Radial Electric Field Profile Research Articles

Poloidal magnetic field reconstruction by laser-driven ion-beam trace probe in spherical tokamak

Abstract The poloidal magnetic field (B_p) plays a critical role in plasma equilibrium, confinement and transport of magnetic confinement devices. Multiple diagnostic methods are needed to complement each other to obtain a more accurate B_p profile. Recently, the laser-driven ion-beam trace probe (LITP) has been proposed as a promising tool for diagnosing B_p and radial electric field (E_r) profiles in tokamaks [Yang X Y et al 2014 Rev. Sci. Instrum. 85 11E429]. The spherical tokamak (ST) is a promising compact device with high plasma beta and naturally large elongation. However, when applying LITP to diagnosing B_p in STs, the larger B_p invalidates the linear reconstruction relationship for conventional tokamaks, necessitating the development of a nonlinear reconstruction principle tailored to STs. This novel approach employs an iterative reconstruction method based on Newton’s method to solve the nonlinear equation. Subsequently, a simulation model to reconstruct the B_p profile of STs is developed and the experimental setup of LITP is designed for EXL-50, a middle-sized ST. Simulation results of the reconstruction show that the relative errors of B_p reconstruction are mostly below 5%. Moreover, even with 5 mm measurement error on beam traces or 1 cm flux surface shape error, the average relative error of reconstruction remains below 15%, initially demonstrating the robustness of LITP in diagnosing B_p profiles in STs.

Analysis of radial electric field in the scrape-off layer in SOLPS-ITER modeling of ASDEX-upgrade and ITER

Formation of the radial electric field profile in the scrape-off layer of the tokamak in the outer midplane is analyzed on the basis of SOLPS-ITER modeling for various regimes of ASDEX-Upgrade and ITER. The radial electric field is a result of the interplay of different contributions to the electron parallel momentum balance equation and the sheath potential drop at the plate, all of the same order. The relative role of these contributions is analyzed for semi-detached and attached divertor conditions. It is demonstrated that in the conduction-limited regime the electric field is positive, while in the semi-detached regime it decreases in absolute value in the major part of SOL and even becomes negative at the separatrix.

Account of non-standard orbits in computations of neoclassical toroidal viscous torque in the resonant plateau regime of a tokamak

This article extends theoretical details based on a short paper originally submitted to the 2022 EPS conference in plasma physics [1]. The quasilinear theory of resonant transport regimes in a tokamak is developed for the general case of orbits forming various classes separated in phase space by homoclinic orbits with infinite bounce time. Beyond standard orbits (banana and passing orbits) also all types of non-standard orbits (e.g. “potato” orbits) are taken into account. In case of a weak radial electric field, such orbits are usually present only near the magnetic axis. If the radial electric field cannot be treated as weak, there can be arbitrary many classes, located elsewhere. The present approach covers all such cases and is demonstrated on a specific example of a radial electric field profile. The resulting quasilinear kinetic equation is applicable to compute neoclassical toroidal viscous (NTV) torque in a tokamak with non-axisymmetric magnetic field perturbations. A fully non-local approach to NTV computation has been realized in the upgraded version of the code NEO-RT. Based on a generalization of magnetic flux surfaces to drift surfaces, the notion of a local thermodynamic equilibrium is extended for our purpose. We obtain an expression for the integral toroidal torque within a chosen flux surface and dicuss means to compute such integrals taking singularities in bounce and precession frequencies into account.

Formation of the radial electric field profile in the WEST tokamak

Sheared flows are known to reduce turbulent transport by decreasing the correlation length and/or intensity of turbulent structures. The transport barrier that takes place at the edge during improved regimes such as H mode, corresponds to the establishment of a large shear of the radial electric field. In this context, the radial shape of the radial electric field or more exactly of the perpendicular E × B velocity appears as a key element in accessing improved confinement regimes. In this paper, we present the radial profile of the perpendicular velocity measured using Doppler back-scattering system at the edge of the plasma, dominated by the E × B velocity, during the first campaigns of the WEST tokamak. It is found that the radial velocity profile is clearly more sheared in lower single null configuration (with the B × ∇B magnetic drift pointing toward the active X-point) than in upper single null configuration for ohmic and low current plasmas (B = 3.7 T and q 95 = 4.7), consistently with the expectation comparing respectively ‘favourable’ versus ‘unfavourable’ configuration. Interestingly, this tendency is sensitive to the plasma current and to the amount of additional heating power leading to plasma conditions in which the E × B velocity exhibits a deeper well in USN configuration. For example, while the velocity profile exhibits a clear and deep well just inside the separatrix concomitant with the formation of a density pedestal during L–H transitions observed in LSN configuration, deeper E r wells are observed in USN configuration during similar transitions with less pronounced density pedestal.

Radial electric field and density fluctuations measured by Doppler reflectometry during the post-pellet enhanced confinement phase in W7-X

Radial profiles of density fluctuations and the radial electric field, E r, have been measured using Doppler reflectometry during the post-pellet enhanced confinement phase achieved, under different heating power levels and magnetic configurations, during the 2018 W7-X experimental campaign. A pronounced E r-well is measured with local values as high as −40 kV m−1 in the radial range ρ ∼ 0.7–0.8 during the post-pellet enhanced confinement phase. The maximum E r intensity scales with both the plasma density and electron cyclotron heating power level, following a similar trend to the plasma energy content. A good agreement is found when the experimental E r profiles are compared to simulations carried out using the neoclassical codes, the drift kinetic equation solver (DKES) and kinetic orbit-averaging solver for stellarators (KNOSOS). The density fluctuation level decreases from the plasma edge toward the plasma core and the drop is more pronounced in the post-pellet enhanced confinement phase than in reference gas-fuelled plasmas. Besides, in the post-pellet phase, the density fluctuation level is lower in the high iota magnetic configuration than in the standard one. To determine whether this difference is related to the differences in the plasma profiles or to the stability properties of the two configurations, gyrokinetic simulations have been carried out using the codes stella and EUTERPE. The simulation results point to the plasma profile evolution after the pellet injection and the stabilization effect of the radial electric field profile as the dominant players in the stabilization of the plasma turbulence.

Turbulence and perpendicular plasma flow asymmetries measured at TJ-II plasmas

Dedicated experiments have been carried out for a systematic comparison of turbulence wavenumber spectra and perpendicular rotation velocity measured at poloidally separated positions on the same flux-surface in the stellarator TJ-II. The rationale behind this study is twofold, namely, validation of the spatial localization of instabilities predicted by gyrokinetic simulations in stellarators and validation of the electrostatic potential variation on the flux surface as calculated by neoclassical codes and its possible impact on the radial electric field. Perpendicular wavenumber spectra and perpendicular rotation velocity profiles have been measured using Doppler reflectometry in two plasma regions poloidally separated as both positive and negative probing beam angles with respect to normal incidence can be selected. A systematic comparison has been carried out showing differences in the perpendicular wavenumber spectrum measured at poloidally separated positions on the same flux-surface, that depend on plasma density, heating conditions and magnetic configuration. The asymmetry found in the standard magnetic configuration under some plasmas conditions, reverses in the high iota configuration. The different intensity in the density fluctuation spectra can be related to the poloidal localization of instabilities found in gyrokinetic simulations. Differences in the radial electric field profile are also found that could be explained to be due to on-surface plasma potential variations.

Physics affecting heavy impurity migration in tokamaks: Benchmarking test-ion code ASCOT against TEXTOR tracer experiment

Abstract Erosion, transport and deposition of wall impurities are major concerns in future magnetic fusion devices, both from the perspective of the fusion plasma and the machine wall. An extensive study on molybdenum transport and deposition performed in the TEXTOR tokamak yielded a detailed deposition map that is ideal for benchmark deposition studies. A qualitative benchmark is attempted in this article with the ASCOT code. We set up a full 3D model of the TEXTOR tokamak and studied the influence of different physical mechanisms and their strengths on molybdenum deposition patterns on the simulated plasma-facing components: atomic processes, Coulomb collisions, scrape-off layer (SOL) profiles, source distribution, marker starting energy, radial electric field strength, SOL flow and toroidal plasma rotation. The outcome comprises 13 simulations, each with 100,000 markers. The findings are: • Toroidal plasma movement, either within the LCFS or as SOL flow, is negligible. • SOL profile and marker starting energy have modest impact on deposition. • Source distribution has a large impact in combination with radial electric field profiles. • The E ⇀ × B ⇀ drift has the highest impact on the deposition profiles.

Development of a multi-channel capacitive probe for electric field measurements with fine spatial and high time resolution.

A capacitive probe [Tan et al., Rev. Sci. Instrum. 88, 023502 (2017)] is one of a few diagnostics that is directly sensitive to the plasma potential. Using this diagnostic technique, a Multi-channel Linear Capacitive Probe (MLCP) is developed for turbulence measurements. The MLCP has 10 spatial channels and provides 9 points of radial electric field measurements simultaneously with a spatial step of 7 mm. A new readout circuit and a correction technique for low frequency attenuation are also developed to achieve the required spatial and time resolution. A performance test of the MLCP using a reversed field pinch plasma confirms that the MLCP resolves sub-centimeter structures of the equilibrium radial electric field profile and fluctuations up to 680 kHz.

The Mochi LabJet Experiment for Measurements of Canonical Helicity Injection in a Laboratory Astrophysical Jet

Abstract The Mochi device is a new pulsed power plasma experiment designed to produce long, collimated, stable, magnetized plasma jets when set up in the LabJet configuration. The LabJet configuration aims to simulate an astrophysical jet in the laboratory by mimicking an accretion disk threaded by a poloidal magnetic field with concentric planar electrodes in front of a solenoidal coil. The unique setup consists of three electrodes, each with azimuthally symmetric gas slits. Two of the electrodes are biased independently with respect to the third electrode to control the radial electric field profile across the poloidal bias magnetic field. This design approximates a shear azimuthal rotation profile in an accretion disk. The azimuthally symmetric gas slits provide a continuously symmetric mass source at the footpoint of the plasma jet, so any azimuthal rotation of the plasma jet is not hindered by a discrete number of gas holes. The initial set of diagnostics consists of current Rogowski coils, voltage probes, magnetic field probe arrays, an interferometer and ion Doppler spectroscopy, supplemented by a fast ion gauge and a retarding grid energy analyzer. The measured parameters of the first plasmas are ∼1022 m−3, ∼0.4 T, and 5–25 eV, with velocities of ∼20–80 km s−1. The combination of a controllable electric field profile, a flared poloidal magnetic field, and azimuthally symmetric mass sources in the experiment successfully produces short-lived (∼10 μs, ≳5 Alfvén times) collimated magnetic jets with a ∼10:1 aspect ratio and long-lived (∼100 μs, ≳40 Alfvén times) flow-stabilized, collimated, magnetic jets with a ∼30:1 aspect ratio.

Internal transport barriers in plasmas with reversed plasma flow

Evidences of internal particle transport barriers have been observed in plasma discharges with reversed plasma flow. To investigate the influence of the radial electric field profile on these barriers, we apply a drift wave map that describe the plasma particle transport and allows the integration of particle drift in the presence of a given electrostatic turbulence spectrum. With this procedure we show that transport barriers due to the shearless flow invariant lines are created inside the plasma. Moreover, by varying the radial electric field profile, we observe the formation and destruction of internal transport barriers constituted by shearless invariant lines, as well as its effects on the transport in the map's phase space. Applicability of our results are discussed for the Texas Helimak, a toroidal plasma device in which the radial electric field can be changed by application of bias potential.

Core radial electric field and transport in Wendelstein 7-X plasmas

The results from the investigation of neoclassical core transport and the role of the radial electric field profile (Er) in the first operational phase of the Wendelstein 7-X (W7-X) stellarator are presented. In stellarator plasmas, the details of the Er profile are expected to have a strong effect on both the particle and heat fluxes. Investigation of the radial electric field is important in understanding neoclassical transport and in validation of neoclassical calculations. The radial electric field is closely related to the perpendicular plasma flow (u⊥) through the force balance equation. This allows the radial electric field to be inferred from measurements of the perpendicular flow velocity, which can be measured using the x-ray imaging crystal spectrometer and correlation reflectometry diagnostics. Large changes in the perpendicular rotation, on the order of Δu⊥∼ 5 km/s (ΔEr ∼ 12 kV/m), have been observed within a set of experiments where the heating power was stepped down from 2 MW to 0.6 MW. These experiments are examined in detail to explore the relationship between heating power temperature, and density profiles and the radial electric field. Finally, the inferred Er profiles are compared to initial neoclassical calculations based on measured plasma profiles. The results from several neoclassical codes, sfincs, fortec-3d, and dkes, are compared both with each other and the measurements. These comparisons show good agreement, giving confidence in the applicability of the neoclassical calculations to the W7-X configuration.

EDGE2D-EIRENE modelling of near SOL Er: possible impact on the H-mode power threshold

Recent EDGE2D-EIRENE simulations of JET plasmas showed a significant difference between radial electric field (Er) profiles across the separatrix in two divertor configurations, with the outer strike point on the horizontal target (HT) and vertical target (VT) (Chankin et al 2016 Nucl. Mater. Energy, doi: 10.1016/j.nme.2016.10.004). Under conditions (input power, plasma density) where the HT plasma went into the H-mode, a large positive Er spike in the near scrape-off layer (SOL) was seen in the code output, leading to a very large E × B shear across the separatrix over a narrow region of a fraction of a cm width. No such Er feature was obtained in the code solution for the VT configuration, where the H-mode power threshold was found to be twice as high as in the HT configuration. It was hypothesised that the large E × B shear across the separatrix in the HT configuration could be responsible for the turbulence suppression leading to an earlier (at lower input power) L–H transition compared to the VT configuration. In the present work these ideas are extended to cover some other experimental observations on the H-mode power threshold variation with parameters which typically are not included in the multi-machine H-mode power threshold scalings, namely: ion mass dependence (isotope H–D–T exchange), dependence on the ion ∇B drift direction, and dependence on the wall material composition (ITER-like wall versus carbon wall in JET). In all these cases EDGE2D-EIRENE modelling shows larger positive Er spikes in the near SOL under conditions where the H-mode power threshold is lower, at least in the HT configuration.

Improvements to an ion orbit loss calculation in the tokamak edge

An existing model of collisionless particle, momentum, and energy ion orbit loss from the edge region of a diverted tokamak plasma has been extended. The extended ion orbit loss calculation now treats losses of both thermal ions and fast neutral beam injection ions and includes realistic flux surface and magnetic field representations, particles returning to the plasma from the scrape off layer, and treatment of x-transport and x-loss. More realistic flux surface geometry allows the intrinsic rotation calculation to predict a peaking in the profile closer to the separatrix, which is consistent with experiment; and particle tracking calculations reveal a new mechanism of “x-transport pumping,” which predicts larger ion losses when coupling conventional ion orbit loss and x-loss mechanisms, though still dominated by conventional ion orbit loss. Sensitivity to these ion orbit loss model enhancements is illustrated by fluid predictions of neoclassical rotation velocities and radial electric field profiles, with and without the enhancements.

Impact of magnetic topology on radial electric field profile in the scrape-off layer of the Large Helical Device

The radial electric field in the plasma edge is studied in the Large Helical Device (LHD) experiments. When magnetic field lines become stochastic or open at the plasma edge and connected to the vessel, electrons are lost faster than ions along these field lines. Then, a positive electric field appears in the plasma edge. The radial electric field profile can be used to detect the effective plasma boundary. Magnetic topology is an important issue in stellarator and tokamak research because the 3D boundary has the important role of controlling MHD edge stability with respect to ELMs, and plasma detachment. Since the stochastic magnetic field layer can be controlled in the LHD by changing the preset vacuum magnetic axis, this device is a good platform to study the properties of the radial electric field that appear with the different stochastic layer width. Two magnetic configurations with different widths of the stochastic layer as simulated in vacuum are studied for low-β discharges. It has been found that a positive electric field appeared outside of the last closed flux surface. In fact the positions of the positive electric field are found in the boundary between of the stochastic layer and the scrape-off layer. To understand where is the boundary of the stochastic layer and the scrape-off layer, the magnetic field lines are analyzed statistically. The variance of the magnetic field lines in the stochastic layer is increased outwards for both configurations. However, the skewness, which means the asymmetry of the distribution of the magnetic field line, increases for only one configuration. If the skewness is large, the connection length becomes effectively short. Since that is consistent with the experimental observation, the radial electric field can be considered as an index of the magnetic topology.

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.

Measurement and modeling of electric field and space-charge distributions in obstructed helium discharge

Axial and radial variations of electric field have been measured in dielectric shielded 0.025 m diameter parallel plate electrode with 0.0065 m gap for 1.6 mA, 2260 V helium dc discharge at 1.75 Torr. The axial and radial electric field profiles have been measured from the Stark splitting of 21S→11 1P transition through collision induced fluorescence from 43D→23P. The electric field values showed a strong radial variation peaking to 500 kV/m near the cathode radial boundary, and decreasing to about 100 kV/m near the anode edge, suggesting the formation of an obstructed discharge for this low nd condition, where n is the gas density and d is the gap distance. The off-axis Stark spectra showed that the electric field vector deviates from normal to the cathode surface which permits longer path electron trajectories in the inter-electrode gap. Also, the on-axis electric field gradient was very small and off-axis electric field gradient was large indicating a radially non-uniform current density. In order to obtain information about the space charge distribution in this obstructed discharge, it was modeled using the 2-d axisymmetric Poisson solver with the COMSOL finite element modeling program. The best fit to the measured electric field distribution was obtained with a space charge variation of ρ(r) = ρ0(r/r0)3, where ρ(r) is the local space charge density, ρ0 = 6 × 10−3 Coulomb/m3, r is the local radial value, and r0 is the radius of the electrode.

Understanding of impurity poloidal distribution in the edge pedestal by modelling

Simulation of an H-mode ASDEX Upgrade shot with boron impurity was done with the B2SOLPS5.2 transport code. Simulation results were compared with the unique experimental data available for the chosen shot: radial density, electron and ion temperature profiles in the equatorial midplanes, radial electric field profile, radial profiles of the parallel velocity of impurities at the low-field side (LFS) and high-field side (HFS), radial density profiles of impurity ions at LHS and HFS. Simulation results reproduce all available experimental data simultaneously. In particular strong poloidal HFS–LFS asymmetry of B5+ ions was predicted in accordance with the experiment. The simulated HFS B5+ density inside the edge transport barrier is twice larger than that at LFS. This is consistent with the experimental observations where even larger impurity density asymmetry was observed. A similar effect was predicted in the simulation done for the MAST H-mode. Here the HFS density of He2+ is predicted to be 4 times larger than that at LHS. Such a large predicted asymmetry is connected with a larger ratio of HFS and LFS magnetic fields which is typical for spherical tokamaks. The HFS/LFS asymmetry was not measured in the experiment, however modelling qualitatively reproduces the observed change of sign of He+parallel velocity to the counter-current direction at LFS. The understanding of the asymmetry is based on neoclassical effects in plasma with strong gradients. It is demonstrated that simulation results obtained with account of sources of ionization, realistic geometry and turbulent transport are consistent with the simplified analytical approach. Difference from the standard neoclassical theory is emphasized.

Cold test of cylindrical open resonator for 42 GHz, 200 kW gyrotron

This paper presents experimental results for cold testing of a gyrotron open resonator. Experiments were carried out to measure resonant frequency and their particular quality factor for TE mode at the frequency 42 GHz. The perturbation technique was used to determine the axial, radial and azimuthal electric field profile for identification of TE031 mode at operating frequency 42 GHz. The good agreement between experimental results and theoretical studies was found. The results verify the design and fabrication of the specific gyrotron cavity.

Effect of ion orbit loss on the structure in the H-mode tokamak edge pedestal profiles of rotation velocity, radial electric field, density, and temperature

An investigation of the effect of ion orbit loss of thermal ions and the compensating return ion current directly on the radial ion flux flowing in the plasma, and thereby indirectly on the toroidal and poloidal rotation velocity profiles, the radial electric field, density, and temperature profiles, and the interpretation of diffusive and non-diffusive transport coefficients in the plasma edge, is described. Illustrative calculations for a high-confinement H-mode DIII-D [J. Luxon, Nucl. Fusion 42, 614 (2002)] plasma are presented and compared with experimental results. Taking into account, ion orbit loss of thermal ions and the compensating return ion current is found to have a significant effect on the structure of the radial profiles of these quantities in the edge plasma, indicating the necessity of taking ion orbit loss effects into account in interpreting or predicting these quantities.

Electrostatic model of radial pn junction nanowires

Poisson's equation is solved for a radial pn junction nanowire (NW) with surface depletion. This resulted in a model capable of giving radial energy band and electric field profiles for any arbitrary core/shell doping density, core/shell dimensions, and surface state density. Specific cases were analyzed to extract pertinent underlying physics, while the relationship between NW specifications and the depletion of the NW were examined to optimize the built-in potential across the junction. Additionally, the model results were compared with experimental results in literature to good agreement. Finally, an optimum device design is proposed to satisfy material, optical, and electrostatic constraints in high efficiency NW solar cells.