Radial Electric Field Structure Research Articles

Nonlinear frequency chirping and radial restructure of the ion-temperature-gradient-driven turbulence

Global nonlinear gyrokinetic simulation of the ion-temperature-gradient (ITG) modes clearly demonstrates the nonlinear phase-space resonance, which can be well understood by the nonlinear frequency chirping due to the nonlinear poloidal acceleration of resonant particles by the large-scale structure of radial electric field rather than the widely discussed local shearing effects of the zonal flows. The nonlinear radial restructure of a single-n ITG mode generates multiple daughter-ballooning-modes.

Hydrogen isotope effect on self-organized electron internal transport barrier criticality and role of radial electric field in toroidal plasmas

Self-organized structure formation in magnetically confined plasmas is one of the most attractive subjects in modern experimental physics. Nonequilibrium media are known to often exhibit phenomena that cannot be predicted by superposition of linear theories. One representative example of such phenomena is the hydrogen isotope effect in fusion plasmas, where the larger the mass of the hydrogen isotope fuel is the better the plasma confinement becomes, contrary to what simple scaling models anticipate. In this article, threshold condition of a plasma structure formation is shown to have a strong hydrogen isotope effect. To investigate the underlying mechanism of this isotope effect, the electrostatic potential is directly measured by a heavy ion beam probe. It is elucidated that the core electrostatic potential transition occurs with less input power normalized by plasma density in plasmas with larger isotope mass across the structure formation. This observation is suggestive of the isotope effect in the radial electric field structure formation.

Characterization of isotope effect on ion internal transport barrier and its parameter dependence in the Large Helical Device

In this paper, the background physics of the isotope effects in the ion internal transport barrier (ITB) are discussed in detail. An heuristic criterion for the ITB strength is defined based on the nonlinear dependence of the ion thermal diffusivity on the local ion temperature in the L-mode phase. Comparing deuterium plasmas and hydrogen plasmas, two isotope effects on the ion ITB are clarified: stronger ITBs formed in the deuterium plasmas and an ITB concomitant edge confinement degradation in the hydrogen plasmas. Principal component analysis reveals that the ion ITB becomes strong when a high input power normalized by the line averaged electron density is applied and electron density profile is peaked. A gyrokinetic simulation suggests that the ITB profile is determined by the ion temperature gradient driven turbulence, while the way the profile saturates in L-mode plasmas is unknown. In the electron density turbulence behavior, a branch transition is observed, where the increasing trend in turbulence amplitude against the ITB strength is flipped to a decreasing trend across the ITB formation. The radial electric field structure is measured by the charge exchange recombination spectroscopy system. It is found that the radial electric field shear plays a minor role in determining the ITB strength.

Structure of the JET edge radial electric field in He and D plasmas

Perpendicular velocity, v ⊥, measurements have been obtained in JET experiments designed to investigate the underlying mechanisms influencing the L–H power threshold. L–H transitions were induced by using both NBI and ICRH in deuterium and helium plasmas. The v ⊥ profile in the low density branch of the L–H transition has a modest or even no well and a marked peak near the separatrix in NBI heated discharges for both D and He plasmas, with a sharper SOL peak for He plasmas. As the line-averaged density increases, the SOL v ⊥ peak decreases, in agreement with the modifications in the electron temperature profile at the divertor target, while the v ⊥ well becomes deeper. Nevertheless, even in the high density branch, a shallow v ⊥ well is found at the L–H transition, v ⊥ ∼ 1–2 km s−1, which is lower by a factor of about two than the contribution from the diamagnetic term. No evidence for the existence of a critical value in v ⊥ is found at JET, particularly for helium plasmas. This may be explained by the existence of an edge toroidal flow relevant mainly at low density where the power threshold is high. In addition, no significant change in the edge v ⊥ is measured preceding the L–H transition.

Frequency and plasma condition dependent spatial structure of low frequency global potential oscillations in the TJ-II stellarator

In this letter, we investigate the spatial structure of a low frequency global potential oscillation, which is likely ascribed as the low frequency zonal flows, in TJ-II laboratory plasmas. In two plasmas produced by different heating schemes (electron cyclotron resonance heating and neutral beam injection heating) and characterized by different mean radial electric field structures, frequency-space-decomposed spectra of the global potential oscillation are obtained. In both cases, the oscillatory field has a single-peaked potential structure and a dipole radial electric field structure. The oscillating structure depends on its frequency as well as on the heating scheme.

Experimental evidence of edge intrinsic momentum source driven by kinetic ion loss and edge radial electric fields in tokamaks

Bulk ion toroidal velocity profiles, V||D+, peaking at 40–60 km/s are observed with Mach probes in a narrow edge region of DIII-D discharges without external momentum input. This intrinsic rotation can be well reproduced by a first principle, collisionless kinetic loss model of thermal ion loss that predicts the existence of a loss-cone distribution in velocity space resulting in a co-Ip directed velocity. We consider two kinetic models, one of which includes turbulence-enhanced momentum transport, as well as the Pfirsch-Schluter (P-S) fluid mechanism. We measure a fine structure of the boundary radial electric field, Er, insofar ignored, featuring large (10–20 kV/m) positive peaks in the scrape off layer (SOL) at, or slightly inside, the last closed flux surface of these low power L- and H-mode discharges in DIII-D. The Er structure significantly affects the ion-loss model, extended to account for a non-uniform electric field. We also find that V||D+ is reduced when the magnetic topology is changed from lower single null to upper single null. The kinetic ion loss model containing turbulence-enhanced momentum transport can explain the reduction, as we find that the potential fluctuations decay with radius, while we need to invoke a topology-enhanced collisionality on the simpler kinetic model. The P-S mechanism fails to reproduce the damping. We show a clear correlation between the near core V||C6+ velocity and the peak edge V||D+ in discharges with no external torque, further supporting the hypothesis that ion loss is the source for intrinsic torque in the present tokamaks. However, we also show that when external torque is injected in the core, it can complete with, and eventually overwhelm, the edge source, thus determining the near SOL flows. Finally, we show some additional evidence that the ion/electron distribution in the SOL is non-Maxwellian.

Edge plasma responses to energetic-particle-driven MHD instability in Heliotron J

Two different responses to an energetic-particle-driven magnetohydrodynamic (MHD) instability, modulation of the turbulence amplitude associated with the MHD instability and dynamical changes in the radial electric field (Er) synchronized with bursting MHD activities, are found around the edge plasma in neutral beam injection (NBI) heated plasmas of the Heliotron J device using multiple Langmuir probes. The nonlinear phase relationship between the MHD activity and broadband fluctuation is found from bicoherence and envelope analysis applied to the probe signals. The structural changes of the Er profile appear in perfect synchronization with the periodic MHD activities, and radial transport of fast ions are observed around the last closed flux surface as a radial delay of the ion saturation current signals. Moreover, distortion of the MHD mode structure is clarified in each cycle of the MHD activities using beam emission spectroscopy diagnostics, suggesting that the fast ion distribution in real and/or velocity spaces is distorted in the core plasma, which can modify the radial electric field structure through a redistribution process of the fast ions. These observations suggest that such effects as a nonlinear coupling with turbulence and/or the modification of radial electric field profiles are important and should be incorporated into the study of energetic particle driven instabilities in burning plasma physics.

Helical modulation of the electrostatic plasma potential due to edge magnetic islands induced by resonant magnetic perturbation fields at TEXTOR

The electrostatic response of the edge plasma to a magnetic island induced by resonant magnetic perturbations to the plasma edge of the circular limiter tokamak TEXTOR is analyzed. Measurements of plasma potential are interpreted by simulations with the Hamiltonian guiding center code Orbit. We find a strong correlation between the magnetic field topology and the poloidal modulation of the measured plasma potential. The ion and electron drifts yield a predominantly electron driven radial diffusion when approaching the island X-point while ion diffusivities are generally an order of magnitude smaller. This causes a strong radial electric field structure pointing outward from the island O-point. The good agreement found between measured and modeled plasma potential connected to the enhanced radial particle diffusivities supports that a magnetic island in the edge of a tokamak plasma can act as convective cell. We show in detail that the particular, non-ambipolar drifts of electrons and ions in a 3D magnetic topology account for these effects. An analytical model for the plasma potential is implemented in the code Orbit, and analyses of ion and electron radial diffusion show that both ion- and electron-dominated transport regimes can exist, which are known as ion and electron root solutions in stellarators. This finding and comparison with reversed field pinch studies and stellarator literature suggest that the role of magnetic islands as convective cells and hence as major radial particle transport drivers could be a generic mechanism in 3D plasma boundary layers.

On the spatial structure of solitary radial electric field at the plasma edge in toroidal confinement devices

The solitary radial electric field in the edge of toroidal plasma is studied based on the electric field bifurcation model. Results are applied to tokamak and helical plasmas, and the dependence of the electric field structure on the plasma parameters and geometrical factors is analyzed. The order of magnitude estimate for tokamak plasma is not far from experimental observations. It is shown that, in helical plasmas, the height of electric field structure is reduced substantially owing to the ripple particle transport, while the width is influenced less. The implications of the results for the limit of achievable gradient in the H-mode pedestal are also discussed.

Observation of multi-scale turbulence and non-local transport in LHD plasmas

We have studied two types of spatio-temporal turbulence dynamics in plasmas in the Large Helical Device, based on turbulence measurements with high spatial and temporal resolution. Applying conditional ensemble-averaging to a plasma with Edge-Localized Modes (ELMs), fast radial inward propagation of a micro-scale turbulence front is observed just after ELM event, and the propagation speed is evaluated as ∼100 m/s. A self-organized radial electric field structure is observed in an electrode biasing experiment, and it is found to realize a multi-valued state. The curvature of the radial electric field is found to play an important role for turbulence reduction.

Characterization of edge radial electric field structures in the Large Helical Device and their viability for determining the location of the plasma boundary

This paper provides a systematic investigation on how plasma conditions (magnetic configuration, collisionality and beta) affect the edge radial electric field (Er) structure derived from charge exchange spectroscopic measurements in the Large Helical Device. We found that the location at which the spatial derivative in the Er structure (∇Er) had a local maximum value shifts outwards from the vacuum last closed flux surface location as the volume-averaged plasma beta (the ratio of the plasma pressure to the magnetic pressure, β ≡ 〈βdia〉 measured by a diamagnetic loop) becomes large. The loss of electrons on the open field lines, leaving the ions behind, might be the physics that determines the positive Er structure just outside the plasma boundary. The collisionality dependence of the experimentally observed Er values inside the plasma boundary is found to be consistent with a neoclassical ambipolar condition, while the Er formation outside the plasma boundary is different from the trend that is predicted by the neoclassical theory inside the plasma boundary. Furthermore, experimental data on saturation in the shift of the location even in a higher β regime (3% ⩽ β ⩽ 4.5%) are presented, inferring and predicting shrinkage of the plasma (i.e. a reduction in the averaged minor radius) in the higher β regime in which the Shafranov shift becomes larger.

Modifications to the edge radial electric field by angular momentum injection in JT-60U and their implication for pedestal transport

The first detailed measurements of ion-impurity dynamics for NBI-heated ELMy H-modes at the edge of the JT-60U tokamak are reported. We investigated the ability of external momentum/power input to modify and control the radial electric field, Er, and pedestal structures. The relationship between Er and pedestal structures of ion-impurity density, ni, and temperature, Ti, during the ELMing H-mode phase for various momentum input directions (i.e. co-, balanced- and counter-NBI) and input powers from perpendicular NBI are compared with the ELM-free phase. The observed trend is that the edge Er-well width increases in the co-NBI discharge, while the Er value at the base of the Er-well becomes more negative in the counter-NBI discharge. The scale length for both ni and Ti in the pedestal is ∼2 cm and values are ∼1 for both ELM-free and ELMing phases with different magnitudes of Er (and/or Er shear). Characteristics of the turbulent density fluctuation, in addition to a uniform toroidal MHD oscillation (i.e. n = 0), during both ELM-free and ELMing phases are also reported.

Ion-cyclotron range of frequencies in the scrape-off-layer: fine structure radial electric fields

Gas-puff-imaging techniques are utilized to detect radial electric field structures in the scrape-off-layer (SOL) of the Alcator C-Mod tokamak via the observation of poloidal motion of advected fluctuations. When the diagnostic's field of view is magnetically connected to the ion-cyclotron range of frequencies (ICRF) active antennas, large (up to 8 km s−1) poloidal velocities are observed in a radial region encompassing both field lines terminating on and those passing in front of the antennas. The radial electric field switches sign indicating a peak in the potential profile corresponding to the transition from piercing to passing field lines. The electric field extends a few centimeters into the SOL and its local magnitude is of order Er ≈ 20–30 kV m−1. The corresponding plasma potentials scale as the square root of RF power; the poloidal structure is peaked when the field lines are connected to the top and bottom of the antenna. This structure is consistent with the presence of potential structures arising as a consequence of sheath rectification of the RF waves. The most striking result, however, is that the radial penetration λ⊥ of the potential structures is an order of magnitude larger than the basic theoretical expectation (λ⊥ ≈ 10δe, where δe is the skin depth). This substantial broadening is expected to have a strong impact on RF impurity physics. A (weak) power dependence observed in the width of the poloidal velocity features is explained as a competition between the RF induced and the background potential gradients.

Numerical simulation of current-free double layers created in a helicon plasma device

Two-dimensional simulations reveal that when radially confined source plasma with magnetized electrons and unmagnetized ions expands into diverging magnetic field B, a current-free double layer (CFDL) embedded in a conical density structure forms, as experimentally measured in the Australian helicon plasma device (HPD). The magnetized electrons follow the diverging B while the unmagnetized ions tend to flow directly downstream of the source, resulting in a radial electric field (E⊥) structure, which couples the ion and electron flows. Ions are transversely (radially) accelerated by E⊥ on the high potential side of the double layer in the CFDL. The accelerated ions are trapped near the conical surface, where E⊥ reverses direction. The potential structure of the CFDL is U-shaped and the plasma density is enhanced on the conical surface. The plasma density is severely depleted downstream of the parallel potential drop (φ||o) in the CFDL; the density depletion and the potential drop are related by quasi-neutrality condition, including the divergence in the magnetic field and in the plasma flow in the conical structure. The potential and density structures, the CFDL spatial size, its electric field strengths and the electron and ion velocities and energy distributions in the CFDL are found to be in good agreements with those measured in the Australian experiment. The applicability of our results to measured axial potential profiles in magnetic nozzle experiments in HPDs is discussed.

Simulation of small size divertor tokamak plasma edge at low density of plasma

A low density plasma edge of small size divertor tokamak has been modeling by “B2SOLPS0.5.2 D” fluid transport code. The results of modeling are: 1) Formation of the strong “ITB” has detected more reliable with discovery that, low density plasma is necessary and important condition for it to form. 2) Reduction of plasma density play significantly role in the formation of the strong ITB as global parameter, possibly through change in the steep density gradient which stabilize “ITG” mode. 3) The radial electric field of small size divertor tokamak plasma edge is plasma density dependence and maximum radial electric field shear is found at low plasma density. 4) In the “NBI” discharge the toroidal (parallel) velocity at low plasma density is co-current and upward direction. 5) The structure of plasma pressure and radial electric field in quiescent H-mode are obtained.

Overview of results from the Large Helical Device

The physical understanding of net-current-free helical plasmas has progressed in the Large Helical Device (LHD) since the last Fusion Energy Conference in Geneva, 2008. The experimental results from LHD have promoted detailed physical documentation of features specific to net-current-free 3D helical plasmas as well as complementary to the tokamak approach. The primary heating source is neutral beam injection (NBI) with a heating power of 23 MW, and electron cyclotron heating with 3.7 MW plays an important role in local heating and power modulation in transport studies. The maximum central density has reached 1.2 × 1021 m−3 due to the formation of an internal diffusion barrier (IDB) at a magnetic field of 2.5 T. The IDB is maintained for 3 s by refuelling with repetitive pellet injection. In a different operational regime with moderate density less than 2 × 1019 m−3, a plasma with a central ion temperature reaching 5.6 keV exhibits the formation of an internal transport barrier (ITB). The ion thermal diffusivity decreases to the level predicted by neoclassical transport. In addition to the rotation driven by the momentum input due to tangential NBI, the existence of intrinsic torque to drive toroidal rotation is identified in the plasma with an ITB. This ITB is accompanied by an impurity hole which generates an impurity-free core. The impurity hole is due to a large outward convection of impurities in spite of the negative radial electric field. The magnitude of the impurity hole is enhanced in the magnetic configuration with a large helical ripple and for heavier atoms. Another mechanism for suppressing impurity contamination is identified at the plasma edge with a stochastic magnetic field. A helical system shares common physics issues with tokamaks such as 3D equilibria, transport in a stochastic magnetic field, plasma response to a resonant magnetic perturbation, divertor physics and the role of radial electric field and meso-scale structure.

Spatio-temporal structure of the edge radial electric field during H-mode in JT-60U

Charge exchange recombination spectroscopy measurements with high spatial and temporal resolution have made the evaluation of the radial electric field (Er) in the JT-60U tokamak peripheral region possible with a better signal-to-noise ratio. In a very low density (<1 × 1019 m−3) L-mode phase, the gradient in Er (or, equivalently, in poloidal rotation, Vθ) was found to start increasing prior to an increase in the ion temperature (Ti). As the Er values in the region r/a > 0.94 started to become negative, down to −40 kV m−1 (similar to Vϕ), the steepening of the Ti profile in the same region accelerated. Even though the numerical value of Vϕ was considerably smaller than that of Vθ, its contribution to shear could be significant: while for r/a ⩾ 0.90 Vϕ became increasingly negative; it simultaneously became increasingly positive for r/a < 0.90. Clean bifurcations in the edge Er values between weak negative and strong negative ones were observed in the later ELM-free H-mode phase, with essentially the same confinement properties corresponding to two very different E × B shearing rates. The ‘normal’ ELMy H-mode took place only after the bifurcations. The results indicate that energy confinement improvement may not necessarily be connected to E × B shear suppression of turbulence.

Simulation of small size divertor tokamak plasma edge under effect of toroidal magnetic field reversal

Asymmetries between the divertor legs of small size divertor (SSD) tokamak plasma edge are noticed to reverse when the direction of toroidal magnetic field is reversed. In the present paper the small size divertor tokamak plasma edge under effect of toroidal magnetic field reversal is simulated by B2SOLPS0.5.2D fluid transport code. The simulation demonstrate the following results: 1) Parallel (toroidal) flow flux and Mach number up to 0.6 at higher plasma density reverse with reverse toroidal magnetic direction in the edge plasma of small size divertor tokamak. 2) The radial electric field is toroidal magnetic direction independence in edge plasma of small size divertor tokamak. 3) For normal and reverse toroidal magnetic field, the strong ITB is located between the positions of the maximum and minimum values of the radial electric field shear. 4) Simulation result shows that, the structure of radial electric field at high field side (HFS) and low field side (LFS) is different. This difference result from the change in the parallel flux flows in the scrape off layer (SOL) to plasma core through separatrix. 5) At a region of strong radial electric field shear, a large reduction of poloidal rotation was observed. 6) The poloidal rotation is toroidal magnetic field direction dependence.

Edge radial electric field structure and its connections to H-mode confinement in Alcator C-Mod plasmas

High-resolution charge-exchange recombination spectroscopic measurements of B5+ ions have enabled the first spatially resolved calculations of the radial electric field (Er) in the Alcator C-Mod pedestal region [E. S. Marmar, Fusion Sci. Technol. 51, 261 (2006)]. These observations offer new challenges for theory and simulation and provide for important comparisons with other devices. Qualitatively, the field structure observed on C-Mod is similar to that on other tokamaks. However, the narrow high-confinement mode (H-mode) Er well widths (5 mm) observed on C-Mod suggest a scaling with machine size, while the observed depths (up to 300 kV/m) are unprecedented. Due to the strong ion-electron thermal coupling in the C-Mod pedestal, it is possible to infer information about the main ion population in this region. The results indicate that in H-mode the main ion pressure gradient is the dominant contributor to the Er well and that the main ions have significant edge flow. C-Mod H-mode data show a clear correlation between deeper Er wells, higher confinement plasmas, and higher electron temperature pedestal heights. However, improved L-mode (I-mode) plasmas exhibit energy confinement equivalent to that observed in similar H-mode discharges, but with significantly shallower Er wells. I-mode plasmas are characterized by H-mode-like energy barriers, but with L-mode-like particle barriers. The decoupling of energy and particle barrier formation makes the I-mode an interesting regime for fusion research and provides for a low collisionality pedestal without edge localized modes.

Observation of the parametric-modulational instability between the drift-wave fluctuation and azimuthally symmetric sheared radial electric field oscillation in a cylindrical laboratory plasma

Observation of the parametric-modulational interaction between the drift-wave fluctuation (7–8 kHz) and azimuthally symmetric sheared radial electric field structure (∼0.4 kHz) in a cylindrical laboratory plasma is presented. Oscillation of the sheared radial electric field is synchronized at modulations of the radial wave number and Reynolds stress per mass density of the drift-wave spectrum. Bispectral analysis at the location where the sheared radial electric field has finite radial wave numbers shows that nonlinear energy transfers from the drift wave to the sheared radial electric field occur. Nonlocal energy transfers of fluctuations via “channel of the azimuthally symmetric sheared radial electric field” in spectral space as well as real space are discovered.