Tokamak Plasma Turbulence Research Articles

Numerical simulations of tokamak plasma turbulence and internaltransport barriers

A wide variety of magnetically confined plasmas, including many tokamaks suchas the JET, TFTR, JT-60U, DIII-D, RTP, show clear evidence for the existenceof the so-called `internal transport barriers' (ITBs) which are regions ofrelatively good confinement, associated with substantial gradients intemperature and/or density. A computational approach to investigating theproperties of tokamak plasma turbulence and transport is developed. Thisapproach is based on the evolution of global, two-fluid, nonlinear,electromagnetic plasma equations of motion with specified sources. In thispaper, the computational model is applied to the problem of determining thenature and physical characteristics of barrier phenomena, with particularreference to RTP (electron-cyclotron resonance heated) and JET (neutral beamheated) observations of ITBs. The simulations capture features associated withthe formation of these ITBs, and qualitativelyreproduce some of the observations made on RTP and JET. The picture of plasmaturbulence suggested involves variations of temperature and density profilesinduced by the electromagnetic fluctuations, on length scales intermediatebetween the system size and the ion Larmor radius, and time scalesintermediate between the confinement time and the Alfvén time(collectively termed `mesoscales'). The back-reaction of such profile`corrugations' (features exhibiting relatively high local spatial gradientsand rapid time variations) on the development and saturation of the turbulenceitself plays a key role in the nonlinear dynamics of the system. Thecorrugations are found to modify the dynamical evolution of radial electricfield shear and the bootstrap current density, which in turn influence theturbulence. The interaction is mediated by relatively long wavelength,electromagnetic modes excited by an inverse cascade and involving nonlinearinstabilities and relaxation phenomena such as intermittency and internal mode locking.

Trapped-ion driven turbulence in tokamak plasmas

Ion turbulence is expected to play an important role in anomalous transport. Thus an original approach is proposed here to study trapped-ion instability. A Vlasov code is used to determine the behaviour of the instability near the threshold and compared with analytical solutions of the Vlasov equation. Some interesting features which appear in the nonlinear regime are discussed.

Radial discontinuities in tokamak magnetohydrodynamic equilibria with poloidal flow

It is shown that transonic poloidal flow leads to ideal magnetohydrodynamic tokamak equilibria with radial discontinuities in the density, pressure, and flow velocity profiles. Transonic profiles are defined as having flow velocities ranging from subsonic to supersonic with respect to the poloidal sound speed (csBp/B). The jump of the equilibrium quantities occurs approximately at the sonic surface and its magnitude is of order ε1/2 (ε is the inverse aspect ratio). Because of the large velocity shear at the sonic surface, transonic profiles may improve energy confinement as suggested by current understanding of tokamak plasma turbulence suppression.

Effect of externally imposed and self-generated flows on turbulence and magnetohydrodynamic activity in tokamak plasmas

The effects of externally imposed and self-generated poloidal flows on turbulence and magnetohydrodynamic (MHD) activity are examined in the context of the possible Electric Tokamak (ET) [Phys. Plasmas 6, 4722 (1999)] plasmas and (circularized) DIII-D-like [Fusion Technol. 8, 441 (1985)] discharges. Global gyrokinetic particle simulations and reduced MHD calculations respectively show that ion temperature gradient driven turbulence (ITGDT) and resistive internal kink MHD activity can be reduced and/or suppressed with experimentally achievable externally imposed flows for possible ET start-up plasmas. Global gyrokinetic particle simulations of ITGDT also serve to demonstrate that self-generated flows are necessary to yield experimentally relevant radial correlation lengths in the case of DIII-D-like discharges.

Comparisons and physics basis of tokamak transport models and turbulence simulations

The predictions of gyrokinetic and gyrofluid simulations of ion-temperature-gradient (ITG) instability and turbulence in tokamak plasmas as well as some tokamak plasma thermal transport models, which have been widely used for predicting the performance of the proposed International Thermonuclear Experimental Reactor (ITER) tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1996 (International Atomic Energy Agency, Vienna, 1997), Vol. 1, p. 3], are compared. These comparisons provide information on effects of differences in the physics content of the various models and on the fusion-relevant figures of merit of plasma performance predicted by the models. Many of the comparisons are undertaken for a simplified plasma model and geometry which is an idealization of the plasma conditions and geometry in a Doublet III-D [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159] high confinement (H-mode) experiment. Most of the models show good agreements in their predictions and assumptions for the linear growth rates and frequencies. There are some differences associated with different equilibria. However, there are significant differences in the transport levels between the models. The causes of some of the differences are examined in some detail, with particular attention to numerical convergence in the turbulence simulations (with respect to simulation mesh size, system size and, for particle-based simulations, the particle number). The implications for predictions of fusion plasma performance are also discussed.

Flux driven turbulence in tokamaks

The work presented deals with tokamak plasma turbulence in the case wherefluxes are fixed and profiles are allowed to fluctuate. These systemsare intermittent. In particular, radially propagating fronts areusually observed over a broad range of time and spatial scales. Theexistence of these fronts provides one possible way to understand thefast transport events sometimes observed in tokamaks. It is also shownthat the confinement scaling law can still be of the gyro-Bohm type inspite of these large scale transport events. Some departure from thegyro-Bohm prediction is observed at low flux, i.e. when the gradientsare close to the instability threshold. Finally, it is found that thediffusivity is not the same for a turbulence calculated at fixed fluxas for a turbulence calculated at fixed temperature gradient, with thesame time averaged profile.

Observation of spatial intermittency in Tokamak plasma turbulence

A sharp variation at some radial positions superimposed on a slow change in the profiles of the fluctuation levels, fluctuation-driven particle and energy fluxes, which is referred as spatial intermittency, is observed in the core plasma of the Keda Tokamak-5C (KT-5C) [World Survey of Activities in Controlled Fusion Research, Nuclear Fusion Special Supplement (International Atomic Energy Agency, Vienna, 1991), p. 190.]. The peaks in the profiles are located in the vicinity of low-q rational surfaces, and fluctuation spectra perpendicular to the magnetic field become more anisotropy there. The intermittency may be related to the radial variations in the nonlinear mode couplings near the low-q resonant surfaces.

Experimental evidence for self-organized criticality in tokamak plasma turbulence

Measurements of plasma turbulence spectra and particle flux from the DIII-D tokamak exhibit significant agreement with predictions of self-organized criticality (SOC) modeling. Power spectra of density n ̃ , potential g̃f, and particle flux Γ, are observed to have three regions of frequency dependence: f 0, f −1 and f −4. In addition, the particle flux probability distribution displays a Γ −1 scaling over two decades in Γ. These results provide the first evidence that the plasma is in a state consistent with SOC models and place a constraint on plasma transport models.

Observation of Low Frequency Ion Mode Turbulence in Tokamak Plasma

Features of a low frequency ion mode were observed together with the electron drift wave type fluctuations by a Langmuir probe array in the bulk plasma inside the velocity shear layer in the KT-5C tokamak. The measured ion mode wavenumber, scaling of the ion mode with chord-averaged density, and the estimated ηi value suggest that the observed ion mode may be the theoretically predicted ηi mode driven by ion temperature gradient.

Evidence for coherent structures within tokamak plasma turbulence

The microstructures of YBa2Cu3O7-delta/PrBa2Cu3O7-delta/YBa2Cu3O7-delta ramp type Josephson junctions with different ramp slopes fabricated on (100) SrTiO3 substrates were studied by means of transmission electron microscopy. The results show that for the ramp slope angles of 15 degrees-40 degrees, the epitaxy was still remained through all layers at the ramp region without the formation of big grain boundaries. No amorphous layers and secondary phases were observed at the barrier interfaces. For a gentle ramp junction, small misoriented grains appeared in some portions of the barrier. The substrate ramp formed during the ion etching process had little influence on the growth of the upper layers. For a steep ramp junction, a dimple was created in the substrate, which caused the bending in the film and the nucleation of misoriented grains, although the epitaxy of the barrier was of good quality. The results demonstrate that the slope angle of the junction ramp is an important factor that influences the performance of the Josephson junctions. (C) 1998 Elsevier Science B.V.

Towards a full self-consistent numerical simulation of tokamak plasma turbulence

This paper is a review of recent advances in numerical simulations of turbulence in fusion plasmas. Recent improvements of fluid and particle simulations are described. The results are compared with challenging issues such as the L - H transition and scaling laws. Finally, the predictive capability of turbulence simulations is addressed.

Density fluctuations in JIPP T-IIU tokamak plasmas measured by a heavy ion beam probe

Multiple and small sample volume measurements of the density turbulence and potential profile measurements in tokamak plasmas were conducted using a heavy ion beam probe. The obtained wavenumber-frequency spectrum S(k, omega ) shows that the cross-sections of neutral beam injection (NBI) heated plasmas are divided into three regions of different turbulence characteristics outside the layer where the direction of the density turbulence propagation reverses, a low frequency and low wavenumber mode travelling in the ion diamagnetic drift direction dominates. The region enclosed by this reversal layer is divided into two parts during nearly perpendicular NBI heating: a region where the propagation velocity is near the Etau /Bt poloidal rotation velocity and a bad curvature region of very small wavenumber and high propagation velocity. The region of high propagation velocity, found in NBI plasmas, disappears in the ohmic plasmas. In addition, a small component that propagates in the ion diamagnetic drift direction is observed in NBI plasmas

Characterization of Magnetic Turbulence in Tokamak Plasmas through Hard X-Ray Spectra

Magnetic turbulence is characterized using anomalous hard x-ray spectra in tokamaks. Two types of spectra are obtained, single slope or normal spectra, and spectra that present roughly two slopes, or anomalous spectra. For normal spectra the amplitude of the turbulence is given by the slope and a lower limit for the radial correlation length of the turbulence is deduced from the maximum detected energy. For anomalous spectra the magnetic turbulence amplitude can be again deduced from the first slope and the radial correlation length can be inferred from the energy at which the slope changes.

Transport in gyrokinetic tokamaks

A comprehensive study of transport in full-volume gyrokinetic (GK) simulations of ion temperature gradient driven turbulence in core tokamak plasmas is presented. Though this ‘‘gyrokinetic tokamak’’ is much simpler than experimental tokamaks, such simplicity is an asset, because a dependable nonlinear transport theory for such systems should be more attainable. Toward this end, two related lines of inquiry are pursued. (1) The scalings of GK tokamaks with respect to important system parameters are studied. In contrast to real machines, the scalings of larger GK systems (a/ρs≳64) with minor radius, with current, and with a/ρs are roughly consistent with the approximate theoretical expectations for electrostatic turbulent transport which exist as yet. Smaller systems manifest quite different scalings. (2) With the goal of developing a first-principles theory of GK transport, the GK data are used to infer the underlying transport physics. The data indicate that, of the many modes k present in the simulation, only a modest number (Nk∼10) of k dominate the transport, and for each, only a handful (Np∼5) of couplings to other modes p appear to be significant, implying that the essential transport physics may be described by a far simpler system than would have been expected on the basis of earlier nonlinear theory alone. Part of this analysis is the inference of the coupling coefficients Mkpq governing the nonlinear mode interactions, whose measurement from tokamak simulation data are presented here for the first time.

The influence of Polarization Currents on the Edge Plasma Turbulence in Tokamaks

AbstractThe nature of edge turbulence in tokamaks and stellarators is associated in literature with the dissipation by currents, flowing through the potential sheath near the surface (SD ‐ surface dissipation). There are two mechanisms for the instability: the flute instability due to the fluctuations of the Pfirsch‐Schlüter currents [1], and an instability due to the fluctuations of polarization currents [2], the latter mechanism taking place only when ▽Te ≠ 0. So far these two mechanisms were considered separately. In the present work the stability of plasma in the scrape‐off‐layer (SOL) of tokamak with a ring poloidal limiter is studied in linear approximation. Both magnetic field toroidicity effects and polarization current fluctuations are taken into account.

Effects of edge plasma turbulence on radial correlation length measurements with BES

The recently developed technique of beam emission spectroscopy (BES) provides a tool to study long-wavelength density turbulence (coherence length ≫ ion gyroradius) in hot tokamak plasmas. To provide an accurate conversion of the measured light intensity fluctuations to a local ñ/n density fluctuation and to assess the influence of density fluctuations in the neutral beam induced by large edge turbulence, a multistate neutral beam excitation/transport code for realistic experimental geometries has been written. Results from this code show that the attenuation of the beam density induced by edge turbulence can give rise to significant levels of common-mode fluctuation power in signals from the plasma core and that the derivation of quantitative values of ñ/n from experimental measurements depends weakly on the radial extent of the density fluctuations.

Spatial resolution of microwave/millimeter-wave reflectometry

Reflectometry is currently being used to investigate density fluctuations and turbulence in tokamak plasmas. However, there are unresolved questions about the spatial resolution and wave number sensitivity of this diagnostic method which impact the interpretation of the data. These questions are currently being addressed in a cylindrical, pulsed filament discharge plasma where ion acoustic waves (10–100 kHz) are launched toward the incident microwaves. Preliminary data supporting the spatially localized nature of reflectometry are presented. A computational model is also being developed to provide quantitative comparisons with experiment.

Beam emission spectroscopy diagnostic for the study of turbulence in Phaedrus-T tokamak plasmas

A flexible beam emission spectroscopy diagnostic system is being installed on the Phaedrus-T tokamak. It consists of a low-power diagnostic neutral beam (H0 or He0) coupled with visible and vacuum UV collection optics to study low-amplitude, high-frequency fluctuations in local plasma density in ohmically and rf-heated plasmas. Neutral beam geometry and optical sightlines are chosen to optimize localization and radial resolution (<1 cm) over the whole plasma region. The ability to inject either a H or He neutral beam and observe in both the vacuum UV and the visible spectral ranges allows a wide choice of atomic transitions (e.g., Hα, Lα, He singlet or triplet lines, etc.) to be compared and optimized for a given experimental condition.

Estimate of the correlation dimension for Tokamak plasma turbulence

The coherent CO2 laser scattering signals from TFR Tokamak plasmas have been analysed using a variant of the algorithm proposed by Grassberger and Procaccia (1983) to determine the correlation exponent of these measured plasma turbulence signals. By comparing the results obtained with a randomly generated test signal, the authors see that the plasma turbulence may be considered a dynamical system which possesses a low correlation exponent (the value of which depends on wavenumber of the measured turbulence), thus indicating the possible existence of a low dimensional attractor. They also show by using different signals acquired at different sampling rates that this low dimensional structure is only observed when the acquisition rate of the turbulence signal is sufficiently rapid.

Numerical simulation of turbulent heat flows

Previous work on simulating turbulence in finite beta tokamak plasmas with isothermal models is extended to include temperature perturbations and temperature gradients in a collisional plasma. Turbulent heat as well as plasma flows are treated. The toroidal ion temperature gradient mode is the dominant source of turbulence in the model. Electron temperature gradients can stabilize the electron collisional drift mode and lead to reverse plasma flows (or thermal pinches). Magnetic electron heat conduction is found to be very small when correlations between temperature and magnetic field perturbations are considered. Quasilinear theory and mixing length rules are found to give a good representation of the results.