The linear behaviors of the double tearing mode (DTM) mediated by parallel electron viscosity in cylindrical plasmas with reversed magnetic shear and thus two resonant rational flux surfaces is numerically investigated. The distance between the two surfaces is found to play an important role for modes with poloidal mode number m>1. Two modes, one of which is centered at the inner rational surface and the other is located between the two surfaces, are simultaneously unstable and the growth rates show the standard single tearing mode (STM) scaling as γ∝R−1/3 when the distance is large (here, the Reynolds number R≡τυ/τh, τυ, and τh are, respectively, the viscosity penetration time of the magnetic field and the Alfvén time for a plasma sheet of width a). The latter is unstable only and the growth rate transits to the standard DTM scaling as γ∝R−1/5 for low-m (e.g., m<4) modes and keeps the STM scaling γ∝R−1/3 for high-m (e.g., m∼10) modes, which are found dominant, when the distance is decreased. In contrast, two unstable modes extending from plasma center to the two rational surfaces, respectively, coexist and the growth rates always show the scaling of γ∝R−1/5, independent of the distance, when the poloidal mode number m=1. The DTMs mediated by electron viscosity are enhanced by plasma resistivity of the range where the growth rate of the mode induced by the latter alone is comparable with that mediated by the former alone and vice versa. Otherwise, the growth rate of the mode is equal to the higher of the modes mediated by resistivity or electron viscosity alone when both of them are taken into account.
Impurity effects on trapped electron modes (TEMs) in tokamak plasmas with inverted electron density profile (IEDP) are numerically investigated with a gyrokinetic integral eigenmode equation. It is found that different from the negative gradient of normal electron density profile, the positive gradient of the IEDP has a stabilizing effect on TEM in the presence of impurity ions. The electron temperature gradient threshold for TEM excitation increases not only with the increasing absolute value of IEDP but also with increasing impurity content. Furthermore, the effects of different impurity species and different impurity peaking profiles on TEMs with the IEDP are analyzed in detail. It is shown that there is a transition point of impurity density profile, on both sides of which the impurity has opposite effects on TEM. The dependence of such a transition point on electron temperature and density gradients is obtained numerically. Besides, the synergistic effects of ion temperature gradient and impurity density gradient are studied, in which a similar transition point of the ion temperature gradient is also identified in the case of outwardly peaked impurity density profile. In addition, impurity effects on the characteristics of mode structure and on the radial transport coefficients in positive and negative magnetic shear regions are discussed as well based on quasi-linear mixing length estimation.
Plasma Position Reflectometry (PPR) is planned to provide plasma position and shape information for plasma operation in future fusion reactors. Its primary function is to calibrate the drift of the magnetic signals due to the integral nature of magnetic measurement. Here, we attempt to measure plasma position using ordinary mode (O-mode) and extraordinary mode (X-mode) reflectometry systems on two tokamaks. A new physical model based on the phase shift is proposed to deduce the relative movement of the cut-off layer without density inversion. We demonstrate the plasma position measurements by absolute measurement from density profile inversion and relative measurement from phase shift. The combination of X-mode and O-mode reflectometers can minimize the limitations of single polarization reflectometry and further increase the accuracy of plasma position measurement. These results could provide an important technical basis for the further development of a real-time control system based on PPR.
To measure plasma density and magnetic fluctuations on the HL-2M tokamak simultaneously, a new diagnostic system combining Doppler backscattering (DBS) and cross-polarization scattering (CPS) is under development. It is essential to understand the propagation of injected and scattered rays to support the electronic/quasi-optical design and subsequent interpretation of the detected signals of the multi-channel DBS/CPS measurements. Thus, ray-tracing analysis with the axisymmetric ray-tracing code BORAY has been performed to estimate the scattering location and wavenumbers of the density and magnetic fluctuations. In addition, the influence of accordance between toroidal and poloidal launch angles is investigated. The received DBS/CPS signal quality can be improved by matching the parallel wavenumber in the direction of magnetic field lines.
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