Cross-field Drift Research Articles

First SOLPS-ITER predictions of the impact of cross-field drifts on divertor and scrape-off layer conditions in double-null configuration of STEP

Introduction of cross-field drifts in SOLPS-ITER simulations of connected double-null plasmas in STEP with the ion ∇B×B drift towards the upper divertors was found to enhance the detachment of the inner divertors with decreased target densities and ion and heat fluxes, while simultaneously complicating the access to detachment in the outer lower divertor by increasing the target temperature and heat loads to levels above the engineering limits. The ∇B×B drift was observed to significantly affect the radial heat transport between the core and the scrape-off layer (SOL), altering the poloidal temperature and pressure profiles and, consequently, the poloidal conductive and convective heat transport in the SOL. As a result, up-down asymmetries of 52:48 and 58:42 biased towards the outer lower and upper inner divertors, respectively, were observed to arise in the unmitigated power entering the divertor regions, breaking the up-down symmetry seen in simulations without the drift terms and contradicting with earlier experimental observations on the low-field side. Moreover, the upstream electron density was found to decrease noticeably in the core and separatrix regions following the activation of the drifts due to an increased share of the neutrals arriving from D2 injections near the upper and lower X-points ionizing already in the private flux regions.

High performance power handling in the absence of an H-mode edge in negative triangularity DIII-D plasmas

Experiments performed during strongly-shaped high-power diverted negative triangularity (NT) experiments in DIII-D achieved detached divertor conditions and a transient-free edge, showcasing the potential for application of NT to a core-edge integrated reactor-like scenario and providing the first characterization of the parametric dependencies for detachment onset. Detached divertor conditions will be required in future devices to mitigate divertor heat fluxes. Access to dissipative divertor conditions was investigated via an increase in upstream density. Detachment onset at the outer strike point was achieved with H-mode level confinement H98−y2∼1 and reactor-relevant normalized pressures βN∼2 . Confinement degradation was observed with deeper detachment, associated with the loss of an electron temperature pedestal. Differences in geometry, radial transport, impact of cross field drifts are discussed to explain differences in access to detachment in NT discharges. Higher normalized densities, with respect to equivalent discharges in positive triangularity, were necessary to achieve detachment, partially explained by the shorter parallel connection length to the targets. The effect of cross-field particle drifts (E×B, B ×∇ B) on access to detachment was demonstrated by the lower upstream density needed to access detachment with ion B ×∇ B drift directed outside of the active divertor (Greenwald fraction fGw∼ 0.9–1.0 vs fGw∼ 1.3). The upstream density at detachment onset was observed to increase linearly with plasma current with ion B ×∇ B drift into the divertor, consistent with the observed narrowing of the scrape-off layer heat flux width λ q . Edge fluid simulations capture separatrix densities needed to achieve detachment in NT plasma and their dependence on drift direction. The ability to reproduce detachment dynamics in NT plasma increases the confidence in future design studies for NT divertors.

Drift of ablated material after pellet injection in a tokamak

Pellet injection is used for fuelling and controlling discharges in tokamaks, and it is foreseen in ITER. During pellet injection, a movement of the ablated material towards the low-field side (or outward major radius direction) occurs because of the inhomogeneity of the magnetic field. Due to the complexity of the theoretical models, computer codes developed to simulate the cross-field drift are computationally expensive. Here, we present a one-dimensional semi-analytical model for the radial displacement of ablated material after pellet injection, taking into account both the Alfvén and ohmic currents which shortcircuit the charge separation creating the drift. The model is suitable for rapid calculation of the radial drift displacement, and can be useful for e.g. modelling of disruption mitigation via pellet injection.

Validation of EDGDE2D-EIRENE predicted 2D distributions of electron temperature and density against divertor Thomson scattering measurements in the low-field side divertor leg in DIII-D

Comparisons of profiles of the electron temperature (Te), density (ne) and pressure (pe) measured with Divertor Thomson Scattering in DIII-D low-confinement mode discharges to predictions from the edge fluid code EDGE2D-EIRENE [1] show that the models implemented in EDGE2D-EIRENE predict the measurements within their collective uncertainties if the Te at the separatrix (Te,sep) is 10 eV, or higher. The simulations do not predict, however, the peaked Te and ne profiles measured adjacent to the target plate when Te,sep, is below 10 eV, i.e., for the plasma downstream from the region of ionization of deuterium atoms. Inclusion of cross-field drifts and a fivefold reduction of radial transport cannot reconcile the discrepancy between the measurements and predictions.

Resonant alpha particle loss in stellarators

Particle resonances in stellarators can produce islands in the space of passing particle orbits without the presence of an unstable Alfvén mode, provided the period of the resonance matches the period of the equilibrium magnetic field. In this case, the equilibrium itself plays the role of a mode amplitude, and the islands appear on surfaces where the orbital helicity matches the field period. At low energy, these surfaces are given by the field line helicity, but at higher energy, cross field drift causes them to move. The resonances are also felt by trapped particles bouncing back and forth on surfaces with matching helicity. The periodic variation of B along these orbits produces local wells, giving loss due to drift while trapped in a well. Stellarator designs that have equilibrium-induced resonance islands exhibit anomalous alpha particle loss and are unsuitable for reactors.

Neutral gas and plasma shielding (NGPS) model and cross-field motion of ablated material for hydrogen–neon mixed pellet injection

A neutral-gas and plasma shielding (NGPS) model is applied for cryogenic hydrogen–neon mixed pellet injection used for the mitigation of tokamak disruptions. The NGPS model is useful to evaluate the characteristics of ionized plasmoid (size, density, temperature, and radiation), while reproducing the scaling of the neutral gas shielding model. It is found that even if one takes into account the optical thickness for radiation, the energy loss due to line radiation associated with neon is strong enough to limit the temperature and the pressure of the ionized plasmoid for pure neon or hydrogen–neon mixed pellets in the early phase of the material homogenization. Consequently, the ionized plasmoid of the neon mixed pellets is expected to homogenize along the magnetic field line where the ablated material is released—without significantly making the cross-field drift motion—as compared to pure hydrogen pellets.

Predictions of radiation pattern and in–out asymmetries in the DEMO scrape-off layer using fluid neutrals

Strongly radiating and detached high-power discharges in present-day full-metal tokamaks have a characteristic radiation pattern involving condensation of radiation near the X-point, with significant radiative losses above the X-point. In contrast, Demonstration Fusion Power Plant (DEMO) divertor exhaust scoping studies using reduced physics models, including a fluid description for the neutrals, place the strongest radiation fronts in the divertor legs, near the separatrix. The present contribution studies sensitivity of the radiation pattern corresponding to maximal divertor impurity radiation to those physics models that are typically neglected in the simulations due to their computational expense: cross-field drifts, complex impurity models and kinetic neutrals. Model benchmarking is carried out in comparison to L-mode discharges, which are shown to feature both divertor and X-point radiation. The simulated plasma conditions with maximal divertor radiation have in–out asymmetries in the divertor legs and at the divertor entrance, and the asymmetries and the radiation patterns are observed to be sensitive to both cross-field drift effects and the neutral model. DEMO simulations, carried out using SOLPS-ITER, show an impact of cross-field drifts on the divertor asymmetries, but the impact is not large enough to move the radiation front from the divertor legs to regions above the X-point.

Hamiltonian in Guiding Center Theory: A Symplectic Structure Approach

The guiding center approximation represents a very powerful tool for analyzing and modeling a charged particle motion in strong magnetic fields. This approximation is based on the conservation of an adiabatic invariant, the magnetic moment. Hamiltonian equations for the guiding center motion are traditionally introduced using a non-canonical symplectic structure. Under such an approach one has to apply the non-canonical Hamiltonian perturbation theory in order to calculate the magnetic moment corrections. In this study we present an alternative approach with canonical Hamiltonian equations for the guiding center motion in time-dependent electromagnetic fields. We show that the derived Hamiltonian decouples three types of motion (gyrorotation, field-aligned motion, and cross-field drifts), and each type is described by a pair of conjugate variables. This form of Hamiltonian and symplectic structure allows easy introduction of adiabatic invariants and can be useful for the analysis of various plasma systems.

Asymptotics of the three-dimensional Vlasov equation in the large magnetic field limit

We study the asymptotic behavior of solutions to the Vlasov equation in the presence of a strong external magnetic field. In particular we provide a mathematically rigorous derivation of the guiding-center approximation in the general three dimensional setting under the action of large inhomogeneous magnetic fields. First order corrections are computed and justified as well, including electric cross field, magnetic gradient and magnetic curvature drifts. We also treat long time behaviors on two specific examples, the two dimensional case in carte-sian coordinates and a poloidal axi-symmetric geometry, the former for expository purposes. Algebraic manipulations that underlie concrete computations make the most of the linearity of the stiffest part of the system of characteristics instead of relying on any particular variational structure.

Improved core-edge compatibility using impurity seeding in the small angle slot (SAS) divertor at DIII-D

Impurity seeding studies in the small angle slot (SAS) divertor at DIII-D have revealed a strong relationship between the detachment onset and pedestal characteristics with both target geometry and impurity species. N2 seeding in the slot has led to the first simultaneous observation of detachment on the entire suite of boundary diagnostics viewing the SAS without degradation of core confinement. SOLPS-ITER simulations with D+C+N, full cross field drifts, and n–n collisions activated are performed for the first time in DIII-D to interpret the behavior. This highlights a strong effect of divertor configuration and plasma drifts on the recycling source distribution with significant consequences on plasma flows. Flow reversal is found for both main ions and impurities affecting strongly the impurity transport and providing an explanation for the observed dependence on the strike point location of the detachment onset and impurity leakage found in the experiments. Matched discharges with either nitrogen or neon injection show that while nitrogen does not significantly affect the pedestal, neon leads to increased pedestal pressure gradients and improved pedestal stability. Little nitrogen penetrates in the core, but a significant amount of neon is found in the pedestal consistent with the different ionization potentials of the two impurities. This work demonstrates that neutral and impurity distributions in the divertor can be controlled through variations in strike point locations in a fixed baffle structure. Divertor geometry combined with impurity seeding enables mitigated divertor heat flux balancing core contamination, thus leading to enhanced divertor dissipation and improved core-edge compatibility, which are essential for ITER and for future fusion reactors.

Progress in DIII-D towards validating divertor power exhaust predictions

UEDGE simulations highlight the role of cross-field drifts on the onset of detached conditions, and new calibrated divertor vacuum ultra violet (VUV) spectroscopy is used to challenge the predictions of radiative constituents in these simulations. UEDGE simulations for DIII-D H-mode plasmas with the open divertor with the ion ∇B-drift towards the X-point show a bifurcated onset of the low field side (LFS) divertor detachment, consistent with experimentally observed step-like detachment onset (Jaervinen A.E. et al 2018 Phys. Rev. Lett. 121 075001). The divertor plasma in the simulations exhibits hysteresis in upstream separatrix density between attached and detached solution branches. Reducing the drift magnitude by a factor of 3 eliminates the step-like detachment onset in the simulations, confirming the strong role of drifts in the bifurcated detachment onset. When measured local plasma densities and temperatures are within proximity of predicted values in the simulations, there is no shortfall of the local emission of the dominant resonant radiating lines. However, the simulations systematically predict a factor of two lower total integrated radiated power than measured by the bolometer with the difference lost through radial heat flow out of the computational domain. Even though there is no shortfall in the emission of the dominant lines, a shortfall of total radiated power can be caused by underpredicted spatial extent of the radiation front, indicating a potential upstream or divertor transport physics origin for the radiation shortfall, or shortfall of radiated power in the spectrum between the dominant lines. In addition to the underpredicted spatial extent, in detached conditions, the simulations overpredict the peak radiation and dominant carbon lines near the X-point, which can be alleviated by manually increasing divertor diffusivity in the simulations, highlighting the ad hoc cross-field transport as one of the key limitations of the predictive capability of these divertor fluid codes.

Simulations of divertor heat flux width using transport code with cross-field drifts under the BOUT++ framework

The fluid transport code [trans-electric field (Er) module] under the BOUT++ framework has been used to simulate divertor heat flux width and boundary Er with all drifts and the sheath potential in the scrape-off layer. The calculated steady state radial Er in the pedestal region has been compared with that of experimental measurements from the Alcator C-Mod tokamak. The magnitude and shape of Er are similar to those of the experimental data. In order to understand the relative role of cross-field drifts vs turbulent transport in setting the heat flux width, four C-Mod enhanced Dα H-mode discharges with a lower single null divertor configuration should be simulated. BOUT++ transport simulations with cross-field drifts included yield similar heat flux width λq to that of experimental measurements (within a factor of 2) from both the probe and the surface thermocouple diagnostics and show a similar trend with plasma current to that of the Eich experimental scaling. The simulations show that both drifts and turbulent transport compete to determine the heat flux width. The magnetic drifts play a dominant role in setting the divertor heat-flux width, while the E × B drift decreases the heat flux width by 10%–25%, leading to improved agreement with the experiment relative to Goldston’s model. A turbulence diffusivity scan (χ⊥) identifies two distinct regimes: a drift dominant regime when χ⊥ is small and a turbulence dominant regime when χ⊥ is large. The Goldston heuristic drift model yields a lower limit of the width λq.

First experimental tests of a new small angle slot divertor on DIII-D

A new small angle slot (SAS) divertor concept has been developed to enhance neutral cooling across the divertor target by coupling a closed slot structure with appropriate target shaping. Initial tests on DIII-D find a strong interplay between such anticipated ‘SAS’ effects and cross-field drifts, favouring operation with the ion B × ∇B drift away from the X-point, as currently employed for advanced tokamaks. This offers the following key improvements relative to DIII-D’s open lower divertor or partially-closed upper divertor: (i) SAS allows for transition to low temperature moderately detached divertor conditions with Te ≲ 10 eV at very low main plasma densities, lower than are usually attainable at all in DIII-D high confinement (H-mode) plasmas as used in these tests; (ii) Pedestal performance and core confinement are significantly improved with SAS. The final confinement collapse associated with the onset of X-point MARFE (multifaceted asymmetric radiation from the edge) following deep detachment occurs at significantly higher pedestal densities, thus widening the window of H-mode operation compatible with a dissipative divertor. For operation with the ion B × ∇B drift toward the X-point, the divertor plasma transitions to a bifurcative detached state at much higher densities, similar to other divertor configurations in DIII-D. These results highlight the strong interplay between divertor closure and drifts, and point to an interesting divertor optimization path to explore that offers potential for future fusion reactors.

Dependence of neutral pressure on detachment in the small angle slot divertor at DIII-D

Abstract Local neutral pressure measurements in the closed small angle slot (SAS) divertor [1,2] on DIII-D show a large increase when the divertor plasma shifts from high recycling into detachment. In-tile pressure gauges were installed to measure the pressure in the near- and far-SOL regions to examine the predicted high neutral pressures and compression. Cross-field drift effects lead to ∼ 10 × higher peak neutral pressure in detachment with the ion ∇B drift toward the divertor compared to out of the divertor, with similar pressures in attached conditions. Drifts also play a role in the neutral distribution in the slot while attached but become less pronounced in detachment once gradient drives reduce. Variation in the outer strike point location found higher neutral pressure and detachment at modestly lower main-plasma density with the strike point positioned away from the designed operation point. Reducing the fraction of the SOL width allowed into the slot increases neutral leakage into the main chamber and increases the main-plasma density required for detachment. Preliminary modeling with the SOLPS code without drifts over-predicts the neutral pressure in detachment by a factor of 2 with the strike point in the designed operation point while more significantly over-predicts the neutral slot compression; experiments show a broader distribution of neutrals through the slot. These measurements are used to help understand detachment and validate divertor design metrics.

UEDGE-predicted impact of molecules on low-field side target detachment in DIII–D

Abstract The impact of fluid molecules on detachment was studied using the edge fluid code UEDGE for a set of DIII–D L-mode plasmas with varying degree of low-field side (LFS) target detachment. A baseline atom-only, fluid-neutral model was compared to models including diffusive deuterium molecules with user-defined molecular temperatures and molecular temperatures solved via an energy equation, respectively. The UEDGE simulations including molecules with their temperature solved via the molecular energy equation displayed improved qualitative agreement with DIII–D measurements. However, at LFS separatrix electron densities below 1.3 × 10 19 m − 3 the LFS target peak electron temperature was over-estimated compared to the DIII–D measurements by a factor of 1.5–2. Kinetic effects, as the SOL collisionalities for LFS separatrix electron densities below 1.3 × 10 19 m − 3 are ν S O L * ≲ 15 , could contribute to this discrepancy. At LFS separatrix electron densities above 1.5 × 10 19 m − 3 UEDGE predicted LFS target peak ion current and electron densities a factor up to ∼ 4 lower than the DIII–D-measured values for all models. The consideration of molecules in UEDGE simulations induced a stable X-point MARFE, while an X-point MARFE was not achieved with the ion-atom model. The X-point MARFE forms due to a high-density front which connects the high-field side (HFS) and LFS divertor legs over the X-point, and is not observed for the atom-only UEDGE simulations. The high-density front forms due to molecular particle dynamics and cross-field drifts increasing the plasma density towards the X-point in the HFS leg.

Impact of drifts on divertor power exhaust in DIII-D

Abstract Radiative divertor experiments and 2D fluid simulations show strong impact of cross-field drifts on the low field side (LFS) divertor target heat flux and volumetric radiation profiles when evolving to detached conditions in DIII-D high confinement mode (H-mode) plasmas with forward and reversed toroidal field configurations. In both field configurations, the peak heat flux is reduced by about a factor of 2 in detachment by D2-injection and by factor of 3 – 4 in detachment by N2-injection. Operating with the B × ∇B-drift towards the X-point (fwd. B T ), the LFS divertor radiation front is observed to shift step-like from the target to near to the X-point at the onset of detachment. In contrast, operating with the B × ∇B-drift away from the X-point (rev. B T ), the radiation front is observed to remain closer to the target plate and to be radially shifted towards the far SOL. These phenomena occur with detachment induced both with N2- and D2-injection. The step-like detachment onset is consistent with recently published theory of the role of poloidal E × B-drift in the private flux region in driving highly non-linear detachment onset in fwd. B T [22].

Asymptotic Behavior for the Vlasov--Poisson Equations with Strong External Magnetic Field. Straight Magnetic Field Lines

The subject matter of this paper concerns the Vlasov-Poisson equations in the framework of magnetic confinement. We study the behavior of the Vlasov-Poisson system with strong external magnetic field, when neglecting the curvature of the magnetic lines. The arguments rely on averaging techniques. We intend to determine second order approximations and to retrieve the usual electric cross field drift, the magnetic gradient drift, etc.

Experimental observation of drift wave turbulence in an inhomogeneous six-pole cusp magnetic field of MPD

This paper presents a detailed study on the controlled experimental observation of drift wave instabilities in an inhomogeneous six pole cusp magnetic field generated by an in-house developed multi-pole line cusp magnetic field device [Patel et al., Rev. Sci. Instrum. 89, 043510 (2018)]. The device is composed of six axially symmetric cusps and non-cusp (in between two consecutive magnets) regions. The observed instability has been investigated in one of these non-cusp regions by controlling the radial plasma density gradient with changing pole magnetic field which is a unique feature of this device. It has been observed that the frequency of the instability changes explicitly with the density gradient. Moreover, the scale lengths of plasma parameters, frequency spectrum, cross-correlation function, and fluctuation level of plasma densities have been measured in order to identify the instability. The cross field drift velocity due to fluctuation in plasma parameters has been measured from the wave number-frequency S (kz, ω) spectrum and verified with the theoretical values obtained from density scale length formula. Further, from the S (kz, ω) spectrum, it has been found that the drift velocity alternates the sign in the consecutive non-cusp regions.

Divertor leg filaments in NSTX-U

This paper presents the first observation of divertor localized turbulence in the NSTX-Upgrade spherical tokamak. Previous work in NSTX discharges (Maqueda et al 2010 Nucl. Fusion 50 075002) described fluctuations on the divertor target due to blobs generated on the low field side midplane. In the region that shows disconnection from upstream turbulence (private flux region and proximity of the strike point), divertor-localized fluctuations are observed via imaging of C III and D-α emission in diverted L-mode discharges and are characterized in this paper. Field-aligned filaments connected to the divertor target plate are radially localized at the separatrix on the outer divertor leg and in the private flux region on the inner divertor leg. These are limited to the region below the X-point with fluctuation levels up to 10%–20%. The filaments have comparable poloidal and radial correlation lengths (10–100 ion gyroradii ) and parallel correlation lengths of several meters. Toroidal mode numbers are in the range of 10–30 and 2–10 for outer and inner leg filaments. The poloidal motion of outer leg filaments has the same direction and comparable magnitude to advection due to drift calculated by the multi-fluid edge transport code UEDGE with inclusion of cross field drifts. Disconnection between inner and outer leg filaments as well as the absence of correlation with upstream turbulence support the hypothesis of X-point disconnection for divertor leg filaments. Simulations with the ArbiTER linear eigenvalue solver and a resistive-balooning model were performed with a simulation grid limited to the divertor legs. Instabilities localized to the bad curvature side of the divertor legs were observed, in qualitative agreement with the experiment.

Impedance and Magnetohydrodynamic Measurements for Label Free Detection and Differentiation of E. Coli and S. Aureus Using Magnetic Nanoparticles.

In this paper, we used the distinguishable surface charge and mass of different bacterial strains for label free detection and differentiation of pathogen through impedance and magnetohydrodynamic (MHD) analysis. For the isolation of Escherichia coli and Staphylococcus aureus, functionalized magnetic nanoparticles (MNPs) were used. The proposed method is aimed at minimizing extensive chemical preparation and labor intensive conventional microbiological processing thereby reducing the detection time. Pathogens isolated from broth cultures using the MNPs were subjected to impedance rate measurement through an arduino-based automated impedance sensor along with differentiation on the basis of Larmor's motion through the MHD approach. The proposed method evidently reports that the two bacterial species bind differently to the MNPs giving appreciable variation in the impedance rate increment for a dc electric field of 250V/m. In addition to this, cross-field drift through 171.4 V/m electric field and a normal magnetic field of 500 Gauss led to lump formation in S. aureus but had no such effect on E. coli. The mobility analysis of the two species of bacteria was also carried out by observing the gyration of bacteria through naked eyes. The mobility of lumped bodies of S. aureus was of the order 10-10 m2/V sec; whereas for dispersed E. coli, it was 10-08 m2/V sec.