To understand the connection between the dynamics of microscopic turbulence and the macroscale power scaling in the L-I-H transition in magnetically confined plasmas, a new time-dependent, one-dimensional (in radius) model has been developed. The model investigates the radial force balance equation at the edge region of the plasma and applies the quenching effect of turbulence via the E × B flow shear rate exceeding the shear suppression threshold. By slightly ramping up the heating power, the spatio-temporal evolution of turbulence intensity, density and pressure profiles, poloidal flow and E × B flow selfconsistently displays the L-H transition with an intermediate phase (I-phase) characterized by limit-cycle oscillations. Since the poloidal flow is partially damped to the neoclassical flow in the edge region, the numerical results reveal two different oscillation relationships between the E × B flow and the turbulence intensity depending on which oscillation of the diamagnetic flow or poloidal flow is dominant. Specifically, by including the effects of boundary conditions of density and temperature, the model results in a linear dependence of the H-mode access power on the density and magnetic field. These results imply that the microscopic turbulence dynamics and the macroscale power scaling for the L-H transition are strongly connected.
Multiple electromagnetic coherent modes with frequencies f ∼ 20–300 kHz and toroidal mode numbers n = 1 and n = 2 have been observed and investigated in radio-frequency heated H-mode plasmas of the EAST tokamak. The experimental results show that the two main branches of these coherent modes are driven by energetic electrons (EEs), which are produced in the processes of radio-frequency current drive and heating. Bicoherence analysis indicates that there are strong nonlinear mode interactions between the two branches (mother waves), i.e. one is in the low-frequency range of f ∼ 20–50 kHz and the other one is in the high-frequency range of f ∼ 120–250 kHz, and their nonlinear couplings can generate many harmonics (daughter waves). Both coherent modes propagate poloidally along the electron diamagnetic drift direction. The gyrokinetic eigenvalue simulations support the view that both the low-frequency and the high-frequency coherent modes observed in EAST are Alfvén eigenmode (AE) type, and the kinetic effects of background plasmas and EEs are responsible for the formation and excitation of AEs, respectively. The low-frequency coherent mode is identified as the kinetic beta-induced Alfvén eigenmode located in the edge, and the high-frequency coherent mode is radially global, which is characterized by a toroidal Alfvén eigenmode (TAE) in the core and also has the components of a kinetic TAE and ellipticity-induced Alfvén eigenmode in the outer region due to the large downshift of the Alfvén continuum gap from the core to the edge in H-mode discharges.
To obtain engineering-feasible designs of stellarators with permanent magnets and simplified coils, a new algorithm has been developed based on Fourier decomposition and surface magnetic charges method. The strong toroidal fields in a quasi-axisymmetric stellarator are still generated by coils. The permanent magnets are designed to compensate the normal magnetic field B n on the plasma surface ∂P created by the coils and plasma. The normal magnetic fields created by the permanent magnets B pmn are calculated as the difference between the magnetic fields created by the surface magnetic charges on the inner surface ∂D and the outer surface ∂D h of the magnets. The Fourier coefficients of the magnet thickness function h θ , ϕ are computed through matrix division operation based on the least square principle with dominant Fourier components selected through 2D Fourier transformation of B pmn. The residual uncompensated B n is minimized through iteration to progressively optimize the thickness function. This new algorithm has been successfully applied to design the permanent magnets of an l = 2 quasi-axisymmetric stellarator with background magnetic field created by 12 identical circular planar coils for demonstrations. High accuracy has been achieved, allowing for a flux-surface-averaged residual B n relative to the total field B n / B ∼ 1.3 × 1 0 − 5 and a maximum residual B n of less than 2 Gs for ∼1 T total field. This new design has some advantages in engineering implementations: all permanent magnet pieces have the same remanence B r; only one single layer of magnets are mounted perpendicular to the winding surface; the magnets can be easily inserted into the cells of a gridded frame attached to the winding surface and fixed with springs from the back, which greatly simplifies the manufacture, assembly and maintenance of the magnets, and thus facilitates precision control and cost reduction.
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