Numerical study of ubiquitous modes in tokamak plasmas in the presence of impurities

Abstract

Abstract As an important branch of trapped electron modes (TEMs), the ubiquitous mode (UM) is a favored subject for the investigation of anomalous energy losses in magnetic fusion plasmas. In this paper, the numerical study of UMs was carried out in tokamak plasmas in the presence of impurities. The physical model and the gyrokinetic equations for TEM (and UM) instability is introduced, including the impurity effect. The numerical results show that impurity species impose significant impacts on the UM instability in many ways, one of which is that impurity effect on UMs is generally stabilizing, and on the whole the stabilizing effect is most pronounced for the case of −0.8 ≲ L ez < 0 ( L ez ≡ L n e / L n z , with L n s = − ∂ ln n s / ∂ r − 1 ). As the impurity charge concentration f z increases, or for the heavier or lower-ionized impurity ions, the UM instability is weaker. Compared to the ion and electron temperature gradient effects, impurity temperature gradient (expressed by η z = L nz / L Tz ) has only a minor effect, while the ratio of electron to impurity temperature τ z has a relatively larger effect on UMs, embodied in the mode linear growth rates and instability windows. The investigation of wavenumber threshold for UM showed that the mode was a fluid-like instability when b i ≡ 1 2 k θ 2 ρ s 2 ∼ n / n e T 3 , and the presence of impurity resulted in the modification of the UM instability window. By surveying the parametric dependences of UMs in the presence of impurities, it is revealed that comparatively, the stabilizing effects of impurity is more pronounced in the regime of larger wavenumber, while the weakening effects of (i) decreasing the fraction of trapped electrons, (ii) increasing the magnetic shear, or (iii) decreasing the electron density gradient on UM instability are relatively more pronounced in the regime of smaller wavenumber. It also indicates that the stabilizing effect of impurity on UMs is owing to the non-resonant mechanism of the UM.