Poloidal Structure of the Turbulence and the Turbulent Flux During Edge Plasma Biasing in the Castor Tokamak

The poloidal structure of the turbulence and the turbulent particle flux in the scrape-off layer (SOL) of the CASTOR tokamak are analysed by means of a poloidal ring of 124 probes distributed uniformly along the whole poloidal circumference. Fluctuation measurements are performed in standard ohmic regime as well as in discharges when a biased electrode is inserted either into the SOL or deeper into the confinement region. It is found that in both cases a strongly sheared radial electric field is created in the SOL, which de-correlates the density and radial velocity fluctuations and reduces their levels. Consequently, the turbulent flux is reduced. However, no phase shift is observed between density and radial velocity fluctuations. When the electrode is localized in the confinement region, all the above effects are less pronounced because of a smaller shear. In addition, the increase of the E × B velocity at biasing leads in both cases to the formation of oscillations in the temporal correlation function. These oscillations are specifically associated to the poloidal mode (m = q), which is created for a limited time and rotates poloidally. This mode does not modify the phase between density and radial velocity fluctuations and has no further effect on the turbulent flux.     

Minimum dissipative relaxed states in toroidal plasmas

Relaxation of toroidal discharges is described by the principle of minimum energy dissipation together with the constraint of conserved global helicity. The resulting Euler-Lagrange equation is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar-Kendall (C-K) eigenfunctions analytically continued in the complex domain. The C-K eigenfunctions are obtained as hypergeometric functions that are solutions of scalar Helmholtz equation in toroidal coordinates in the large aspect-ratio approximation. Equilibria are constructed by assuming the current to vanish at the edge of plasma. For the m=0, n=0 (m and n are the poloidal and toroidal mode numbers respectively) relaxed states, the magnetic field, current, q (safety factor) and pressure profiles are calculated for a given value of aspect-ratio of the torus and for different values of the eigenvalue λ _{r 0}. The new feature of the present model is that solutions allow for both tokamak as well as RFP-like behaviour with increase in the values of λ _{r 0}, which is related directly to volt-sec in the experiment.     

Turbulence investigations during ergodic divertor operation with induced 2/1 tearing mode

Within the last year of TEXTOR operation a major part of the experiments were dedicated to the interaction of the ergodized plasma edge, induced by the dynamic ergodic divertor (DED), with the core plasma. Systematic experiments are performed in the 3/1 configuration of the DED. Depending on , the DED generates a locked 2/1 mode in the plasma at a critical current in the DED coils. Different diagnostics were used to measure the plasma response in the core and edge. The investigations in this paper are focused on the measurement of density fluctuation and the analysis of the coherent-mode structure outside the q = 2 surface using O-mode poloidal correlation reflectometry. A reduction of the quasi-coherent mode amplitude and frequency is observed, caused by the 2/1 mode together with a decrease of the density scale length. Moreover, the deduced poloidal rotation velocity at the q = 3 surface changes from the electron to the ion diamagnetic drift direction with the onset of the 2/1 island. Also a reduction of the density fluctuations is observed as well as a decrease in the poloidal correlation length. From Ar-injection a delayed inward propagation of the emission maximum is observed for different Ar ionization stages when the 2/1 mode is generated.Similar experiments with a slowly rotating DED show that the steepened density gradients are spatially localized and confirm the hypothesis that the 2/1 mode is responsible for the observations.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Stability-transport modeling of the SINP tokamak discharges

A one-dimensional stability transport code has been developed to simulate the evolution of tokamak plasma discharges. Explicit finite-difference methods have been used to follow the temporal evolution of the electron temperature equation. The poloidal field diffusion equation has been solved at every time step. The effects of MHD instabilities have been incorporated by solving equations for MHD mixing and tearing modes as and when required. The code has been applied to follow the evolution of tokamak plasma discharges obtained in the Saha Institute of Nuclear Physics (SINP) tokamak. From these simulations, we have been able to identify the possible models of thermal conductivity, diffusion and impurity contents in these discharges. Effects of different MHD modes have been estimated. It has been found that in low q ₀ discharge m=1, n=1 and m=2, n=1 modes play major role in discharge evolution. These modes are found to result in the positive jump in the loop voltage which was also observed in the experiments. Hollow current density profile j _φ and negative shear in the q profile have also been found in the rising phase of a discharge.     

HL-2A装置中的带状流三维特性研究和探针设计

HL-2A装置边缘等离子体测地声模带状流的三维特征采用外中平面上三组三台阶探针阵列组成具有环向、极向和径向分辨的独特结构的探针系统进行了研究.其中两组具有极向距离为65mm的三台阶5探针阵列组成极向带状流10探针组,另一组电动式带状流6探针阵列与带状流10探针组之间的环向距离为800mm. 此外,采用快速往复气动6探针组研究了磁分界面附近的温度、密度、雷诺协强及其径向分布.在HL-2A装置上同时观测到测地声模带状流(频率f=7kHz)的极向和环向对称性(m≈0,n 关键词： 三台阶式ZF探针 带状流 三维空间结构     

Control of flow in forced jets: a comparison of round and square cross sections

Abstract  

Direct numerical simulation of incompressible, spatially developing round and square jets at a Reynolds number of 1,000 is performed. The effect of two types of inlet perturbation on the flow structures is analyzed. First, dual-mode excitation, which is a combination of axisymmetric perturbation at preferred mode frequency and helical perturbation at sub-harmonic frequency is used, having a disturbance frequency ratio equal to R _f  = 2. It is observed that the circular and square jets bifurcate and spread on one of the orthogonal planes forming a Y-shape jet in the downstream while no spreading is visible on the other plane. The second type of perturbation is a flapping excitation at a sub-harmonic frequency, St _F = 0.2. It leads to a Y-shape bifurcation for both square and circular jets. On the other hand, for flapping excitation at the preferred mode frequency, namely, St _F = 0.4, a circular jet bifurcates into a Ψ-shape whereas the square jet reveals simple spreading.     

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.     

Pion mass dependence of the <Emphasis Type="Italic">K</Emphasis><Subscript><Emphasis Type="Italic">l</Emphasis>3</Subscript> semileptonic scalar form factor within finite volume

We calculate the scalar semileptonic kaon decay in finite volume at the momentum transfer t _m =(m _K −m _π )², using chiral perturbation theory. At first we obtain the hadronic matrix element to be calculated in finite volume. We then evaluate the finite size effects for two volumes with L=1.83 fm and L=2.73 fm and find that the difference between the finite volume corrections of the two volumes are larger than the difference as quoted in Boyle et al. (Phys. Rev. Lett. 100:141601, 2008). It appears then that the pion masses used for the scalar form factor in ChPT are large which result in large finite volume corrections. If appropriate values for pion mass are used, we believe that the finite size effects estimated in this paper can be useful for lattice data to extrapolate at large lattice size.     

Electron temperature (T e) measurements by Thomson scattering system

Thomson scattering technique based on high power laser has already proved its superoirity in measuring the electron temperature (T _e and density (n _e) in fusion plasma devices like tokamaks. The method is a direct and unambiguous one, widely used for the localised and simultaneous measurements of the above parameters. In Thomson scattering experiment, the light scattered by the plasma electrons is used for the measurements. The plasma electron temperature is measured from the Doppler shifted scattered spectrum and density from the total scattered intensity. A single point Thomson scattering system involving a Q-switched ruby laser and PMTs as the detector is deployed in ADITYA tokamak to give the plasma electron parameters. The system is capable of providing the parameters T _e from 30 eV to 1 keV and n _e from 5 × 10¹²cm⁻³−5 × 10¹³cm⁻³. The system is also able to give the parameter profile from the plasma center (Z=0 cm) to a vertical position of Z=+22 cm to Z=−14 cm, with a spatial resolution of 1 cm on shot to shot basis. This paper discusses the initial measurements of the plasma temperature from ADITYA.     

Effects of edge-localized mode-induced neoclassical toroidal viscosity torque on the toroidal intrinsic rotation in the EAST tokamak

Intrinsic rotation has been observed in lower hybrid current-driven (LHCD) H-mode plasmas with type-III edge-localized modes (ELMs) on Experimental Advanced Superconducting Tokamak (EAST), and it is found that the edge toroidal rotation accelerated before the onset of the ELM burst. Magnetic perturbation analysis shows there is a perturbation amplitude growth below 30 kHz corresponding to the edge rotation acceleration. Using the filament model, the neoclassical toroidal viscosity (NTV) code shows there is a co-current NTV torque at the edge, which may be responsible for the edge rotation acceleration. For maximum displacement ～1 cm and toroidal mode number n=15, the calculated torque density is ～0.44 N/m², comparable with the average edge toroidal angular momentum change rate ～1.24 N/m². Here, the 1 cm maximum magnetic surface displacement estimated from the experimental observation corresponds to a maximum magnetic perturbation ～ 10^?3–10^?2 T, in accordance with magnetic perturbation measurements during ELMs. By varying n from 10 to 20, the magnitude of the edge NTV torque density is mainly ～0.1–1 N/m². This significant co-current torque indicates that the NTV theory may be important in rotation problems during ELMs in H-mode plasmas. To better illuminate the problem, magnetic surface deformation obtained from other codes is desired for a more accurate calculation.     

An approximate analysis of the interaction between two tearing modes of the same helicity

The interaction between tearing modes with the mode numbersm=1,n=1 andm=2,n=2 is investigated for different initial amplitudes of the modes, using a single helicity approximation, a step-current profile and a time-independent resistivity. Also included are the results on the temporal behaviour of the amplitude of the uncoupled modem=2,n=2 in the situation with identical equilibrium parameters as ours.     

Anharmonic Oscillator and Double-Well Potential: Approximating Eigenfunctions

A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by V=m ² x ²+g x ⁴ at arbitrary g ≥ 0 for m ²>0 and m ²<0, respectively, is presented. It is shown that if this approximation is taken as unperturbed problem it leads to an extremely fast convergent perturbation theory Mathematics Subject Classifications(2000) 34L40, 34B08, 41A99     

<Emphasis Type="Italic">xPert</Emphasis>: computer algebra for metric perturbation theory

We present the tensor computer algebra package xPert for fast construction and manipulation of the equations of metric perturbation theory, around arbitrary backgrounds. It is based on the combination of explicit combinatorial formulas for the nth order perturbation of curvature tensors and their gauge changes, and the use of highly efficient techniques of index canonicalization, provided by the underlying tensor system xAct, for Mathematica. We give examples of use and show the efficiency of the system with timings plots: it is possible to handle orders n = 4 or n = 5 within seconds, or reach n = 10 with timings below 1 h.     

Scrape-off-layer current model for filament structure observed during edge-localized modes in the DIII-D tokamak

The plasma in tokamaks often exhibits a relaxation oscillation called the edge-localized mode (ELM), which is generally attributed to MHD instability driven by strong gradients at the plasma boundary. It is shown here that field-aligned currents flowing just outside the boundary may also play a role in the ELM process. The poloidal perturbation magnetic field during ELMs in the DIII-D tokamak calculated from measured currents can reproduce prominent observed features, including a narrow magnetic structure at the outboard midplane similar to filaments observed earlier in DIII-D and NSTX.     

The strange quark mass from QCD sum rules

The strange quark mass is calculated from QCD sum rules for the divergence of the vector as well as axialvector current in the next-next-to-leading logarithmic approximation. The determination for the divergence of the axial-vector current is found to be unreliable due to large uncertainties in the hadronic parametrisation of the two-point function.From the sum rule for the divergence of the vector current, we obtain a value of (1 GeV)=189±32 MeV, where the error is dominated by the unknown perturbativeO( _s ³ ) correction. Assuming a continued geometric growth of the perturbation series, we findm _s =178±18 MeV. Using both determinations ofm _s , together with quark-mass ratios from chiral perturbation theory, we also give estimates of the light quark massesm _u andm _d.     

第Ⅱ种强度不等的两态叠加多模叠加态光场的等阶N次方H压缩1腔模总数与压缩阶数两者之积取偶数的情形

利用多模压缩态理论研究了第种强度不等的非对称两态叠加多模叠加态光场|Ψ_Ⅱ^(ab)〉q的等阶N次方H压缩特性.结果发现:1)当腔模总数q与压缩阶数N的乘积取偶数,亦即qN=2p时,无论p=2m(m=1,2,3,…,…),还是p=2m+1(m=0,1,2,3,…,…),只要各模的初始相位差(φ_j^(a)-φ_j^(b))、态间的初始相位差(θ_nq^(aR)-θ_nq^(bR))及光子干涉项的幅度 1R_j^(a)R_j^(b)等分别满足一定的条件,则态|Ψ_||^(ab)〉q的第一和第二正交分量总可分别呈现出周期性变化的等阶N次方H压缩效应.2)当qN=2p且p=2m+1(m=0,1,2,3,…,…)时,若构成态|Ψ_Ⅱ^(ab)〉q的两个不同的量子光场态中各对应模的强度(即平均光子数)和初始相位相等,亦即R_j^(a)=R_j^(b)和φ_j^(a)=φ_j^(b)(j=1,2,3,…,q),则态|Ψ_Ⅱ^(ab)〉q可呈现出“等阶N次方H压缩简并”现象.     

Non‐paraxial theory of self‐focusing/defocusing of Hermite cosh Gaussian laser beam in rippled density plasmas

Present research work focuses on study of self‐focusing and self‐trapping of Hermite cosh Gaussian (HchG) laser beams in rippled density plasma by considering relativistic non‐linearity. The coupled non‐linear differential equations for the beam width parameters (for modes m = 0, 1, and 2) were derived by employing higher‐order correction in comparison to paraxial ray theory by expanding dielectric function and eikonal up to r⁴ terms. It is observed that the inclusion of higher‐order terms significantly influence the off‐axial properties for m ≥ 1 mode indices. Furthermore, the effect of parameters including beam intensity, ripple factor, depth of density modulation, and decentred parameter on self‐focusing and self‐trapping is analysed and discussed both analytically and numerically.     

Internal magnetic field measurement in tokamak plasmas using a Zeeman polarimeter

In a tokamak plasma, the poloidal magnetic field profile closely depends on the current density profile. We can deduce the internal magnetic field from the analysis of circular polarization of the spectral lines emitted by the plasma. The theory of the measurement and a detailed design of the Zeeman polarimeter constructed to measure the poloidal field profile in the ADITYA tokamak are presented. The Fabry-Perot which we have employed in our design, with photodiode arrays followed by lock-in detection of the polarization signal, allows the measurement of the fractional circular polarization. In this system He-II line with wavelength 4686 Å is adopted as the monitoring spectral line. The line emission used in the present measurement is not well localized in the plasma, necessiating the use of a spatial inversion procedure to obtain the local values of the field.     

Reflection of cold atoms from an array of current-carrying wires

We report the realization of a new type of magnetostatic mirror for slowly moving atoms which comprises a planar array of parallel wires alternately carrying electric current in opposite directions. One of the features of this atomic mirror is that the magnetic field may be readily varied, switched or modulated by altering the current in the wires. Reflection signals close to 100% at a pulsed current of 3 A are demonstrated for a beam of free-falling laser-cooled cesium atoms at normal incidence. The current dependence of the reflection signals exhibits structure which is associated with the sequential onset of reflection of cesium 6² S _1/2 , F=4 atoms in the m=+4, +3, +2 and +1 magnetic states. Measurements of the spatial distribution of the reflected atoms indicate the reflection is predominantly specular at currents of 3 A. Received: 31 August 1998 / Accepted: 6 October 1998     

Characteristics of electron cyclotron resonance plasma formed by lower hybrid current drive grill antenna

A 3.7 GHz system, which is meant for LHCD experiments on ADITYA tokamak, is used for producing ECR discharge. The ECR discharge is produced by setting the appropriate resonance magnetic field of 0.13 T, with hydrogen at a fill pressure of about 5 × 10⁻⁵ Torr. The RF power, up to 10 kW (of which ∼50% is reflected back), with a typical pulse length of 50 ms, is injected into the vacuum chamber of the ADITYA tokamak by a LHCD grill antenna and is used for plasma formation. The average coupled RF power density (the RF power/a typical volume of the plasma) is estimated to be ∼5 kW/m³. When the ECR appears inside the tokamak chamber for the given pumping frequency (f = 3.7 GHz) a plasma with a density (n _e) ∼ 4 × 10¹⁶ m⁻³ and electron temperature ∼8 eV is produced. The density and temperature during the RF pulse are measured by sets of Langmuir probes, located toroidally, on either side of the antenna. H_α signals are also monitored to detect ionization. An estimate of density and temperature based on simple theoretical calculation agrees well with our experimental measurements. The plasma produced by the above mechanism is further used to characterize the ECR-assisted low voltage Ohmic start-up discharges. During this part of the experiments, Ohmic plasma is formed using capacitor banks. The plasma loop voltage is gradually decreased, till the discharge ceases to form. The same is repeated in the presence of ECR-formed plasma (RF pre-ionization), formed 10 ms prior to the loop voltage. We have observed that (with LHCD-induced) ECR-assisted Ohmic start-up discharges is reliably and repeatedly obtained with reduced loop voltage requirement and breakdown time decreases substantially. The current ramp-up rates also decrease with reduced loop voltage operation. These studies established that ECR plasma formed with LHCD system exhibits similar characteristics as reported earlier by dedicated ECR systems. This experiment also addresses the issue of whether ECR plasma formed with grill antenna exhibits similar behavior as that formed by single waveguide ECR antenna. Our experimental observations suggest that the characteristics of (LHCD system-induced) ECR-assisted Ohmic start-up discharges show similar properties, reported earlier with normal ECR-assisted Ohmic start-up discharges and hence LHCD system may be used as ECR system at reduced toroidal magnetic field for other applications like wall conditioning.