Tokamak residual zonal flow level in near-separatrix region

Residual zonal flow level is calculated for tokamak plasmas in the near-separatrix region of a diverted tokamak. A recently developed method is used to construct an analytic divertor tokamak configuration. It is shown that the residual zonal flow level becomes smaller but still keeps finite near the separatrix because the neoclassical polarisation mostly due to the trapped particles goes larger in this region.     

The strongest magnetic barrier in the DIII-D tokamak and comparison with the ASDEX UG

Magnetic perturbations in tokamaks lead to the formation of magnetic islands, chaotic field lines, and the destruction of flux surfaces. Controlling or reducing transport along chaotic field lines is a key challenge in magnetically confined fusion plasmas. A local control method was proposed by Chandre et al. [Nucl. Fusion 46, 33–45 (2006)] to build barriers to magnetic field line diffusion by addition of a small second-order control term localized in the phase space to the field line Hamiltonian. Formation and existence of such magnetic barriers in Ohmically heated tokamaks (OHT), ASDEX UG and piecewise analytic DIII-D [Luxon, J.L.; Davis, L.E., Fusion Technol. 8, 441 (1985)] plasma equilibria was predicted by the authors [Ali, H.; Punjabi, A., Plasma Phys. Control. Fusion 49, 1565–1582 (2007)]. Very recently, this prediction for the DIII-D has been corroborated [Volpe, F.A., et al., Nucl. Fusion 52, 054017 (2012)] by field-line tracing calculations, using experimentally constrained Equilibrium Fit (EFIT) [Lao, et al., Nucl. Fusion 25, 1611 (1985)] DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. This second-order approach is applied to the DIII-D tokamak to build noble irrational magnetic barriers inside the chaos created by the locked resonant magnetic perturbations (RMPs) (m, n)=(3, 1)+(4, 1), with m and n the poloidal and toroidal mode numbers of the Fourier expansion of the magnetic perturbation with amplitude δ. A piecewise, analytic, accurate, axisymmetric generating function for the trajectories of magnetic field lines in the DIII-D is constructed in magnetic coordinates from the experimental EFIT Grad-Shafranov solver [Lao, L, et al., Fusion Sci. Technol. 48, 968 (2005)] for the shot 115,467 at 3000 ms in the DIII-D. A symplectic mathematical map is used to integrate field lines in the DIII-D. A numerical algorithm [Ali, H., et al., Radiat. Eff. Def. Solids Inc. Plasma Sc. Plasma Tech. 165, 83 (2010)] based on continued fraction decomposition of the rotational transform labeling the barriers for selecting and identifying the strongest noble irrational barrier is used. The results are compared and contrasted with our previous results on the ASDEX UG. About six times stronger a barrier can be built in the DIII-D than in the ASDEX UG. High magnetic shear near the separatrix in the DIII-D is inferred as the possible cause of this. Implications of this for the DIII-D and the International Thermonuclear Experimental Reactor (ITER) are discussed.     

Coordinate transformation and construction of finite element mesh in a diverted tokamak geometry

A coordinate transformation technique between straight magnetic field line coordinate system (Ψ, θ) and Cartesian coordinate system (R, Z) is presented employing a Solov'ev solution of the Grad-Shafranov equation. Employing the equilibrium solution, the poloidal magnetic flux Ψ(R, Z) of a diverted tokamak, magnetic field line equation is solved computationally to find curves of constant poloidal angle θ, which provides us with explicit relations R = R(Ψ, θ) and Z = Z(Ψ, θ). Correspondingly, conversion from one coordinate to the other along particle trajectories in the vicinity of separatrix is demonstrated. Based on the magnetic structure, a finite element mesh is generated in a diverted tokamak geometry to solve Poisson's equation.     

HL-2A单零偏滤器的位形特征

利用积分方法对多种电流剖面下HL2A装置单零偏滤器位形特征进行了计算研究。积分方法的优点是可以在任意电流剖面下求解具有X-点的自由边界的Grad-Shafranov方程。对HL2A装置而言,大体上可以在合理设定的分界面形状下,经几次叠代计算出各组极向场线圈(垂直场,三对多极场和多极补偿场以及水平场)中的电流。HL-2A的单零偏滤器位形基本上是圆截面加上在X-点附近的局部形变。对刮离区和偏滤器靶板区磁力线特性进行了分析以确定偏滤器的品质。     

Growth rate of peeling mode in the near separatrix region of diverted tokamak plasma

An analytical expression of the peeling mode in the near separatrix region of diverted tokamak plasma is derived. It is shown that in diverted plasmas both with single and double X points, though the perturbed potential energy of the unstable peeling mode tends to be large, its growth rate becomes very small due to the even larger kinetic energy. Compared to some recent studies that give qualitatively correct results about this growth rate, our result is directly related with the diverted equilibrium quantities suitable for application to realistic experiments.     

The Role of Radial Electric Fields in the Tokamaks TEXTOR-94, CASTOR, and T-10

Radial electric fields (E _r) and their role in the establishment of edge transport barriers and improved confinement have been studied in the tokamaks TEXTOR-94 and CASTOR, where E _r is externally applied to the plasma in a controlled way using a biased electrode, as well as in the tokamak T-10 where an edge transport barrier (H-mode) is obtained during electron-cyclotron resonance heating (ECRH) of the plasma.The physics of radial currents was studied and the radial conductivity in the edge of TEXTOR-94 (R = 1.75 m, a = 0.46 m) was found to be dominated by recycling (ion-neutral collisions) at the last closed flux surface (LCFS) and by parallel viscosity inside the LCFS. From a performance point of view (edge engineering), such electrode biasing was shown to induce a particle transport barrier, a reduction of particle transport, and a concomitant increase in energy confinement. An H-mode-like behaviour can be induced both with positive and negative electric fields. Positive as well as negative electric fields were shown to strongly affect the exhaust of hydrogen, helium, and impurities, not only in the H-mode-like regime.The impact of sheared radial electric fields on turbulent structures and flows at the plasma edge is investigated on the CASTOR tokamak (R = 0.4 m, a = 0.085 m). A non-intrusive biasing scheme that we call "separatrix biasing" is applied whereby the electrode is located in the scrape-off layer (SOL) with its tip just touching the LCFS. There is evidence of strongly sheared radial electric field and E×B flow, resulting in the formation of a transport barrier at the separatrix. Advanced probe diagnosis of the edge region has shown that the E×B shear rate that arises during separatrix biasing is larger than for standard edge plasma biasing. The plasma flows, especially the poloidal E×B drift velocity, are strongly modified in the sheared region, reaching Mach numbers as high as half the sound speed. The corresponding shear rates ( 5×10⁶ s^-1) derived from both the flow and electric field profiles are in excellent agreement and are at least an order of magnitude higher than the growth rate of unstable turbulent modes as estimated from fluctuation measurements.During ECRH in the tokamak T-10 (R = 1.5 m, a = 0.3 m), a regime of improved confinement is obtained with features resembling those in the H-mode in other tokamaks. Using a heavy ion beam probe, a narrow potential well is observed near the limiter together with the typical features of the L-H transition. The time evolution of the plasma profiles during L-H and H-L transitions is clearly correlated with that of the density profile and the formation of a transport barrier near the limiter. The edge electric field is initially positive after the onset of ECRH. It changes its sign during the L-H transition and grows till a steady condition is reached. Similar to the biasing experiments in TEXTOR-94 and CASTOR, the experimentally observed transport barrier is a barrier for particles.     

Analytic description of tokamak equilibrium sustained by high fraction bootstrap current

By using an expansion technique based on the tokamak ordering, the Grad－Shafranov equation is analytically solved for tokamak equilibrium sustained by a full bootstrap current. This approximate approach is suitable for equilibria with non-circular cross-sections of modest ellipse and triangular deformations. As an input parameter set, the plasma pressure profile and the electron and the ion temperature profiles can be selected as arbitrary functions of the averaged minor radius. Equilibrium properties of this plasma are discussed.     

A new model analysis of the third harmonic voltage in inductive measurement for critical current density of superconducting films

The critical current density J c is one of the most important parameters of high temperature superconducting films in superconducting applications,such as superconducting filter and superconducting Josephson devices.This paper presents a new model to describe inhomogeneous current distribution throughout the thickness of superconducting films applying magnetic field by solving the differential equation derived from Maxwell equation and the second London equation.Using this model,it accurately calculates the inductive third-harmonic voltage when the film applying magnetic field with the inductive measurement for J c.The theoretic curve is consistent with the experimental results about measuring superconducting film,especially when the third-harmonic voltage just exceeds zero.The J c value of superconducting films determined by the inductive method is also compared with results measured by four-probe transport method.The agreements between inductive method and transport method are very good.     

Physical mechanisms in divertors and their impact on the core

The magnetic separatrix in a diverted tokamak determines the boundary between closed and open magnetic field lines. Even though the main influences on the physics of SOL and core regions may be different and shift from the plasma-neutral coupling and impurity radiation in the scrape-off layer (SOL) to anomalous plasma transport in the core, the influence of this boundary persists over some width, both into the core region and into the SOL. We give a short review of the progress in the divertor-SOL physics and discuss the links between edge core and SOL plasmas which are likely to have an important role in different edge-plasma phenomena.     

Numerical analysis of high Mach flow and flow reversal in the experimental advanced superconducting tokamak divertor

The B2-Eirene (SOLPS 4.0) code package is used to investigate the plasma parallel flow, i.e., the scrape-off layer (SOL) flow, in the experimental advanced superconducting tokamak (EAST) divertor. Simulation results show that the SOL flow in the divertor region can exhibit complex behaviour, such as a high Mach flow and flow reversal in different plasma regimes. When the divertor plasma is in the detachment state, the high Mach flow with approaching or exceeding sonic speed is observed away from the target plate in our simulation. When the divertor plasma is in the high recycling state, the flow reversal with a small Mach number (|M|< 0.2) is observed near the X-point along the separatrix region. The driving mechanisms for the high Mach flow and the reversed flow are analysed theoretically through momentum and continuity equations, respectively. The profile of the ionization sources is shown to be a possible formation condition causing the complex behaviour of the SOL flow. In addition, the effects of the high Mach flow and the flow reversal on the impurity transport are also discussed in this paper.     

低混杂波高N‖分量对EAST等离子体电流驱动的影响

EAST等离子体高约束模运行条件下，在等离子体边缘区域观测到明显的等离子体电流带.在EAST托卡马克装置非圆截面平衡位形下，使用射线追踪方法研究低混杂波高平行折射率N_‖分量对电流驱动的影响.结果表明：当-8≤N_‖≤-6时，平行折射率分量能够在小半径（0.7 < r/a < 1）区域驱动kA量级的等离子体电流.对于具有台基区、等离子体边缘温度更高的电子温度剖面，驱动电流的位置r/a>0.9.低混杂波朗道阻尼的理论分析与数值模拟结果一致.另外，高N_‖低混杂波在等离子体边缘的功率沉积和电流驱动与电子温度分布和发射谱分布相关.     

Simultaneous catalytic regime of tritium and helium-3 in D-D fusion without external breeding

A catalytic regime of tritium and helium-3 in deuterium-deuterium fusion, including ion-electron collisions, mechanical expansion, bremsstrahlung radiation, inverse Compton scattering losses and reacting particles energy effect has been investigated. In this paper a new fuel configuration, DT _x ³He _y , is formed by adding ³He to DT fuel. According to our calculations this fuel (DT _x=0.0112 ³He _y=0.0399) has greater energy gain than the fuel (DT _x =0.0112) used by Eliezer et al [Eliezer et al, Nucl. Fusion 40, 195 (2000)] and also it does not require external tritium and helium-3 breeding. Furthermore, neutron yields in D-D and D-T reactions are reduced due to the reduced quantity of initial amount of deuterium and tritium.     

HL-2A装置偏滤器位形超声分子束注入深度观测

用22道Hα辐射测量阵列观测了HL-2A装置偏滤器位形超声分子束的注入过程。观测结果表明：在HL-2A装置偏滤器位形下,当分子束注入气源压强大于1MPa时,Hα辐射沿径向分布存在两个峰值,其第二个Ha辐射峰值位于r/a~0.8附近,表明大部分氢粒子在等离子体边缘(SOL区域)即被离解或电离,但仍有部分氢粒子沉积在分界面内5cm。     

Fine structure of splitting of the separatrix of a nonlinear resonance

This report is a continuation of an analysis, initiated elsewhere V.V. Vecheslavov and B. V. Chirikov, Zh. éksp. Teor. Fiz. 114, 1516 (1998) [JETP 86, 823 (1998)], of the effect of splitting of the separatrix of a nonlinear resonance for the model of standard mapping, based on results of direct measurements of the splitting angle α(K), where K is the system parameter. Measurements were made in the previously used wide range 0.1≳α≳10⁻²⁰⁸ (1⩾K⩾0.0004), but with significantly higher relative (better than 10⁵⁰) and average (∼10⁻⁵⁵) accuracy. This procedure made it possible to substantially refine the effects observed in Ref. 1 and construct qualitatively new empirical dependences providing reliable extrapolation of the data obtained for the angle and the invariant in the intermediate asymptotic limit K≲10⁻² beyond the limits of the investigated region. The results obtained by us can be useful for further development of the theory of separatrix splitting and formation of the stochastic layer of a nonlinear resonance. Zh. éksp. Teor. Fiz. 116, 336–346 (July 1999)     

Design study of 3-D tomography diagnostics for spherical tokamaks

A novel three-dimensional (3-D) tomography software has been developed for spherical tokamak (ST) plasmas with thin central coils. It enables us to measure whole 3-D annular profiles of ST plasma emissivity (line spectrum etc.) using limited number of detectors located on a sphere outside of its separatrix. The numbers and positions of detectors have been optimized for STs that contain low-n toroidal modes from n = 1 to 5. Mathematical method allowing for the removal of the thin central coil from the region of reconstruction and to reconstruct STs with single and double axes are also discussed. The shadow effect of center coil region was found to limit the reconstruction accuracy, indicating that the low-aspect ratio torus (ST) is essential to this new 3-D tomography diagnostics. Received 17 August 2000 and Received in final form 16 November 2000     

Investigation of the dependency of JET midplane separatrix density as a function of engineering parameters

Midplane separatrix density is a crucial parameter in tokamaks since it strongly impacts divertor conditions. Scaling midplane separatrix density, n_{e, SEP} , and pedestal density, n_{e, PED} , as function of engineering parameters such as auxiliary heating P_injected, toroidal magnetic field B_T, and plasma poloidal current I_p are relevant to observe the effect of tuning these parameters on, for example, quality of confinement and divertor regime governed by n_{e, PED} and n_{e, SEP} , respectively. Thus, a dataset of JET H-mode pulses performed with Iter like wall (ILW) has been analysed. Midplane density data are collected from an HRTS (high-resolution Thomson scattering) diagnostic and n_{e, SEP} is determined using the power balance method. Parallel heat flux model is chosen using transport code SOLEDGE2D (S2D) applying power balance method over a simulated n_{e, SEP} and T_{e, SEP} profiles to obtain separatrix positions. The parameters are averaged over time windows with order of (85–185 ms ) and the magnetic configuration has been fixed to avoid divertor geometrical effect on n_{e, SEP} determination, configuration chosen is corner–corner. A ratio between separatrix density and pedestal density at outer midplane ranges between 0.3 and 0.7 on the data set. A scaling law of n_{e, SEP}/n_{e, PED} is obtained as function of P_injected, B_T, and I_P.     

Study of the critical current density and the thermodynamic critical field in deuterated κ-(BEDT-TTF)2Cu[N(CN)2]Br organic superconductor

ABSTRACT

We have studied the reversible and irreversible part of the hysteresis loops as a function of slow cooling rate through the order–disorder transformation near 80?K for the deuterated (κ-D₈-Br) κ-(BEDT-TTF)₂Cu[N(CN)₂]Br organic superconductor. We estimated the critical current density J_C and the thermodynamic critical field H_C from the magnetic hysteresis loops. Temperature dependence of the critical current density derived from the irreversible part using Bean’s model. The thermodynamic critical field H_C has been obtained from the reversible part of the hysteresis loops.     

Integral equation theory of the exchange potential,HOMO–LUMO properties,and sum rules for the exchange-correlation force

Recently, a formally exact integral equation for the exchange potential V _x(r) has been presented by the authors. In the admittedly simplistic limit in which Slater–Kohn–Sham and Hartree–Fock determinants become equal, this integral equation reduces to that given by Della Sala and Görling. Here, a proposal is made to relate, but now approximately, the formally exact equation for V _x(r) to HOMO–LUMO properties. The addition of a correlation contribution V _c(r) to V _x(r), the sum being the exchange-correlation potential V _xc(r), is finally considered, some exact properties and especially sum rules for the force ??V _xc/?r being the focus.     

Overview of edge electrostatic turbulence experiments on TCV

Experiments on edge turbulence in the TCV tokamak have been performed for the first time at the beginning of 2003. This paper presents an overview of some of the results obtained, concentrating in particular on two areas: universality of density fluctuations and the dynamical coupling between radial turbulent-driven fluxes and parallel flows.Plasma fluctuations in the edge of the TCV tokamak have been found to exhibit statistical properties which are universal across a broad range of discharge conditions. Analysis of the time series of density fluctuations in the entire scrape-off layer (SOL) region from just inside the magnetic separatrix to the plasma-wall interface, yields a probability distribution function (PDF) of density which conforms closely to a Gamma distribution. In the wall vicinity, the density fluctuations exhibit clear evidence of self-similarity and are characterised by a PDF with universal shape and with a standard deviation proportional to the mean density. It is also found that radial particle-flux fluctuations scale solely with the mean density. Such findings indicate that it may be possible to improve the prediction of transport in the critical plasma-wall interaction region of future large-scale tokamaks.Recent experiments on JET [C. Hidalgo et al.: Phys. Rev. Lett. 91 (2003) 065001] have investigated a possible link between turbulent transport and the parallel flows. Similar experiments have been performed on TCV for a variety of plasma conditions and flow magnitudes. Although correlations have been found as seen on JET, especially in the wall vicinity, it appears that the magnitude of the coupling is insufficient to drive any significant flow.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Threshold effects in the interaction of a plasma with injected pellets in the T-10 tokamak

Sharp changes (peaks and dips) of the radiation signal from carbon pellets injected into the plasma in the tokamak are related to the level of introduced disturbances. The threshold size (near 0.3 mm) is determined beginning with which a pellet in the ohmic plasma of the T-10 tokamak initiates tearing processes in a region with q < 2 and Kadomtsev reconnection in the central region with q = 1. A model describing ablation under the conditions of pellet-induced reconnections is proposed. This model satisfactorily describes the observed shape of the ablation rate curve.