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.     

Intermittent Structures in the High Field Side Boundary of the HYBTOK-II Tokamak

The spatial and temporal characteristics of the turbulence in the inboard and outboard scrape-off layer (SOL) of tokamak HYBTOK-II have been studied using poloidal probe array. Bursty behaviour with intermittent bursts was observed for both outboard and inboard SOL. In the inboard (high field side), high level of density fluctuations has been observed. The fluctuations in the high field side and low field side are identical in statistics that is non-Gaussian one.     

等离子体湍流理论研究的最新进展

评述和分析了磁约束核聚变理论研究、数值模拟和实验研究等方面最近几年共同关心的一个重要问题——寻找托卡马克等离子体湍流中的带状剪切流（zonal flows）。简要介绍了作者最近对电阻性-重力模湍流中的带状剪切流的研究结果。 Progress of the research on the zonal flows in tokamak plasma turbulence is surveyed, especially it is reviewed that the zonal flows observed in the experiments and numerical simulations on atmosphere turbulence and ocean turbulence and the discovery of H-mode in tokamak experiments how lead the researchers in magnetic confinement fusion community to find out the existence of the zonal flow in tokamak plasma turbulence and subsequently give the experimental verification of its existence. Finally, the results of our research on zonal flow generation and evolution in resistive-g mode turbulence are presented in brief.     

Mirnov coil data analysis for tokamak ADITYA

The spatial and temporal structures of magnetic signal in the tokamak ADITYA is analysed using recently developed singular value decomposition (SVD) technique. The analysis technique is first tested with simulated data and then applied to the ADITYA Mirnov coil data to determine the structure of current peturbation as the discharge progresses. It is observed that during the current rise phase, current perturbation undergoes transition from m=5 poloidal structure to m=4 and then to m=3. At the time of current termination, m=2 perturbation is observed. It is observed that the mode frequency remains nearly constant (≈10 kHz) when poloidal mode structure changes from m=4 to m=2. This may be either an indication of mode coupling or a consequences of changes in the plasma electron temperature and density scale length.     

An Analytical Approach to the Turbulence-Relaxed State in Tokamak Plasmas

Starting from the continuity, temperature, and motion equations of the trapped electron fluid in generaltokamak magnetic field with positive or reversed shear and the definition of Lagrangian invariant, dL / dt = ( t u. )L =0, where u is convective velocity, the trapped electron dynamics is considered in the following two assumptions: (i) theturbulence is low frequency electrostatic, and (ii) L is a functional only of the density n, temperature T, and magneticfield B, and the effect of perturbation potential φ is included in the convective velocity u, i.e., u is a functional of n,T, B, and φ. The Lagrangian invariant hidden in the trapped electron dynamics is strictly found: L= ln[(n/B)c1(T/B2/3)c2], where c1 and c2 are dimensionless changeable parameters and c1 ∝ c2. From this Lagrangian invariant thewhich, in the limit of large aspect ratio, reduce to n(r)q(r) = const. and T3/2(r)q(r) = const., respectively. The lattertwo scaling laws are compared with existent experimental results, being in good agreement.     

Multifractal analysis of plasma turbulence in biasing experiments on Castor tokamak

Experiments as well as some stochastic models have shown that behaviour of the transport in the edge plasma in fusion devices should be considered as a multi-scale phenomenon. The multifractal statistics describes processes as a multiplicative cascade with a complex self-similarity. The multifractal analysis, which enables to clearly demonstrate the turbulent properties of plasma, was applied to fluctuating signals in the biasing experiments. The influence of the biasing parameters is shown. A comparison with other types of the analysis is illustrated, too. Presented at the Workshop “Electric Fields, Structures and Relaxation in Edge Plasmas”, Tarragona, Spain, July 3–4, 2005.     

Investigation of the plasma potential oscillations in the range of geodesic acoustic mode frequencies by heavy ion beam probing in tokamaks

Specific oscillations within a range of 20 kHz (20 kHz-mode) were investigated on the T-10 and TEXT tokamaks using Heavy Ion Beam Probe (HIBP) diagnostic. Regimes with ohmic heating on both machines, and with off-axis ECRH in T-10 were studied. It was shown that 20 kHz-modes are mainly the potential oscillations. The power spectrum of the oscillations has the form of a solitary quasi-monochromatic peak with a contrast range of (3–5). They are the manifestation of torsional plasma oscillations with poloidal wavenumber m = 0, called zonal flows. It was shown that in TEXT the radial electric field oscillations exist in a limited radial range of 0.65 > < 0.95. The frequency of 20 kHz-mode is varied in the region of observation; it diminishes to the plasma edge. In T-10, after ECRH switch-on, the frequency increases, correlating with the growth of the electron temperature T _e. In both machines the frequency of the 20 kHz-mode varies with local T _e: f T _e ^1/2 , which is consistent with theoretical scaling for geodesic acoustic modes (GAM): f _GAM c _s/R T _e ^1/2 , where c _s is the speed of sound. The absolute frequencies are close to GAM values within a factor of unity.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Microwave Correlation Reflectometry for Tokamak CASTOR

A correlation reflectometer in 8-mm wavelength range has been constructed and installed on CASTOR tokamak. The reflectometer can operate on three fixed frequencies (29, 33, and 35 GHz). This is universal correlation sine-cosine reflectometer, which can work in poloidal or toroidal correlation regime and in ordinary mode (O-mode) and/or extraordinary mode (X-mode). A computational method of a direct evaluation of the phase fluctuations as well as absolute value of the phase from sine-cosine data has been developed. Using this method the relative plasma density fluctuations in the CASTOR core plasma has been determined in the range of few percent under assumption of parabolic density distribution.     

An Analytical APproach to the Turbulence—Relaxed State in Tokamak Plasmas

Starting from the continuity, temperature, and motion equationsof the trapped electron fluid in general tokamak magnetic fieldwith positive or reversed shear and the definition of Lagrangianinvariant, dL/dt≡(partial_t+u•▽)L=0, whereu is convective velocity, the trapped electron dynamics is considered in the following two assumptions: (i)the turbulence is low frequency electrostatic, and (ii) L is a functional only of the density n, temperature T, and magnetic field B, and the effect of perturbationpotential φ is included in the convective velocity u, i.e., u is a functional of n, T, B, and φ. The Lagrangian invariant hidden in the trapped electron dynamics is strictly found:L=ln[(n/B)^c₁(T/B^2/3)^c₂], wherec₁ and c₂ are dimensionless changeable parameters and c₁∝c₂. From this Lagrangian invariantthe turbulent particle and electronthermal transport scaling laws are derived:〈n>_ψq(ψ)=const. and〈T^3/2>_ψq(ψ)=const.,which, in the limit of large aspect ratio, reduce ton(r)q(r)=const. and T^3/2(r)q(r)=const., respectively. The latter two scalinglaws are compared with existent experimental results, being in goodagreement.     

Numerical simulation of ion acoustic turbulence

Extensive simulation studies of ion acoustic turbulence carried out at the Max Planck Institute and at the Los Alamos National Laboratory are compared. Simulations of theB=0 case carried out at the two laboratories agree when the Sagdeev scaling law without theT _e/T_i dependence is used to compare them. Typical results are shown. The level of turbulence is found to be quite high in spite of the low anomalous collision frequency. The role of the differential drift distribution in these simulations is discussed extensively.     

Poloidal inhomogenity of the particle fluctuation induced fluxes near the LCFS at lower hybrid heating and improved confinement transition at the FT-2 tokamak

This paper deals with the new spectral and microturbulence experimental data and their analysis, which show that the radial electric field E _r generated at the lower hybrid heating (LHH) in the FT-2 is high enough to form the transport barriers. The ETB is formed when LHH is switched off. The radial fluctuation-induced E × B drift flux densities near LCFS in SOL are measured at two different poloidal angles. For this purpose two Langmuir probes located at low and high field sides of the torus are used. Registration of the poloidal and radial components of the electric field and density fluctuations at the same time during one discharge permits to measure the poloidal asymmetry of the transport reduction mechanism of the radial and poloidal particle fluxes in the SOL. The absolute fluctuation levels show dependence on the sign of E _r shear. The modification of the microscale turbulence by the poloidal E _r × B rotation shear _{E × B} at the L-H transition near LCFS is also studied by X-mode fluctuation reflectometry. The new data were obtained by spatial spectroscopic technique.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Ion acoustic turbulence and anomolous transport

Theoretical interpretation of ion acoustic turbulence is shown to require the use of renormalized turbulence theory for calculating the turbulent spectra and transport coefficients. The physics of solitons, double layers, and ion phase space holes have an impact on the one-dimensional problem.     

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.     

Nonperturbative renormalization group approach to turbulence

We suggest a new, renormalization group (RG) based, nonperturbative method for treating the intermittency problem of fully developed turbulence which also includes the effects of a finite boundary of the turbulent flow. The key idea is not to try to construct an elimination procedure based on some assumed statistical distribution, but to make an ansatz for possible RG transformations and to pose constraints upon those, which guarantee the invariance of the nonlinear term in the Navier-Stokes equation, the invariance of the energy dissipation, and other basic properties of the velocity field. The role of length scales is taken to be inverse to that in the theory of critical phenomena; thus possible intermittency corrections are connected with the outer length scale. Depending on the specific type of flow, we find different sets of admissible transformations with distinct scaling behaviour: for the often considered infinite, isotropic, and homogeneous system K41 scaling is enforced, but for the more realistic plane Couette geometry no restrictions on intermittency exponents were obtained so far. Received: 28 December 1997 / Accepted: 6 August 1998     

Affine turbulence

We present a generalization of the multiplicative model for velocity increments involving an affine process. The consequences on the shape of the probability distribution functions for the velocity increments are explored, and shown to be better compatible with the existence of a scale variation of the skewness. Received 29 March 1999 and Received in final form 14 September 1999     

A study on turbulence modulation via an analysis of turbulence anisotropy-invariants

We investigate the turbulence modulation by particles in a turbulent two-phase channel flow via an analysis of turbulence anisotropy-invariants. The fluid turbulence is calculated by a large eddy simulation with a point-force two-way coupling model and particles are tracked by the Lagrangian trajectory method. The channel turbulence follows the two-component turbulence state within the viscous sub-layer region and outside the region the turbulence tends to follow the right curve of the anisotropy-invariant....     

Study of particle transport in ac plasmas on HT-7 tokamak

The particle transport coefficients were investigated in ac plasmas by density modulation method on HT-7 tokamak. It is observed that the particle diffusion coefficient (D) is almost the same in various cases and varies with the electron density. The convection velocity (V) is equal to the value of inward pinch velocity (VE×B) for low and high density discharges. The particle confinement time becomes much higher when the directions of plasma current and toroidal field are uniform.