beta limit, constrained by the mode, is calculated for the equilibrium of HL-2A by using the GATO code. Approximately the same beta limit is obtained for configurations with a value of the axial safety factor q0 both larger and less than 1. Without the stabilization of the conducting wall, the beta limit is found to be 0.821% corresponding to a normalized beta value of β c N =2.56 for a typical HL-2A discharge with a plasma current Ip=0.245 MA, and the scaling of β c N ∼constant is confirmed.

The tokamak with weak or negative magnetic shear and internal transport barrier (ITB) is considered to be the most promising approach to improving fusion performance. The hollow current density profile, as well as the reversed <i>q</i> profile (negative magnetic shear), is one of the key conditions for improving core confinement in advanced tokamak schemes. In the Huanliuqi 2A (HL-2A) experiment, a hollow current distribution with a discharge duration of about 100 ms is successfully achieved by injecting the pellets in the Ohmic discharge. The discharge is characteristic of circular equilibrium configuration and three frozen pellets are injected continuously at three different time moments. As a result, the hollow current profiles are formed in the plasma with weak hollow electron temperature in the core region. At the same time, the hollow currents are combined with the reversed magnetic shear profiles. Because the power of Ohmic heating is not so high and there is no external auxiliary heating, we can see only a trend of the formation of weak internal transport barrier in the stable hollow current discharge stage. However, the electron thermal diffusivity decreases significantly after the pellets have been injected. The deep injection of frozen pellets improves the energy confinement. The enhancement of plasma performance is due to the peaked electron density profile in the center, caused by pellet injection and the negative magnetic shear in the plasma center. It is concluded that the electron density profile peaked highly in the core plasma, caused by pellet injection, is beneficial to the improvement of particle confinement and plays an important role in enhancing the energy confinement. In addition, it is also demonstrated that, in general, during a hollow current discharge, the poloidal beta <inline-formula><tex-math id="M2">\begin{document}$ {\beta }_{\mathrm{p}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M2.png"/></alternatives></inline-formula> value and normalized beta <inline-formula><tex-math id="M3">\begin{document}$ {\beta }_{\mathrm{N}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M3.png"/></alternatives></inline-formula> value are both obviously low although the reversed magnetic shear is conducive to stabilizing ballooning modes and weakening the drift instabilities. However, comparing with the hollow current profile, the plasma with peaked current profile is very beneficial to the improvement of beta limit. In order to improve the <inline-formula><tex-math id="M4">\begin{document}$ {\beta }_{\mathrm{N}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="18-20210641_M4.png"/></alternatives></inline-formula> limit, a conductive wall is necessary to be placed near the plasma boundary. The results of HL-2A pellet injection experiments present a possibility of obtaining high parameter discharge on a limiter tokamak.

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.