Search

Heavy ion beam probe (HIBP) systems have been designed for the new tokamak, PLATO [A. Fujisawa, AIP Conf. Proc. 1993, 020011 (2018)]. The designs have been completed, and the installations are in progress. Two HIBPs are being installed in toroidal sections 180° apart to investigate long-range correlations in the toroidal direction. Each HIBP consists of an injection beamline and a detection beamline as usual. Yet, one of the HIBPs is equipped with an additional detection beamline; the measurement positions of its two detection beamlines can be placed on almost the same magnetic surface yet at poloidal angles that differ by ∼180°. The use of three detection beamlines allows us to investigate spatial asymmetry and long-range correlations in both the toroidal and poloidal directions, simultaneously. The detected beam intensity is expected to be enough for turbulence measurements in almost the entire plasma region when the electron density is up to 1 × 1019 m−3 by selecting appropriate ion species for the probe beam. Each detector has three channels 10 mm apart, allowing measurement of local structures of micro-scale turbulence. Therefore, using the HIBPs on the PLATO tokamak will enable both local and global properties of plasma turbulence to be investigated, simultaneously.

A tomography system is installed as one of the diagnostics of new age to examine the three-dimensional characteristics of structure and dynamics including fluctuations of a linear magnetized helicon plasma. The system is composed of three sets of tomography components located at different axial positions. Each tomography component can measure the two-dimensional emission profile over the entire cross-section of plasma at different axial positions in a sufficient temporal scale to detect the fluctuations. The four-dimensional measurement including time and space successfully obtains the following three results that have never been found without three-dimensional measurement: (1) in the production phase, the plasma front propagates from the antenna toward the end plate with an ion acoustic velocity. (2) In the steady state, the plasma emission profile is inhomogeneous, and decreases along the axial direction in the presence of the azimuthal asymmetry. Furthermore, (3) in the steady state, the fluctuations should originate from a particular axial position located downward from the helicon antenna.

This paper presents the experimental identification of the dynamic interaction between three fluctuations excited by different thermodynamical forces in a linear plasma. The observed fluctuations are characterized as an axial symmetric mode, a drift wave, and an azimuthally symmetric potential fluctuation from the spatiotemporal structures measured with Langmuir probe arrays. The intermittent burst of the axial symmetric mode is observed by the instantaneous wave number spectrum. The energy transfer analysis revealed that the axially symmetric mode gains energy from the other mode during the burst while the drift wave loses energy. The intermittent burst synchronizes with the azimuthal symmetric potential fluctuation.

This article assesses current understanding of hysteresis in transport relations, and its impact on the field. The rapid changes of fluxes compared to slow changes of plasma parameters are overviewed for both core and edge plasmas. The modulation ECH experiment is explained, in which the heating power cycles on-and-off periodically, revealing hysteresis and fast changes in the gradient–flux relation. The key finding is that hystereses were observed simultaneously in both the the gradient–flux and gradient–fluctuation relations. Hysteresis with rapid timescale exists in the channels of energy, electron and impurity densities, and plausibly in momentum. Advanced methods of data analysis are explained. Transport hysteresis can be studied by observing the higher harmonics of temperature perturbation in heating modulation experiments. The hysteresis introduces the term , which depends on the harmonic number m in an algebraic manner (not exponential decay). Next, the causes of hysteresis and its fast timescale are discussed. The nonlocal-in-space coupling works here, but does not suffice. One mechanism for 'the heating heats turbulence' is that the external source S in phase space for heating has its fluctuation in turbulent plasma. This coupling can induce the direct input of heating power into fluctuations. The height of the jump in transport hysteresis is smaller for heavier hydrogen isotopes, and could be one of the origins of isotope effects on confinement. Finally, the impacts of transport hysteresis on the control system are assessed. Control systems must be designed so as to protect the system from sudden plasma loss.

A three-dimensional turbulence simulation is performed in order to understand the role of spiral structures observed in Kelvin-Helmholtz turbulence. The simulation is performed by introducing a vorticity source to drive the plasma rotation. By scanning the intensity of the vorticity source, a quasi-periodic formation of a spiral structure is obtained above a certain source intensity. The quasi-periodic oscillation can be seen in the fluctuation energy and the background, which exhibits a limit cycle oscillation. We clarify the roles of the spiral formation in the limit cycle oscillation: The dynamical change in the radial variation of the phase of the fluctuations causes a strong coupling of the fluctuations with the background through the transport of particles and momentum. The formation mechanism of the spiral structure is also studied. An instability due to the combination of the cylindrical effect and the flow inhomogeneity is consistent with the fluctuation which drives the spiral structure obtained in the simulation.A three-dimensional turbulence simulation is performed in order to understand the role of spiral structures observed in Kelvin-Helmholtz turbulence. The simulation is performed by introducing a vorticity source to drive the plasma rotation. By scanning the intensity of the vorticity source, a quasi-periodic formation of a spiral structure is obtained above a certain source intensity. The quasi-periodic oscillation can be seen in the fluctuation energy and the background, which exhibits a limit cycle oscillation. We clarify the roles of the spiral formation in the limit cycle oscillation: The dynamical change in the radial variation of the phase of the fluctuations causes a strong coupling of the fluctuations with the background through the transport of particles and momentum. The formation mechanism of the spiral structure is also studied. An instability due to the combination of the cylindrical effect and the flow inhomogeneity is consistent with the fluctuation which drives the spiral structure obtained...

The conditional average is a technique to extract a typical waveform from bursty or quasi-periodic phenomena regarded as a combination of deterministic trend and residual fluctuations (or probabilistic part). The article proposes a new conditional average technique that is an extension from what is called the template method that allows automatic selection, using the correlation analysis, of the identical events of the phenomena. The proposed method is applied on a quasi-periodic oscillation observed in a linear magnetized plasma, and successfully divides the phenomenon into the deterministic trend and residual fluctuations. Moreover, the statistical error analysis on the power of the residual fluctuations discloses the presence of mutual interactions between the deterministic trend and the residual fluctuations.

Theories to understand the steep and localized radial electric field in the edge of toroidal plasma, which appears in conjunction with H-mode, is revisited based on the electric field bifurcation model. Key elements in the models of the L-H transition (including the toroidal effects on the dielectric constant and the effects of the curvature of radial electric field on turbulence suppression) are assessed. Results are applied to tokamak and helical plasmas, for which data with high-resolution have been obtained recently. The status of quantitative tests on various mechanisms through comparison with experimental observations is also addressed. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Emission intensity \(\epsilon \) from plasmas is a complicated function of electron temperature Te and electron density ne. To understand the dependence of \(\epsilon \) on Te and ne, an experiment...

The neutral drag effect on the parallel velocity gradient driven instability (PVG) in the presence of density inhomogeneity is theoretically investigated. The dispersion relation of PVG mode with the effect of the density gradient and neutral particle drag is derived, and its solution is analytically obtained. The neutral particle drag gives rise to the phase shift between parallel flow and electrostatic potential fluctuations and modifies the parallel compression. As a result, the stability of the PVG mode changes. It is found that the neutral particle drag does not only reduce but also enhances the instability. Specifically, near the marginal condition, the neutral particle effect suppresses the density gradient effect, and the parameter region where the PVG mode is linearly unstable significantly expands.

In this paper, we evaluated electron temperature fluctuations by using a conditional sampling and a statistical phase detection method. These methods allow us to reconstruct probe I − V characteristics at each time delay; that is, we can extract electron temperature and ion saturation current fluctuations in high temporal resolution without complex electronic circuits. Our method was applied to two quasi-coherent fluctuations observed in a linear magnetized plasma device, PANTA. We observed spatiotemporal structures of electron temperature and ion saturation current fluctuations. The results revealed the amplitudes and phase relation between electron temperature and density fluctuations.

The fundamental mechanisms of plasma turbulence have been investigated in linear devices, which have simplified magnetic geometries. Our simulation researches, using fluid models for collisional plasmas, are described on competitive nature of plasma turbulence in this article. Multiple turbulent structures, multiple inhomogeneities of different particle species and multiple instability drives play important roles, and their competitions determine the nonlinear plasma states. Even in this simplified configuration, a variety of states can be attained, so the detailed studies are useful to understand the fundamental mechanisms of structural formation and bifurcation in the magnetically confined plasmas.

We propose a novel mechanism of enhancement of turbulence by energetic-particle-driven geodesic acoustic modes (EGAMs). The dynamics of drift-wave-type turbulence in the phase space is investigated by wave-kinetic equation. Spatially inhomogeneous turbulence in the presence of a transport barrier is considered. We discovered that trapping of turbulence clumps by the EGAMs is the key parameter that determines either suppress or enhance turbulence. In regions where turbulence is unstable, EGAM suppresses the turbulence. In contrast, in the stable region, EGAM traps clumps of turbulence and carries them across the transport barrier, so that the turbulence can be enhanced. The turbulence trapped by EGAMs can propagate independent of the gradients of density and temperature, which leads to non-Fickian transport. Hence, there appear a new global characteristic velocity, the phase velocity of GAMs, for turbulence dynamics, in addition to the local group velocity and that of the turbulence spreading. With these effect, EGAMs can deteriorate transport barriers and affect turbulence substantially. This manuscript provides a basis to consider whether a coherent wave breaks or strengthen transport barriers.

It is demonstrated that the zonal flow is controlled by the parallel flow in the cylindrical plasmas. A three-dimensional turbulence simulation is performed, based on the reduced fluid model. The background parallel flow is applied by introducing the time independent parallel momentum source. Changing the magnitude of the momentum source, the behavior of the zonal flow is investigated. The drift wave turbulence is affected by the parallel flow, and it shows the spatial competition between turbulence modes. The spatial competition appears/disappears abruptly, depending on the intensity of the parallel momentum source. As a consequence of the transition between the turbulence state, the radial profile of the turbulence drastically changes, which leads to the change of the turbulence force to drive the zonal flow. In this way, the parallel flow indirectly affects the zonal flow through the deformation of the turbulence.

The novel technique of dynamical mode decomposition (DMD) is applied to the outputs of a numerical simulation of Kelvin–Helmholtz turbulence in a cylindical plasma, so as to capture and quantify the time evolution of the dominant nonlinear structures. Empirically, these structures comprise rotationally symmetric deformations together with spiral patterns, and they are found to be identified as the main modes of the DMD. A new method to calculate the time evolution of DMD mode amplitudes is proposed, based on convolution-type correlation integrals, and then applied to the simulation outputs in a limit cycle regime. The resulting time traces capture the essential physics far better than Fourier techniques applied to the same data.\ud \ud

An analysis method is developed for imaging measurement systems, such as the tomography system or fast camera imaging, in order to extract the spatial structure properties of fluctuation. In this analysis method, rectangular functions and Fourier series are adopted for the basis functions of the radial and azimuthal coordinates, respectively. The examples of this analysis method show that this method is useful for quantifying the spatial structure of the 2D image such as the radial profile of the power and the rotation angle of each azimuthal mode. The method proposed in this article allows us to elucidate the features of the 2D spatial structure of phenomena in magnetized plasma.An analysis method is developed for imaging measurement systems, such as the tomography system or fast camera imaging, in order to extract the spatial structure properties of fluctuation. In this analysis method, rectangular functions and Fourier series are adopted for the basis functions of the radial and azimuthal coordinates, respectively. The examples of this analysis method show that this method is useful for quantifying the spatial structure of the 2D image such as the radial profile of the power and the rotation angle of each azimuthal mode. The method proposed in this article allows us to elucidate the features of the 2D spatial structure of phenomena in magnetized plasma.

We experimentally investigate the roles of drift wave type fluctuations interacting with zonal flow. The drift wave type fluctuations examined in this paper are characterized by nonlinear solitary wave, splash, and solitary eddy [Arakawa et al., Sci. Rep. 6, 33371 (2016)]. Compared to the nonlinear solitary wave, splash has a short lifetime, while solitary eddy has a long lifetime. Excitation/damping of the splash and the solitary eddy are synchronized with zonal perturbation. The roles of the splash and the solitary eddy in transport processes are also discussed. Solitary eddy contributes to momentum transport and accelerates zonal flow. The particle flux driven by the solitary eddy and the splash is in the inward and outward directions, respectively, with similar magnitudes.

The streamer-driven particle flux is evaluated experimentally in a linear cylindrical plasma. The streamers, a radially elongated and azimuthally localized structure created in turbulent plasma, really induce ballistic transport, and directly connect the plasma core to the edge within one order faster time scale than that of turbulence. The occurrence of large transport deviates from a Gaussian distribution and is likely to obey a power law. The fundamental plasma experiment clearly shows the significant and essential contributions of streamers to cross-field transport and structural formation of turbulent plasmas.The streamer-driven particle flux is evaluated experimentally in a linear cylindrical plasma. The streamers, a radially elongated and azimuthally localized structure created in turbulent plasma, really induce ballistic transport, and directly connect the plasma core to the edge within one order faster time scale than that of turbulence. The occurrence of large transport deviates from a Gaussian distribution and is likely to obey a power law. The fundamental plasma experiment clearly shows the significant and essential contributions of streamers to cross-field transport and structural formation of turbulent plasmas.

Turbulence and its structure formation are universal in neutral fluids and in plasmas. Turbulence annihilates global structures but can organize flows and eddies. The mutual-interactions between flow and the eddy give basic insights into the understanding of non-equilibrium and nonlinear interaction by turbulence. In fusion plasma, clarifying structure formation by Drift-wave turbulence, driven by density gradients in magnetized plasma, is an important issue. Here, a new mutual-interaction among eddy, drift wave and flow in magnetized plasma is discovered. A two-dimensional solitary eddy, which is a perturbation with circumnavigating motion localized radially and azimuthally, is transiently organized in a drift wave – zonal flow (azimuthally symmetric band-like shear flows) system. The excitation of the eddy is synchronized with zonal perturbation. The organization of the eddy has substantial impact on the acceleration of zonal flow.

The variety of scalar and vector fields in laboratory and nature plasmas is formed by plasma turbulence. Drift-wave fluctuations, driven by density gradients in magnetized plasmas, are known to relax the density gradient while they can generate flows. On the other hand, the sheared flow in the direction of magnetic fields causes Kelvin-Helmholtz type instabilities, which mix particle and momentum. These different types of fluctuations coexist in laboratory and nature, so that the multiple mechanisms for structural formation exist in extremely non-equilibrium plasmas. Here we report the discovery of a new order in plasma turbulence, in which chained structure formation is realized by cross-interaction between inhomogeneities of scalar and vector fields. The concept of cross-ferroic turbulence is developed and the causal relation in the multiple mechanisms behind structural formation is identified, by measuring the relaxation rate and dissipation power caused by the complex turbulence-driven flux.

A numerical measurement module simulating a heavy ion beam probe was developed, and numerical measurements of electrostatic potential and density fluctuations are carried out for 3-D turbulent data generated by a global simulation of drift-interchange mode turbulence in helical plasmas. The deviation between measured and local values is estimated. It is found that the characteristic structures can be detected in spite of the screening effect due to the finite spatial resolution.

Selection rule of the radial propagation direction of geodesic acoustic modes (GAMs) is investigated. Here, we study the influence of nonlinear coupling with drift wave turbulence on the propagation direction of GAMs. Based on wave-kinetic equation for the turbulence, the phase-space dynamics is numerically solved and the nonlinear saturated states are obtained, where the phase-space consists of the real space and the wavenumber space. A wave pattern of the GAM in a nonlinear saturated state varies to form a standing wave, outward and inward propagating waves, depending on the peak radial wavenumber of the turbulence. The impact of nonlinear coupling with turbulence is discussed by deriving the GAM dispersion relation that includes the effect of the turbulence.

Numerical diagnostics using 3-D simulation data are carried out to capture fluctuation properties in helical plasmas. Here Ion-Temperature-Gradient (ITG) turbulence data are used, obtained by the gyrokinetic code GKV-X with realistic magnetic configuration. Fluctuations are calculated in the field aligned coordinates, which have long wave lengths in the magnetic field direction and are anisotropic in the radial and poloidal directions, and their features are represented in the experimental frame. For the validation, the density fluctuation spectrum is calculated, which is integrated along the line of sight as in the phase contrast imaging signals. From that integrated signal its vertical profile is reconstructed by utilizing the variation of the direction of the magnetic field, as the operation carried out in experimental data. Usually in experiments, there exists limitation on the observation region and spatial resolution, so difference between the deteriorated and real spectra is confirmed by numerical simulations with variations related to the spatial limitations. ITG modes have a characteristic wavelength and frequency, and are identified with the sufficient spatial resolution even from the integrated signal by comparing the wavenumber spectra at different radial positions. Combination of multiple flux-tube data is also tested for calculation to give fluctuations spreading in wider radial ranges of plasma. These fluctuation spectra are compared with the experimental one for comprehensive understanding of experimental observations.

Streamers and their mediator have been known to exist in linear cylindrical plasmas [Yamada et al., Nat. Phys. 4, 721 (2008)]. Conditional averaging is applied to extract the nonlinear characteristics of a mediator, which has been simply treated as a linear wave. This paper reports that a mediator should have higher harmonic components generated by self-couplings, and the envelope of a streamer should be generated with not only fundamental but also higher harmonic components of the mediator. Moreover, both the mediator and the envelope of the streamer have common features with solitary waves, i.e., the height should increase inversely as the square of their localization width.

In order to observe spatial profiles of energetic particle driven modes, measurement signal of Heavy Ion Beam Probe (HIBP) is formulated theoretically, focusing on effects of the fast ion density fluctuation and attenuation of the injected beam (line-integral effect). Obtained formula is applied to the density fluctuation measurement of energetic-particle driven geodesic acoustic modes (EGAMs). Intensity of the fluctuation obtained by the HIBP can be up-down asymmetric in the poloidal cross-section due to the effect of the fast ion density fluctuation, when the electron loss cross-section of HIBP due to fast ions is comparable to that due to electrons. A possibility to measure the fast ion density by HIBP is discussed, and the experimental guideline for the specification of the resonance which drives the EGAM is presented.

The three-dimensional structures of the streamer and its carrier waves and mediator were observed in a linear plasma device for the first time. Not only the cross-sectional structure but also the a...

Plasma flows can be driven by turbulent stresses from excited modes in magnetized plasmas. Our recent numerical simulation of resistive drift wave turbulence in a linear device has shown that the radial inhomogeneity of the neutral density affects azimuthal flow generation by changing the phase structure of the most unstable eigenmodes. Eigenmode analyses show that the mode structure has a complex Bessel-type function shape in the central region of the plasma, and the imaginary part arises from the radial inhomogeneity of the damping term caused by ion-neutral collisions. The amplitude of turbulent stress is proportional to the inhomogeneity under a marginally stable condition. Global structural formation is an important factor for determining the plasma turbulent state, and this result clearly shows that several kinds of radial background distributions, the plasma and neutral densities in this case, can influence the global structures.

The spatio-temporal dynamics of turbulence with the interaction of geodesic acoustic modes (GAMs) are investigated, focusing on the phase-space structure of turbulence, where the phase-space consists of real-space and wavenumber-space. Based on the wave-kinetic framework, the coupling equation between the GAM and the turbulence is numerically solved. The turbulence trapped by the GAM velocity field is obtained. Due to the trapping effect, the turbulence intensity increases where the second derivative of the GAM velocity (curvature of the GAM) is negative. While, in the positive-curvature region, the turbulence is suppressed. Since the trapped turbulence propagates with the GAMs, this relationship is sustained spatially and temporally. The dynamics of the turbulence in the wavenumber spectrum are converted in the evolution of the frequency spectrum, and the simulation result is compared with the experimental observation in JFT-2M tokamak, where the similar patterns are obtained. The turbulence trapping effect is a key to understand the spatial structure of the turbulence in the presence of sheared flows.

It is important to consider a combination of inhomogeneities, which drive and/or damp instabilities in magnetized plasmas. The inhomogeneity of neutral particle density is taken into account for analyzing turbulent states in linear devices by combining two kinds of simulations in this research. One is a simulation for 2D profiles of neutral particles and the other is that for resistive drift wave turbulence. Radial and axial profiles of neutral particles are calculated by the Monte Carlo method with a configuration of linear device PANTA. The ratio for ionization of neutral particles depends on the electron temperature, and the higher temperature in the operation range makes the neutral density smaller near the center of the plasma. Then, the radial profile of the ion-neutral collision frequency is set by introducing these neutral density profiles into resistive drift wave turbulence simulations. Smaller ion-neutral collision frequency makes the instabilities more unstable, and its inhomogeneity enhances mean electrostatic potential formation. The eigenmode structure is changed with the inhomogeneous ion-neutral collision frequency, and convective derivative nonlinearity generates the azimuthal flow near the center of the plasma. Two roles of the neutral particles on the turbulence, the direct change in linear instabilities and formation of background flows, become clear.

Équipe 107 : Physique des plasmas chauds; International audience; To understand turbulent transport in magnetized plasmas, an end-plate biasing experiment was performed in a linear magnetized plasma device, PANTA. Here we report the change of bi-coherence among fluctuations during biasing. During biasing, coupling with drift waves is decrease, and that with the mediator is increase.

In the edge transport barrier of H-mode plasmas, a large poloidal flow exists and the electrostatic potential and density can have steep gradients both in the radial and poloidal directions. The accessibility to a two-dimensionally steep structure is demonstrated by solving the model equation including the poloidal structure, combined with the equation giving the time evolution of the radial electric field. The analysis is carried out with the parameter set of the electrode biasing experiment and shows the existence of the convective particle flux arising from poloidal inhomogeneity. This study provides an essential explanation for improving the transport analyses in H-modes by taking account of the two-dimensional effect in toroidal plasmas.

A novel stacked combline antenna was fabricated for driving plasma current in order to control the rotational transform profile in the Large Helical Device. The antenna has ten elements facilitating excitation of fast-wave traveling in the toroidal direction.Each antenna element has an electrical length of a half-wavelength and is supported at the midpoint from the back plate by a metallic block. Such an antenna has two modes: even and odd. A mixed excitation of these modes will reduce the current drive efficiency. The electrical properties of this antenna were studied in an attempt to find ways of exciting a traveling wave of pure even mode. A matching section was used in combination and proved to be a good measure to improve the directionality over that of a bare combline antenna. It is confirmed in this paper that the fabricated real antenna has fairly good even-mode purity keeping the odd-mode intensity at a tolerable level. An antenna with insulating supports instead of the metallic supports is also examined, and it is found that even-mode purity is further improved. For practical uses, an entire system including impedance matching and power circulation is proposed, and sensitivity to a change in plasma loading ismore » analyzed. Finally, the power-handling capability is discussed including estimations of plasma loading and driven current reaching an assertion of consistency with the experimental goal.« less

In tokamak H-mode, a large poloidal flow exists in an edge transport barrier, and the electrostatic potential and density profiles can be steep both in the radial and poloidal direction. Two-dimensional structures of the potential, density and flow velocity near the edge of a tokamak plasma are investigated. The model includes the nonlinearity in bulk-ion viscosity and turbulence-driven shear viscosity. For the case with a strong radial electric field (H-mode), a two-dimensional structure in a transport barrier is obtained, giving a poloidal shock with a solitary radial electric field profile. The poloidal electric field induces convective transport in the radial direction, and poloidal asymmetry makes the flux-surface-averaged particle flux direct inward with a pinch velocity on the order of 1 [m/s]. A large poloidal flow with radial shear enhances the inward pinch velocity. The abrupt increase of this inward ion and electron flux at the onset of L-to-H-mode transition explains the rapid establishment of the density pedestal at the transition.

The 'fishbone' fast wave travelling wave antenna was developed for LHD to provide a capability for rotational transform profile control by current drive. The fishbone antenna is equivalent to two combline antennae stacked vertically. The antenna operates around 75 MHz and excites a wavenumber of 14 m−1 when the phase difference between adjacent current straps is 90°. A test of a combline antenna with plasma load on the TST-2 spherical tokamak suggested the possibility that this type of antenna does not need to be installed in the immediate vicinity of the last closed flux surface. Optimization of the design was performed based on measurements on mock-up antennas and model calculations. In the fishbone antenna, controlled excitation of the even mode (with currents in the top and bottom halves of a current strap in the same direction) is necessary. A predominant excitation of the even mode was realized in the LHD fishbone antenna with simulated loading by selecting an appropriate operating frequency.

The mechanism for formation of a steep structure in the radial electric field is a key issue in plasma confinement. Properties of the radial electric field bifurcation are studied taking into account the effect of electrode biasing. The radial electric field structure is determined by the charge conservation equation. From the nonlinear mechanism associated with local current due to ion bulk viscosity, a transition can take place. Various types of radial electric field structures with multiple peaks are allowed for the same boundary condition. The ion orbit loss term breaks the symmetry of the radial current similarly to the ambipolar radial electric field. A radial current driven by the electrode plays the role of a control parameter in a transition similarly to the pressure gradient. A phase diagram is given in the spontaneous drive vs external drive space. Differences in the radial shape of solitary electric field structures are demonstrated in the presence of spatial varying components. This study clarifies the mechanisms of nonlinear structure formation in transport barriers.

Radial electric field bifurcation induced by electrode biasing near the tokamak edge is considered in this paper. The radial electric field structure is analysed including two non-linear terms in the radial current, namely the neoclassical term and the orbit loss term. Their competition gives various radial electric field structures, and biasing transition is compared with spontaneous transition. Bifurcation has different features for positive and negative biasing, with a larger number of structures available for the negative biasing case. Effectiveness of the solitary radial electric field structures induced by biasing for confinement improvement is discussed.