Fluctuation-induced Particle Flux Research Articles

Fluctuation-induced inward particle flux during L–I–H transition on HL-2A tokamak

The inward particle flux associated with the global long-lived mode (LLM) during the L–I–H transition on HL-2A tokamak has been measured. The inward particle flux arises from the phase change between density and radial velocity fluctuations, where density and velocity fluctuations are strongly correlated with magnetic fluctuations of LLM. Moreover, the radial velocity and its gradient rather than poloidal flow shear play an important role in particle transport associated with the large-scale mode. The strong nonlinear coupling between LLM and ambient turbulence has been confirmed, and this may contribute to most of the inward particle flux in the LLM during the I-phase state.

Multifield measurement of magnetic fluctuation-induced particle flux in a high-temperature toroidal plasma

Magnetic fluctuation-induced particle transport is explored in the high-temperature, high-beta interior of the Madison symmetric torus (MST) reversed-field pinch by performing a multifield measurement of the correlated product of magnetic and density fluctuations associated with global resistive tearing modes. Local density fluctuations are obtained by inverting the line-integrated interferometry data after resolving the mode helicity through correlation techniques. The local magnetic and current density fluctuations are then reconstructed using a parameterized fit of Faraday-effect polarimetry measurements. Reconstructed 2D images of density and current density perturbations in a poloidal cross section exhibit significantly different spatial structure. Combined with their relative phase, the magnetic-fluctuation-induced particle transport flux and its spatial distribution are resolved. The convective magnetic fluctuation-induced particle flux profile is measured for both standard and high-performance plasmas in MST with tokamak-like confinement, showing large reduction in the flux during improved confinement.

Observation of fluctuation-driven particle flux reduction by low-frequency zonal flow in a linear magnetized plasma

Low-frequency zonal flow (ZF) has been observed in a linear magnetic plasma device, exhibiting significant intermittency. Using the conditional analysis method, a time-averaged fluctuation-induced particle flux was observed to consistently decrease as ZF increased in amplitude. A dominant fraction of the flux, which is driven by drift-wave harmonics, is reversely modulated by ZF in the time domain. Spectra of the flux, together with each of the related turbulence properties, are estimated subject to two conditions, i.e., when potential fluctuation series represents a strong ZF intermittency or a very weak ZF component. Comparison of frequency-domain results demonstrates that ZF reduces the cross-field particle transport primarily by suppressing the density fluctuation as well as decorrelating density and potential fluctuations.

Transport and drift-driven plasma flow components in the Alcator C-Mod boundary plasma

Boundary layer flows in the Alcator C-Mod tokamak are systematically examined as magnetic topology (upper versus lower-null) and plasma density are changed. Utilizing a unique set of scanning Langmuir–Mach probes, including one on the high-field side (HFS) midplane, the poloidal variation of plasma flow components in the parallel, diamagnetic and radial directions are resolved in detail. It is found that the plasma flow pattern can be decomposed into two principal parts: (1) a drift-driven component, which lies within a magnetic flux surface and is divergence-free and (2) a transport-driven component, which gives rise to near-sonic parallel flows on the HFS scrape-off layer (SOL). Toroidal rotation, Pfirsch–Schlüter and transport-driven contributions are unambiguously identified. Transport-driven parallel flows are found to dominate the HFS particle fluxes; the total poloidal-directed flow accounts for ∼1/3 to all of the ion flux arriving on the inner divertor. As a result, heat convection is found to be an important player in this region, consistent with the observation of divertor asymmetries that depend on the direction of B × ∇B relative to the active x-point. In contrast, the poloidal projection of parallel flow in the low-field SOL largely cancels with Er × B flow; toroidal rotation is the dominant plasma motion there. The magnitude of the transport-driven poloidal flow is found to be quantitatively consistent with fluctuation-induced radial particle fluxes on the low-field side (LFS), identifying this as the primary drive mechanism. Fluctuation-induced fluxes on the HFS are found to be essentially zero, excluding turbulent inward transport as the mechanism that closes the circulation loop in this region.

Analysis of the temperature influence on Langmuir probe measurements on the basis of gyrofluid simulations

The influence of the temperature and its fluctuations on the ion saturation current and the floating potential, which are typical quantities measured by Langmuir probes in the turbulent edge region of fusion plasmas, is analysed by global nonlinear gyrofluid simulations for two exemplary parameter regimes. The numerical simulation facilitates a direct access to densities, temperatures and the plasma potential at different radial positions around the separatrix. This allows a comparison between raw data and the calculated ion saturation current and floating potential within the simulation. Calculations of the fluctuation-induced radial particle flux and its statistical properties reveal significant differences to the actual values at all radial positions of the simulation domain, if the floating potential and the temperature-averaged density inferred from the ion saturation current is used.

Practical solutions for reliable triple probe measurements in magnetized plasmas

The triple probe method to obtain local, time-resolved measurements of density, electron temperature and plasma potential is investigated in detail. The difficulties in obtaining reliable measurements with this technique are discussed and overcome. These include phase delay errors, ion sheath expansion and limited bandwidth due to stray capacitance to ground. In particular, a relatively simple electronic circuit is described to strongly reduce stray capacitance. Measurements with the triple probe are presented in a plasma characterized by interchange-driven turbulence in the TORPEX device. The measured time-averaged and time-dependent, conditionally averaged parameters are cross-checked with other Langmuir probe based techniques, and show good agreement. Triple probe measurements show that electron temperature fluctuations are sufficiently large, such that the identification of plasma potential fluctuations with fluctuations of the floating potential is not a good approximation. Over a large radial region, the time-averaged fluctuation-induced particle flux can, however, be deduced from floating potential only. This is because the phase shift between density and electron temperature is close to zero there and temperature fluctuations do not give rise to a net radial particle transport.

Experimental investigations of turbulent structure propagation across a [formula omitted]-velocity shear

The influence of an externally generated E × B shear flow on the propagation of structures in drift-wave turbulence is investigated in a linear laboratory plasma device. Spatiotemporal studies of the dynamics of turbulent structures reveal that structures have a radial component of propagation, thereby contributing mainly to the fluctuation induced particle flux and leading to intermittent density fluctuations in the edge plasma. A radially localized radial E × B -velocity shear layer is generated by a biased emissive filament. The shear layer modifies the phase between density and potential fluctuations, which results in a reduction of transport driven by electrostatic turbulence. A shear decorrelation of the structures, i.e. a decrease of their radial correlation length, is not observed.

Measurement of magnetic fluctuation-induced particle flux (invited)

Magnetic field fluctuation-induced particle transport has been directly measured in the high-temperature core of the MST reversed field pinch plasma. Measurement of radial particle transport is achieved by combining various interferometry techniques, including Faraday rotation, conventional interferometry, and differential interferometry. It is observed that electron convective particle flux and its divergence exhibit a significant increase during a sawtooth crash. In this paper, we describe the basic techniques employed to determine the particle flux.

Laser-heated emissive plasma probe

Emissive probes are standard tools in laboratory plasmas for the direct determination of the plasma potential. Usually they consist of a loop of refractory wire heated by an electric current until sufficient electron emission. Recently emissive probes were used also for measuring the radial fluctuation-induced particle flux and other essential parameters of edge turbulence in magnetized toroidal hot plasmas [R. Schrittwieser et al., Plasma Phys. Controlled Fusion 50, 055004 (2008)]. We have developed and investigated various types of emissive probes, which were heated by a focused infrared laser beam. Such a probe has several advantages: higher probe temperature without evaporation or melting and thus higher emissivity and longer lifetime, no deformation of the probe in a magnetic field, no potential drop along the probe wire, and faster time response. The probes are heated by an infrared diode laser with 808 nm wavelength and an output power up to 50 W. One probe was mounted together with the lens system on a radially movable probe shaft, and radial profiles of the plasma potential and of its oscillations were measured in a linear helicon discharge.

Cross-Field Transport by Instabilities and Blobs in a Magnetized Toroidal Plasma

The mechanisms for anomalous transport across the magnetic field are investigated in a toroidal magnetized plasma. The role of plasma instabilities and macroscopic density structures (blobs) is discussed. Examples from a scenario with open magnetic field lines are shown. A transition from a main plasma region into a loss region is reproduced. In the main plasma, which includes particle and heat source locations, the transport is dominated by the fluctuation-induced particle and heat flux associated with a plasma instability. On the low-field side, the cross-field transport is ascribed to the intermittent ejection of macroscopic blobs propagating toward the outer wall. It is shown that instabilities and blobs represent fundamentally different mechanisms for cross-field transport.

Turbulence and transport measurements with cold and emissive probes in ISTTOK

A probe array consisting of three emissive probes and one cold cylindrical probe was developed for edge plasma measurements in ISTTOK. Emissive probes are particularly suitable for turbulence studies as they are able to deliver a more accurate measure of the plasma potential by reducing the effect of temperature fluctuations. The probe array has the advantage of recording the density, the electric field and their fluctuations simultaneously. Radial plasma profiles were recorded with and without negative edge biasing by an emissive electrode. The statistical properties of the poloidal electric field and of the turbulent particle flux, measured with cold and emissive probes, were compared. Both the root mean square of the poloidal electric field and the fluctuation-induced particle flux were found to be significantly larger when measured with the emissive probes, indicating that temperature fluctuations are important for the measurement of the particle flux. The probability distribution of the particle flux was also found to be more peaked and asymmetric when measured with the emissive probes.

Edge fluctuation studies in Heliotron J

Low frequency and small-scale fluctuations of density and potential near the last closed flux surface are investigated by using Langmuir probes for the second harmonic ECH plasmas in a helical-axis heliotron device, Heliotron J. The existence of a plasma layer with a radial electric field shear was indicated near the last closed flux surface. Near this layer, the reversal of phase velocity and de-correlation of the fluctuations were observed. On the other hand, it is suggested that a considerable fraction of the fluctuation induced particle flux is carried off through the intermittent events. Preliminary analyses to classify the PDFs of the ion-saturation current fluctuation as stable Lévy distributions demonstrate that the Lévy index decreases from the inner to the outer region of edge plasma, suggesting that the PDFs near the boundary region of Heliotron J are nearly Gaussian, whereas at the outer regions of plasma they become strongly non-Gaussian.

On the interpretation of fluctuation and E×B turbulent transport measured by Langmuir probes in fusion plasmas

Plasma fluctuations and fluctuation-induced particle fluxes have been investigated in the plasma edge of the TJ-II stellarator using Langmuir probes. Simultaneous measurements of plasma fluctuations carried out by probes located in and out of the probe body sheath show similar results in the normalized level of fluctuations in the ion saturation current. However, floating potential fluctuations measured in the co and counter direction of the magnetic field on the sheath probe body show slight but significant differences. The local radial electrostatic turbulent driven transport measured in and out of the probe body sheath shows consistent results, within the errors bars due to uncertainties in the determination of the effective probe collecting area; the normalized local radial transport to the average ion saturation current (the effective velocity which is not affected by uncertainties in the probe area) show consistent results. These results and previous findings call into question the recent interpretation of probe measurements on the basis of the influence of the probe’s pre-sheath zone [B. Labombard, Phys. Plasmas. 9, 1300 (2002)].

Peripheral fluctuations and particle transport during an L-H transition in the FT-2 tokamak

Experimental data on the processes in edge plasma that accompany the transition to an improved confinement regime during lower hybrid heating in the FT-2 tokamak are presented. The poloidal and radial distributions of the plasma parameters and drift particle fluxes were measured with the use of mobile mulitielectrode Langmuir probes and were found to be substantially nonuniform in the poloidal direction. The evolution of the plasma parameters in the course of heating and during an L-H transition is investigated. It is shown that, in FT-2 experiments, the drift of plasma particles in a slowly varying (quasi-steady) electric field and the fluctuation-induced particle fluxes make comparable contributions to the radial particle transport, whereas the contribution of fluctuations to poloidal plasma fluxes is negligibly small. The effective coefficient of radial diffusion is determined. The measurement results show that the L-H transition is accompanied by a substantial decrease in this coefficient.

An interpretation of fluctuation induced transport derived from electrostatic probe measurements

Fluctuation-induced particle fluxes (Γñφ̃) in the edge of Alcator C-Mod [Phys. Plasmas 1, 1511 (1994)] are inferred from a fast-scanning probe using standard analysis techniques. The magnitude and profile shape of Γñφ̃ is clearly inconsistent with fluxes inferred from global particle and power balance. These differences are difficult to reconcile if Γñφ̃ is interpreted as a measure of the particle flux in the unperturbed plasma. However, if Γñφ̃ is reinterpreted as the particle flux which must “fill-in” the presheath zone formed by the probe, these inconsistencies are eliminated. In this case, an effective diffusivity in the presheath zone (Dps) can be estimated from Γñφ̃. Dps is found to be in the range of diffusivities inferred from global particle balance (DSOL), indirectly supporting the hypothesis. However, the profile of Dps and its dependency on discharge conditions are markedly different than DSOL, implying that Dps is also not simply related to transport in the unperturbed plasma.

Structure and properties of the electrostatic fluctuations in the far scrape-off layer region of Alcator C-Mod

The temporal statistics of density and potential fluctuations measured in both the main chamber and divertor far scrape-off layer (SOL) regions (>5 mm outside the magnetic separatrix) of the Alcator C-Mod tokamak [I. M. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] are found to change markedly with plasma density. As the plasma density is increased, the fluctuations become correlated over long and short time scales and exhibit a higher level of persistence and intermittency. Correspondingly, fluctuation-induced cross-field particle fluxes are found to increase by a factor of ∼5 when the plasma density is doubled. These observations are consistent with results from SOL particle balance, which indicate an increased level of cross-field transport as the density is raised. These observations also support the idea that SOL transport dynamics behave as a self-organized system, particularly at high plasma densities.

An investigation of density fluctuations and electron transport in the Madison Symmetric Torus reversed-field pinch

The origin of large scale density fluctuations and their role in electron transport has been investigated in the Madison Symmetric Torus reversed-field pinch [R. N. Dexter et al., Fusion Tech. 19, 131 (1991)]. At medium frequencies (10–30 kHz), ñ is associated with core-resonant magnetic fluctuations having poloidal mode number m=1 and toroidal mode numbers n=6–10. These chord-averaged density fluctuations are shown to be coherent with large scale radial flow fluctuations, permitting fluctuation-induced particle flux of the form 〈ñṽr〉 to be studied. In the edge, although amplitudes are large, ñ and ṽr are out of phase, consistent with advection of the mean density gradient by perturbed magnetic field lines and no electron transport. During improved confinement discharges, produced by inductive current drive, both fluctuation amplitudes and the total radial electron flux are greatly reduced over the entire plasma cross section.

Radial electrostatic flux inferred from core measurements of potential and density fluctuations

Broadband potential fluctuations and electrostatic fluctuation induced particle flux have been measured in the core of a medium size tokamak plasma for the first time. Density fluctuations and wave numbers were simultaneously measured. Measurements indicate that radial electrostatic fluctuation induced particle flux in the core region, at the normalized radii of 0.17<ρ<0.38, due to modes with wave numbers less than 4 cm−1 is small in magnitude, is likely directed inward, and cannot account for particle flux predicted by the continuity equation and particle source codes. Estimates of electrostatic energy flux are also significantly less than values predicted via power balance analysis. Asymmetries in coherent density and potential fluctuation levels on closed flux surfaces are evident. Relative fluctuation levels ñ/n and φ̃ tend to increase with radius, and the fluctuations are Boltzmann-like in the region 0.17⩽ρ⩽0.38. The direction of mode propagation is in the electron diamagnetic drift direction. Corresponding phase velocities, vph∼3.5×105 cm/s, are similar to drift wave velocities.

Modelling of the Effect of the Sheared Poloidal Flow on the Electrostatic Turbulence on the CASTOR Tokamak

Electrostatic drift turbulence of the edge plasma in the CASTOR tokamak is studied numerically by using the Hasegawa-Wakatani equations. The fluctuations of plasma density and potential as well as the corresponding fluctuation-induced particle flux are calculated for regimes with various plasma poloidal flows. Results of numerical simulations are in a reasonable agreement with experimental results.

Anomalous transport in tokamaks: examples of its suppression

Studies conducted towards an understanding of improved plasma confinement in small and large tokamaks are presented. In STOR-M, Ohmic H-modes can be induced by various means. The most recent finding is that injection of a high density compact torus triggers a sustained H-mode. For bias induced H-mode, direct evaluation of fluctuation induced particle flux has been made for Ohmic H-modes. The particle flux is intermittent and the average changes its sign from radially outward in L-mode to radially inward in H-mode. The direction and magnitude of the flux are predominantly determined by the phase difference between the density and potential fluctuations. Nonlinear correlation studies have also been made between two radial positions. In L-mode, the inner region behaves as a master and outer region as slave. In H-mode, the relationship is reversed.For high performance negative shear discharges in large tokamaks, the radial derivative of the Shafranov shift Δ′ is shown to have efficient stabilizing influence on the trapped electron drift mode and kinetic ballooning mode (KBM). The ion temperature gradient (ITG) mode is well stabilized at a modest α (the ballooning parameter).