Transport in the plasma edge of a tokamak with high MHD activity

Summary Electrostatic turbulence and various aspects of magnetic fluctuations have been investigated, in the edge region of the TBR-1 tokamak, by using a set of Langmuir and magnetic probes, and a triple probe. Measurements of plasma parameters such as plasma potential, density, temperature and magnetic field were taken in order to elucidate, the effect on transport of the electrostatic and magnetic fluctuations in the edge. The fluctuations levels are found to be higher than in most tokamaks. The particle flux is outward and slightly higher than that calculated from Bohm diffusion, and occurs in the frequency region typical of the macroscopic MHD oscillations. The Mirnov-oscillation frequencies in TBR-1 are higher than those observed in other tokamaks and, consequently, there is an uncommon superposition between the Mirnov and turbulent density fluctuations spectra. This fact and the presence of high MHD activity may contribute to elucidate the possible influence of the magnetic oscillations on the electrostatic transport observed in the plasma edge. Work partially supported by FAPESP and CNPq.     

The Influence of Stochastic Layers of Magnetic Field Lines on Transport Barrier Formation in a Stellarator System

The results of local measurements of RF discharge plasma parameters in the process of internal transport barriers (ITB) formation in the vicinity of rational magnetic surfaces in the Uragan-3M torsatron are presented. The following phenomena were observed in the process of ITB formation: widening of the radial density distribution, formation of plateaus on radial density and electron temperature distributions, formation of regions with high shear of poloidal plasma rotation velocity and radial electric field in the vicinity of stochastic layers of magnetic field lines, decrease of density fluctuations and their radial correlation length, decorrelation of density fluctuations, and increase of the bootstrap current.After the ITB formation, the transition to the improved plasma confinement regime takes place. The transition moves to the beginning of the discharge with the increase of heating power. The possible mechanism of ITB formation near rational surfaces is discussed.     

On the possible role of the bootstrap effect in the RF current drive experiments

Conditions of existence of the bootstrap effect at anomalous diffusion in tokamaks are discussed. Assuming that these conditions are fulfilled at lower hybrid current drive, various models of anomalous diffusion and of temperature profiles are considered. Toroidal current density profiles and related quantities are calculated, demonstrating strong dependences on the electron temperature profiles and on the effective ion charge Z_eff. Recommendations for experimental revealing the bootstrap current are presented.     

Diffusion of stable electron-hole plasmas in magnetic fields

The transport of a semiconductor plasma, composed of electrons and holes, can be described with the aid of moments relativ to the conditional one particle density function. To calculate these moments, an operator equation is given which was derived with the generalized Stratonovich method. This equation is extended by taking recombination and scattering with a lattice into account. The coefficient functions are determined for stable and homogeneous systems in a self-consistent manner. In particular, the spatial diffusion of test particles in a strong magnetic field is considered, neglecting quantum effects. The anomalous contribution to the diffusion across the magnetic field is calculated explicitly and compared with that for a high temperature plasma. It is shown, that anomalous diffusion is possible also in stable systems, provided the time dependence of the stochastic electric field is determined by the polarization due to the test particle.     

Theoretical Study of the Structure of the Electric Field in Helical Toroidal Plasmas

A set of transport equations is analyzed, including the bifurcation of the electric field. The structure of the electric field is studied by use of the theoretical model for the anomalous transport diffusivities. A steep gradient of the radial electric field (E _r) is obtained at the electric domain, where the electric domain is the structure of the electric field in which the ambipolar E _r spatially changes from the electron root (E _r>0) to the ion root (E _r<0). The suppression of the anomalous transport diffusivity is studied in the presence of a strong shear of the electric field. The hard transition between the multiple ambipolar solutions in the structure of the radial electric field is examined. The details of the structure of the electric domain interface are investigated.     

Velocity Fluctuations and Transport in the JET Boundary Region

A new approach for turbulent fluxes and _E×B measurements in the bulk plasma is proposed. It is based in the measurement of fluctuations in the phase velocity of fluctuations. The structure of turbulence has been investigated in the JET plasma boundary region with a fast reciprocating Langmuir probe system. Fluctuations in the radial and poloidal phase velocity have been computed from floating potential and ion saturation current measurements. The correlation between density fluctuations and fluctuations in the radial velocity of fluctuations signals show a good agreement with the turbulent transport computed from the correlation between density and poloidal electric field fluctuations. These results suggest that turbulent transport might be computed in the plasma core from measurement of density fluctuations. E×B sheared flows, both constant and varying in time, are close to the critical value to trigger the transition to improve confinement regimes below the power threshold to trigger the formation of transport barriers.     

Giant electron tails and passing electron pinch effects in tokamak-core turbulence

The anomalous particle transport in a tokamak core is believed to be linked to the advection of magnetically trapped electrons alone, owing to the passing electrons maintaining a thermal equilibrium along the field lines. Surprisingly, in nonlinear numerical studies, the radial flux of passing electrons rivals that of the trapped ones. The strong interaction of passing electrons and electric fluctuations is mediated by long tails of the modes along the magnetic field, which are generated by the passing electrons in the first place.     

Two-dimensional structure and particle pinch in tokamak H mode

Two-dimensional structures of the electrostatic 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 the 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 inward particle pinch is induced from this poloidal asymmetric electric field, and increases as the radial electric field becomes stronger. 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, which is responsible for the observed spontaneous self-reorganization into an improved confinement regime.     

EFFECT OF RADIAL ELECTRICAL FIELD ON NEOCLASSICAL TRANSPORT IN TOKAMAKS

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Electrostatic Probes for Studying Transport Properties in Tokamak Plasmas

Electrostatic probes for measuring the boundary plasma in tokamaks are reviewed and presented. Transport properties in JFT‐2, the ion temperature and the magnetic surface in JFT‐2M and floating potential fluctuations during the strong additional heating in JT‐60 are measured by several types of electrostatic probe the above‐mentioned purposes. The Langmuir probe including the double probe is applied to measure the spatial profile of boundary plasma in JFT‐2. The ion sensitive probe, the rotating cylindrical double probe, the asymmetric double probe and the differential double probe are applied to measure the ion temperature and magnetic surface in JFT‐2M. The reciprocating Langmuir probe applied to JFT‐2M observes the potential and density fluctuations and a new type probe is proposed for the quick diagnostic of core hot plasmas as a development of this probe. The fluctuation observed in JT‐60 is identified to be the ion cyclotron instability of the hot plasma caused by the strong anisotropy of the ion distribution function (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the low-threshold parametric mechanism of the anomalous power absorption in electron cyclotron resonance heating experiments in toroidal devices

The experimental conditions that facilitate the excitation of parametric decay instabilities upon the electron cyclotron resonance heating of a plasma at the second harmonic extraordinary wave in tokamaks and stellarators and, as a result, make anomalous absorption of microwave power possible have been analyzed. It has been shown that, in the case of a nonmonotonic radial profile of the plasma density, when the beam of electron cyclotron waves passes near the equatorial plane of a toroidal device, the parametric excitation of electron Bernstein waves, as well as the generation of ion Bernstein waves propagating from the parametric decay region to the nearest ion cyclotron harmonic, where they efficiently interact with ions, is possible. The proposed theoretical model can explain the anomalous generation of accelerated ions observed upon electron cyclotron heating in small and moderate toroidal facilities.     

Initial Measurements of Plasma Potential in the Core of the MST Reversed Field Pinch with a Heavy Ion Beam Probe

Measurement of the plasma potential in the core of MST marks both the first interior potential measurements in an RFP, as well as the first measurements by a Heavy Ion Beam Probe (HIBP) in an RFP. The HIBP has operated with (20-110) keV sodium beams in plasmas with toroidal currents of (200-480) kA over a wide range of densities and magnetic equilibrium conditions. A positive plasma potential is measured in the core, consistent with the expectation of rapid electron transport by magnetic fluctuations and the formation of an outwardly directed ambipolar radial electric field. Comparison between the radial electric field and plasma flow is underway to determine the extent to which equilibrium flow is governed by E×B. Measurements of potential and density fluctuations are also in progress.Unlike HIBP applications in tokamak plasmas, the beam trajectories in MST (RFP) are both three-dimensional and temporally dynamic with magnetic equilibrium changes associated with sawteeth. This complication offers new opportunity for magnetic measurements via the Heavy Ion Beam Probe (HIBP). The ion orbit trajectories are included in a Grad-Shafranov toroidal equilibrium reconstruction, helping to measure the internal magnetic field and current profiles. Such reconstructions are essential to identifying the beam sample volume locations, and they are vital in MST's mission to suppress MHD tearing modes using current profile control techniques. Measurement of the electric field may be accomplished by combining single point measurements from multiple discharges, or by varying the injection angle of the beam during single discharges.The application of an HIBP on MST has posed challenges resulting in additional diagnostic advances. The requirement to keep ports small to avoid introducing magnetic field perturbations has led to the design and successful implementation of cross-over sweep systems. High levels of ultraviolet radiation are driving alternative methods of sweep plate operation. While, substantial levels of plasma flux into the HIBP diagnostic chambers has led to the use of magnetic plasma suppression.     

Model for the transition to the radiatively improved mode in a tokamak

A model for the transition to the radiatively improved (RI) mode triggered in tokamaks by seeding of impurities is proposed. This model takes into account that with increasing plasma effective charge the growth rate of the toroidal ion temperature gradient (ITG) instability, considered nowadays as the dominant source of anomalous energy losses in low-confinement (L) mode, decreases. As a result the plasma density profile peaks due to an inward convection generated by trapped electron turbulence. This completely quenches ITG induced transport and a bifurcation to the RI mode occurs. Conditions necessary for the L-RI transition are investigated.     

Synergy of anomalous transport and radiation in the density limit

The critical plasma density n(cr) above which the edge anomalous transport in tokamaks is dominated by drift resistive ballooning instability is found analytically. In this transport regime, the drastic increase of particle losses and drop of the edge temperature provoke a strong increase in impurity radiation, and thermal equilibrium does not exist if the density is ramped up above the ultimate limit n(max). Because of the nonlinear character of impurity radiation, this density limit n(max) is very close to n(cr) and practically does not change with the ion effective charge. The importance of the synergy between the anomalous transport and impurity radiation for the density limit phenomenon is confirmed by the results of numerical simulations.     

Roles of electric field on toroidal magnetic confinement

Theoretical research on the influence of electric field on toroidal magnetic confinement is surveyed. The static electric field is first described. A physical picture of the radial electric field generation and its influence on confinement are shown. Neoclassical effects as well as the non-classical processes are discussed. Emphasis is made on the connection with improved confinement. Convective cells with a nonuniform potential on the magnetic surface are also discussed. The roles of the fluctuating electric field are then reviewed. Recent progress in anomalous transport theory is addressed. Through these surveys, the impact of experiments using the heavy ion beam probes on modern plasma physics is illustrated     

Effects of Applied DC Radial Electric Fields on Particle Transport in a Bumpy Torus Plasma

The toroidal ring of plasma contained in the NASA Lewis Bumpy Torus may be biased to positive or negative potentials approaching 50 kilovolts by applying DC voltage to twelve or fewer midplane electrode rings. The electric fields, which are responsible for raising the ions to high energies by ExB/B2 drift, then point radially outward or inward. The profiles of plasma number density are observed to be flat or triangular across the plasma diameter. The absence of a second derivative in the density profile, combined with the flat electron temperature profiles which are observed, implies that the radial transport processes are not diffusional in nature and are dominated by the strong radial electric fields which are applied to the plasma. Evidence from a paired comparison test shows that the plasma number density and confinement time can increase more than an order of magnitude if the electric field acting along the minor radius of the toroidal plasma points inward, relative to the values observed when the electric field points radially outward. Some characteristic data taken under nonoptimized conditions yielded the highest plasma number density (2.7 × 1011/cc on axis) and the longest particle containment times (1.9 milliseconds) observed so far in this experiment.     

Numerical Modeling on Heat Transport Across Stochastic Magnetic Field

The heat diffusion across the stochastic magnetic field is studied numerically. The stochastic field is generated by the overlap of two magnetic islands. The parameter w/w_c, is found tobe an important parameter in charactering the transport, where w is the magnetic island width, and w_c is the critical island width for flattening the electron temperature across an island. For w/w_c < 1, the enhanced radial heat diffusivity χ_r is proportional to the parallel heat diffusivity χ_∥, and the heat transport is dominated by the additive effect of individual islands. For w/w_c > 3, χ_r is also proportional to χ_∥ and the additional degradation of the energy confinement due to stochastic magnetic field becomes apparent. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Energy Selecting Action of Limiters on Particle Fluxes Penetrating into the SOL-Plasma

A simple model of the penetration of particle effluxes from the core plasma into the SOL-plasma of tokamaks is proposed. The assumptions made are free streaming of particles parallel to the magnetic field and anomalous particle transport perpendicular to the toroidal field with a constant radial velocity. The model has been proved for measured particle fluxes of Li which was injected into the core plasma of the tokamak T-10. The dependence of the Li-particle flux on the minor radius as well as toroidal asymmetries in the SOL-plasma can be explained by the results of the calculations.