No abstract

Typical ELMy H-mode discharges have been achieved on the HL-2A tokamak with combined auxiliary heating of NBI and ECRH. The minimum power required is about 1.1 MW at a density of 1.6 × 10 19 m −3 and increases with a decrease in density, almost independent of the launching order of the ECRH and NBI heating. The energy loss by each edge localized mode (ELM) burst is estimated to be lower than 3% of the total stored energy. At a frequency of typically 400 Hz, the energy confinement time is only marginally reduced by the ELMs. The supersonic molecular beam injection fuelling is found to be beneficial for triggering an L-H transition due to less induced recycling and higher fuelling efficiency. The dwell time of the L-H transition is 20-200 ms, and tends to decrease as the power increases. The delay time of the H-L transition is 10-30 ms for most discharges and is comparable to the energy confinement time. The ELMs with a period of 1-3 ms are sustained for more than ten times the energy confinement time with enhanced confinement factor H 89 > 1.5, which tends to decrease with the total heating power. The confinement time in the H-mode discharges increases with plasma current approximately linearly.

In HL-2A, the characteristics of the edge plasma instabilities and their effects on the dynamical evolution of the pedestal in H-mode plasmas have been investigated. In the edge pedestal region with steep pressure gradient, a quasi-coherent mode (QCM) has been observed in density fluctuations with a frequency range of 50-100 kHz. It appears during the edge localized mode (ELM)-free period after the L-H transition and prior to the first ELM. A threshold in the pedestal density gradient has been identified for the excitation of this mode. The QCM can also be observed during inter-ELM periods. It is excited early in the inter-ELM period, and disappears when the ELM onset starts. The radial wave-number of the mode is estimated with two radially separated reflectometers. It shows that the mode is radially propagating inward. The poloidal wave number estimated with the Langmuir probes is k θ ~ 0.43 cm −1 . The mode propagates poloidally in the electron diamagnetic direction in the plasma frame. The toroidal mode number, deduced from Mirnov signals, is n ~ 7. The corresponding poloidal mode number is m ~ 21 according to the local safety factor value. The analysis for the dynamical evolution of the pedestal during the ELM cycle clearly shows that the mode is excited before the ELM onset. During and after the ELM crash, the mode disappears. It suggests that the QCM is driven by the pedestal density gradient, and the mode in return regulates the pedestal density evolution.

In this paper, an overview of the magnetohydrodynamic instabilities induced by energetic electrons on HL-2A is given and some new phenomena with high-power electron cyclotron resonance heating (ECRH) are presented. A toroidal Alfvén eigenmode with frequency from 200 to 350 kHz is identified during powerful ECRH. In the lower frequency range from 10 to 35 kHz, which is in the beta-induced Alfvén eigenmode frequency range, the coexistence of multi-mode is found during the high-power ECRH for the first time. The spectra become wide when the power is sufficiently high. The frequencies of the modes increase with and are much lower than the Alfvén frequency. The relationship between the mode frequency and (7/4 + Te/Ti)1/2 (Ti)1/2 can be obtained by statistical data analysis. Between the two previous frequency ranges, a group of new modes with frequencies from 50 to 180 kHz is observed with high-power ECRH and neutral beam injection heating together. The modes have clear frequency chirping within several milliseconds or several tens of milliseconds, which are identified as energetic particle mode like instabilities. The new features of the fishbone instability excited by energetic electrons are identified. It is interesting to find the frequency jump phenomena in the high-power ECRH. The difference between the low and high frequencies increases with ECRH power. The frequency jumps between 8 and 15 kHz within about 25 ms periodically, when the power is 1.2 MW.

We derive a set of modified Poisson-Nernst-Planck (mPNP) equations for ion transport from the variation of the free energy functional which includes the many-body Coulomb correlation in media of variable dielectric coefficient. The correlation effects are considered through the Debye charging process in which the self energy of an ion is governed by the generalized Debye-Hückel equation. We develop the asymptotic expansions of the self energy taking the ion radius as the small parameter such that the multiscale model can be solved efficiently by numerical methods. It is shown that the variations of the energy functional give the self-energy-modified PNP equations which satisfy a proper weak formulation. We present numerical results from different asymptotic expansions with a semi-implicit conservative numerical method and investigate the effect of the Coulomb correlation.

An important property of the phaseless far field patterns with incident plane waves is the translation invariance. Thus it is impossible to reconstruct the location of the underlying scatterers. By adding a reference point scatterer into the model, we design a novel direct sampling method using the phaseless data directly. The reference point technique not only overcomes the translation invariance, but also brings a practical phase retrieval algorithm. Based on this, we propose a hybrid method combining the novel phase retrieval algorithm and the classical direct sampling methods. Numerical examples in two dimensions are presented to demonstrate their effectiveness and robustness.

Abstract. Significant experimental advances have been made on HL-2A tokamak along with substantial improvement and development of hardware. The three dimensional spectral structures of the low frequency zonal flow, the geodesic acoustic mode (GAM), and quasi-mode-like low frequency fluctuations have been observed simultaneously for the first time. In addition, the spectral structure of the density fluctuation at GAM frequency is also identified. A spontaneous particle transport barrier has been observed in Ohmic discharges without any external momentum input. The barrier is evidenced by particle perturbation study using modulated SMBI and microwave reflectometry. The non-local transport effect with new features induced by SMBI has been investigated. The e-fishbone instability excited by energetic electrons of non-Maxwellian distribution has been investigated via 10-channel CdTe hard x-ray detector. It is found that the e-fishbone is correlated with the existence of energetic electrons of 30-70 keV. The experiment shows that the suppression of m/n = 2/1 tearing modes can be sustained by ECRH with low modulation frequency of about 10 Hz. Extended confinement improvement is obtained after the mode suppression.

We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using the different component of the far field patterns. Only inner products are involved in the computation, thus the novel sampling methods are very simple and fast to be implemented. With the help of the factorization of the far field operator, we give a lower bound of the proposed indicator functionals for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functionals decay like the Bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functionals continuously dependent on the far field patterns, which further implies that the novel sampling methods are extremely stable with respect to data error. For the case when the observation directions are restricted into the limited aperture, we firstly introduce some data retrieval techniques to obtain those data that can not be measured directly and then use the proposed direct sampling methods for location and shape reconstructions. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed sampling methods, even for multiple multiscale cases and limited-aperture problems.