Edge Current Density Research Articles

Technical note: Computational study on thermal management schemes for tumor-treating fields therapy.

The study focuses on thermal management in tumor-treating fields (TTFields) therapy, crucial for patient compliance and therapeutic effectiveness. TTFields therapy, an established treatment for glioblastoma, involves applying alternating electric fields to the brain. However, managing the thermal effects generated by electrodes is a major challenge, impacting patient comfort and treatment efficiency. This research aims to explore methods for controlling temperature increases during TTFields therapy without reducing its duty cycle. The study emphasizes optimizing electrode configurations and array arrangements to mitigate temperature rise, thereby maintaining therapy effectiveness and patient compliance. Using a simplified multi-layer tissue model and finite element analysis, various electrode configurations and array shapes were tested in COMSOL Multiphysics v6.0. Adjustments included changing the electrode gel layer radius from 8 to 12mm, electrode spacing, and transitioning to a more uniform array arrangement, such as a square array or a circular array. The study revealed a strong correlation between high temperatures and edge current density distributions on electrodes. It was found that increasing the electrode gel layer's diameter, enlarging electrode spacing, and adopting a uniform array arrangement markedly mitigated temperature rises. By increasing the gel layer radius from the original 10 to 12mm, a reduction in the peak temperature increases of approximately 0.3°C was observed. Changing the layout from rectangular to circular with the same area further reduced the peak temperature rise by 0.5°C. Additionally, enlarging the spacing between electrodes also contributed to temperature control. By integrating these strategies, we designed a new circular electrode array with an electrode spacing of 45mm and a gel radius of 12mm, successfully reducing the peak temperature from 42.1°C to 40.8°C, effectively achieving temperature control. The research demonstrates that improving electrode and array configurations can effectively manage temperature in TTFields therapy without compromising treatment duration. This strategy is crucial as TTFields therapy relies on prolonged field exposure for effectiveness. The findings offer valuable insights into thermal management in electrode array design and could lead to enhanced patient compliance and treatment efficacy in TTFields therapy.

Impacts of recycling impurity on the background ELM behavior during repetitive radiative divertor experiments in EAST

A significant change in the background ELM behavior prior to neon (Ne) seeding has been observed in a series of repetitive radiative divertor experiments in EAST. With similar operational parameters, the ELM behavior before Ne seeding changes from large to mixed ELMs, and finally evolves to pure small ELMs. Meanwhile, a significant increase in both Ne and high-Z impurity (W and Mo) emissions has been observed in the bulk plasma, suggesting the retention and recycling of Ne impurity from the wall surface. Experimental results show that the variation in background ELM behavior is highly correlated with the occurrence of high-Z impurity accumulation. The increased accumulation of high-Z impurities leads to a lower electron temperature both in the plasma core and edge, accompanied by a higher and more peaked electron density in the plasma core. Pedestal linear stability analysis reveals that the decreased pedestal electron temperature and thus the lower pressure gradient and lower edge current density are the primary reason for the change of background ELM behavior. The concentration of recycling Ne in the bulk plasma is estimated to be ∼1% in the discharges with pure small ELMs.

Spatial heterodyne spectroscopy for fast local magnetic field measurements of magnetized fusion plasmas.

A novel spectroscopy diagnostic for measuring internal magnetic fields in high temperature magnetized plasmas has been developed. It involves spectrally resolving the Balmer-α (656nm) neutral beam radiation split by the motional Stark effect with a spatial heterodyne spectrometer (SHS). The unique combination of high optical throughput (3.7 mm2sr) and spectral resolution (δλ ∼ 0.1 nm) allows these measurements to be made with time resolution ≪1ms. The high throughput is effectively utilized by incorporating a novel geometric Doppler broadening compensation technique in the spectrometer. The technique significantly reduces the spectral resolution penalty inherent to using large area, high-throughput optics while still collecting the large photon flux provided by such optics. In this work, fluxes of order 1010s-1 support the measurement of deviations of <5 mT (ΔλStark ∼ 10-4 nm) in the local magnetic field with 50 µs time resolution. Example high time resolution measurements of the pedestal magnetic field throughout the ELM cycle of a DIII-D tokamak plasma are presented. Local magnetic field measurements give access to the dynamics of the edge current density, which is essential to understanding stability limits, edge localized mode generation and suppression, and predicting performance of H-mode tokamaks.

Cavity-induced chiral edge currents and spontaneous magnetization in two-dimensional electron systems

We consider a laterally confined two-dimensional electron gas (2DEG), placed inside a gyrotropic cavity. Splitting of the circularly polarized electromagnetic modes leads to the emergence of the ground state spontaneous magnetization, anomalous Hall effect and chiral edge currents in 2DEG. We examine the dependence of the magnetization and edge current density on the system size for two particular cases of the confining potential: infinite wall and parabolic potentials. We show that paramagnetic and diamagnetic contributions to the edge currents have qualitatively different dependence on the system size. These findings pave the route to the design quantum electrodynamic engineering of the material properties of the mesoscopic electron systems.

Design study of an edge current density diagnostic using new high-performance single-channel beam emission spectrometers at DIII-D.

A novel Motional Stark Effect spectroscopy system has been designed for application at the DIII-D tokamak. The system is optimized for studies of the poloidal and toroidal magnetic field in the plasma pedestal region with frame rates of up to 10kHz. Light from an existing high-photon-throughput collection lens is analyzed using four single-channel f/2.8 Czerny-Turner spectrometers that use custom-made lens systems instead of mirrors. Each spectrometer has two separate outgoing legs and is operated in a positive grating order, which allows for simultaneous observations of D-alpha and D-beta spectra. Forward modeling using the code FIDASIM shows a radial resolution of the system close to 0.6cm and sufficiently good spectral resolution when masking the high throughput light collection lens in the horizontal direction to avoid overly strong Doppler broadening of beam emission lines. Moreover, a detailed sensitivity study considering realistic levels of readout and photon noise shows that the poloidal and toroidal magnetic field strengths can be inferred with an uncertainty of less than 1%, which will allow the inference of changes of the plasma current during transient events.

Local measurements of the pedestal magnetic field profile throughout the ELM cycle on DIII-D

New high speed localized measurements of the pedestal magnetic field during the edge localized mode (ELM) cycle of a DIII-D High confinement mode (H-mode) discharge indicate a temporally and spatial complex redistribution of the edge current density profile, jedge. The measurement technique extracts the magnetic field magnitude, B, via the spectral separation of Stark-split neutral beam radiation in the pedestal. Single spatial channel measurements from a novel spatial heterodyne spectrometer are validated in discharges with core current profile changes. The technique measures Stark-splitting changes that imply B changes as small as 1 mT with high time resolution (50 μs). At normalized poloidal flux ψn=1.0, B appears saturated in the inter-ELM period and then rapidly decreases in &amp;lt;200 μs by ∼1%, before edge recycling emission begins to increase. Radially inboard of jedge, B increases at the ELM crash. The behavior is consistent with a rapid collapse of jedge at the ELM crash and subsequent pedestal recovery. In some discharges, at ψn&amp;lt;0.96, changes in B are observed throughout the ELM cycle. In others, B recovers and is relatively stable until a few ms leading up to the next crash. Measurements of B during the H-mode transition show a large increase at ψn=1 with little change at ψn=0.9, consistent with the formation of the edge bootstrap current density peak. The ψn=0.9 spectrum is complicated by predicted changes to the Stark component intensities with density at the L–H transition.

Technical note: Evaluation of methods for reducing edge current density under electrode arrays for tumor-treating fields therapy.

Tumor-treating fields (TTFields) therapy is increasingly utilized clinically because of its demonstrated efficacy in cancer treatment. However, the risk of skin burns must still be reduced to improve patient safety and posttreatment quality of life. The purpose of this study was to evaluate the methods of constructing electrode arrays that reduce current density exceeding threshold values, which can cause skin burns during TTFields therapy. Electrode and body models were generated using COMSOL software. The body model had the dielectric properties of the scalp. The average current density beneath the central region of the electrode was maintained at ∼31mA/cm2 RMS. The deviations in current density at the edges of the electrode were reduced by three methods: adjustment of the ceramic thickness ratio of the center to the edge from 1/5 to 4/5, adjustment of the radius of the metal plate from 5.0 to 8.0mm, and insertion of an insulator of width 0.5 to 2mm at the edge. While using a single circular electrode, adjustment of the ceramic thickness ratio, adjustment of the metal plate radius, and insertion of an insulator near the edge reduced the deviations of current density by 14.6%, 67.7%, and 75.3%, respectively. Similarly, while using circular electrode arrays, inserting an insulator at the edge of each electrode reduced the deviations of current density significantly, from 8.62 to 2.40mA/cm2 . Insertion of an insulator at the edge of each electrode was found to be the most effective method of attaining uniform current density distribution beneath the electrode, thereby lowering the risk of adverse effects of TTFields therapy.

Kink–ballooning mode in circular tokamak plasma

Peeling–ballooning modes, which are driven by gradients of parallel current and pressure in the pedestal, are widely accepted as the instability triggering large Edge Localized Modes (ELMs). However, the current-driven mode related to ELMs is not fully understood. This paper is about comparing the kink mode to the peeling mode, and the modified current profiles are specifically made to be simultaneously kink stable/peeling unstable or vice versa so that the two modes (or the modes coupled to peeling modes) can be compared. Caltrans-Corsica is used to generate a series of equilibria with modified edge current profiles. Based on these equilibria, the effects of edge current density on plasma instabilities are studied with the three-field BOUT++ elm-pb code. The results suggest that kink–ballooning modes can drive ELMs in some peeling-stable regions. Compared to the peeling–ballooning mode, kink–ballooning modes have comparatively lower poloidal resonant modes and growth rates at low toroidal mode numbers.

Robustness of quantized transport through edge states of finite length: Imaging current density in Floquet topological versus quantum spin and anomalous Hall insulators

The theoretical analysis of topological insulators (TIs) has been traditionally focused on infinite homogeneous crystals with band gap in the bulk and nontrivial topology of their wavefunctions, or infinite wires whose boundaries host surface or edge metallic states. However, experimental devices contain finite-size topological region attached to normal metal (NM) leads, which poses a question about how precise is quantization of longitudinal conductance and how electrons transition from topologically trivial NM leads into the edge states. This is particularly pressing issues for recently conjectured two-dimensional (2D) Floquet TI where electrons flow from time-independent NM leads into time-dependent edge states---the very recent experimental realization of Floquet TI using graphene irradiated by circularly polarized light did not exhibit either quantized longitudinal or Hall conductance. Here we employ charge conserving solution for Floquet-nonequlibrium Green functions (NEGFs) of irradiated graphene nanoribbon to compute longitudinal two-terminal conductance, as well as spatial profiles of local current density as electrons propagate from NM leads into the Floquet TI. In the case of Floquet TI both bulk and edge local current densities contribute equally to total current, which leads to longitudinal conductance below the expected quantized plateau that is slightly reduced by edge vacancies. We propose two experimental schemes to detect coexistence of bulk and edge current densities within Floquet TI: (i) drilling a nanopore in the interior of irradiated region of graphene will induce backscattering of bulk current density, thereby reducing longitudinal conductance by $\sim 28$%; (ii) imaging of magnetic field produced by local current density using diamond NV centers.

A pilot study: Efficient electrowinning of tellurium from alkaline solution by cyclone electrowinning technology

Efficient electrowinning is critical for industrial tellurium (Te) production. To overcome the bottlenecks of a low production rate and low recovery in conventional processes, Te electrowinning tests with three different current densities were conducted in an industrial pilot-scale cyclone electrowinning cell. A numerical simulation of the flow field and electric field in the electrowinning cell was undertaken and the results were visualized by finite-element analysis using COMSOL Multiphysics. The cathode Te purity and production parameters were compared with those of the traditional technology. The numerical simulations and pilot-scale test results indicated that the electrolyte flow rate near the cathode wall remained above 0.15 m·s−1 because of the high flow velocity at the base. A feasible condition for Te electrowinning with high current densities was provided based on the electrode reaction kinetics. Te was deposited stably at a large scale and at high current densities up to 200 A·m−2. Efficient Te electrowinning was achieved with a high current efficiency of 97.1% on an industrial scale. The production rate was increased from 0.88 kg·m−2·d−1 to 5.04 kg·m−2·d−1 and the final electrolyte concentration was reduced from 80 g·L−1 to 30 g·L−1. A 2 N Te product was obtained with a recovery of 85.22%, and the Te purity after casting increased to 4 N. The excessive current density at the edge of the cathode sheet that was caused by the edge effect resulted in the formation of prominent nodules. The cathode sheet disintegrated because of an excessive deposition current and uneven edge current density.

Understanding the reduction of the edge safety factor during hot VDEs and fast edge cooling events

In the present work, a simple analytical approach is presented in order to clarify the physics behind the edge current density behavior of a hot plasma entering in contact with a resistive conductor. As has been observed in recent simulations [C. R. Sovinec and K. J. Bunkers, Plasma Phys. Controlled Fusion 61(2), 024003 (2019)], when a plasma comes in contact with a highly resistive wall, large current densities appear at the edge of the plasma. The model shows that this edge current originates from the plasma response, which attempts to conserve the poloidal magnetic flux (Ψ) when the outer current is being lost. The loss of outer current is caused by the high resistance of the outer current path compared with the plasma core resistance. The resistance of the outer path may be given by plasma contact with a very resistive structure or by a sudden decrease in the outer plasma temperature (e.g., due to a partial thermal quench or due to a cold front penetration caused by massive gas injection). For general plasma geometries and current density profiles, the model shows that, given a small change in minor radius (δa), the plasma current is conserved to first order [δIp=0+O(δa2)]. This conservation comes from the fact that total inductance remains constant (δL=0) due to an exact compensation of the change in external inductance with the change in internal inductance (δLext+δLint=0). As the total current is conserved and the plasma volume is reduced, the edge safety factor drops according to qa∝a2/Ip. Finally, the consistency of the resulting analytical predictions is checked with the help of free-boundary MHD simulations.

Long-lived coupled peeling ballooning modes preceding ELMs on JET

In some JET discharges, type-I edge localised modes (ELMs) are preceded by a class of low-frequency oscillations (Perez et al 2004 Nucl. Fusion 44 609). While in many cases the ELM is triggered during the growth phase of this oscillation, it is also observed that this type of oscillation can saturate and last for several tens of ms until an ELM occurs. In order to identify the nature of these modes, a wide pre-ELM oscillation database, including detailed pedestal profile information, has been assembled and analysed in terms of MHD stability parameters. The existence domain of these pre-ELM oscillations and the statistical distribution of toroidal mode numbers (n) up to n = 16 have been mapped in ballooning alpha () and either edge current density () or pedestal collisionality () coordinates and compared to linear MHD stability predictions. The pre-ELM oscillations are reliably observed when the ratio is high enough for the pedestal to access the coupled peeling-ballooning (PB) domain (aka stability nose). Conversely, when the pedestal is found to be in or near the high-n ballooning domain (which is at low ratio), ELMs are usually triggered promptly, i.e. with no detectable pre-ELM oscillations, or with pre-ELM oscillations only observable on ECE whose n appears to be too high to be resolved by the magnetics. Individual discharges can sometimes exhibit a fairly wide range of pre-ELM mode numbers, but for a wider database, the statistical n-number domains are found to be well ordered along the stability boundary and behave as expected from PB theory: the higher the ratio, the lower the mode’s measured n tends to be. Within the measurement uncertainties, the measured n is usually found to be compatible with the most unstable n predicted by the linear stability code MISHKA1. These results confirm the earlier hypothesis that these modes are coupled peeling-ballooning modes, and extend and generalise to higher-mode numbers the work by Huysmans et al (1998 Nucl. Fusion 38 179), who identified the lowest n modes as pure external kink modes. Since the destabilisation of PB modes is widely accepted to give rise to ELMs, the mode saturation and delayed ELM triggering that is sometimes observed is rather unexpected. Possibilities to reconcile the extended lifetime of these modes with current ELM models are briefly discussed, but will require further investigation.

Design of the Synthetic Aperture Microwave Imager Upgrade for measurement of the edge current density on MAST-U

The Synthetic Aperture Microwave Imager (SAMI) has demonstrated the feasibility of 2D Doppler backscattering for measurement of the edge magnetic pitch angle on MAST and NSTX-U. The aim of SAMI-Upgrade (SAMI-U) is to build on this methodology to produce higher quality pitch angle data simultaneously in multiple spatial locations, enabling calculation of the edge current density. This movement from proof of principle to production quality necessitates several alterations to the design. There will be a fourfold increase in the number of antennas, as minimising the sidelobe level is key to ensuring maximum resolution in the reconstructed Doppler backscattered power map. SAMI-U will actively probe the plasma with two frequencies at the same time. These correspond to two different backscattering locations in the edge plasma which allows the edge current density to be calculated from the measured magnetic field vector. Dual-polarised sinuous antennas will be used in the array as they are planar and broadband. Polarisation separation is necessary for differentiation between the O-and X-mode cut off surfaces, as their locations can be separated by up to a few centimetres. Due to spatial constraints many of the components will be placed on a PCB behind each antenna. FPGAs will be used to stream the high data throughput, over 16 GB s−1, into PC memory.

Estimating the performance of lithium beam measurements of current density and electron density in an H-mode pedestal.

The lithium beam is an effective diagnostic tool for investigation of stability and particle transport in the pedestal. It was used successfully to measure edge current density on DIII-D, achieving qualitative agreement with neoclassical models. Electron density profiles were also measured. Proposed upgrades will continue these measurements with higher reliability as well as explore edge current measurements using spectroscopy. The optics will be redesigned to optimize throughput and aperture broadening and to replace the photomultiplier tubes with avalanche photodiodes. The new system will yield detailed measurements of the pedestal, complementing existing diagnostics for investigating pedestal stability, edge localized mode cycle, and particle transport through the pedestal.

Inter-ELM evolution of the edge current density in JET-ILW type I ELMy H-mode plasmas

Recent studies (Maggi et al 2015 Nucl. Fusion 55 113031; Maggi et al 2017 Nucl. Fusion 57 116012) have shown that on JET with the Be/W ITER-like wall (JET-ILW) in high β discharges with high D2 gas rates, the inter-ELM temperature pedestal growth is saturated half way through the ELM cycle, leading to plasmas with reduced confinement, and that the linear MHD stability of these pedestals is inconsistent with the peeling–ballooning paradigm (Snyder et al 2002 Phys. Plasmas 9 2037–43; Wilson et al 2002 Phys. Plasmas 9 1277–86). In this paper, the inter-ELM evolution of the edge current density is investigated in a wide range of type I ELMy H-modes on JET-ILW. It is found that in discharges at a low gas rate, the peak edge bootstrap current continuously increases until the ELM crashes, while it saturates during the ELM cycle at high gas rates. The effect of current diffusion on the build-up of the edge current inter-ELM is assessed by simulating the Ohmic current contribution with the JETTO transport code. The simulations indicate that current diffusion contributes little to the time evolution of the total edge current in the second half of the ELM cycle and the total current is dominated by the bootstrap current. Therefore, current diffusion does not explain why JET-ILW type I ELMy pedestals at a high gas rate and high βN are found to be stable to peeling–ballooning modes.

The comparison between modeling of edge localized modes with a current relaxation model and experiment on EAST

The distinctions of edge localized mode (ELM) frequency distributions between moderate and high edge current density cases were observed on the experiment advanced superconducting tokamak. In this paper, a current relaxation model is applied to explain this new observation. It has been demonstrated that the ELM frequency is very sensitive to the edge current density and the edge safety factor by the model predictions. The results also show that, in the large edge current density case, the ELM frequency is subject to a single-peak distribution; while in the moderate edge current density case, the ELM frequency is subject to a roughly multi-peak distribution.

Connection between plasma response and resonant magnetic perturbation (RMP) edge localized mode (ELM) suppression in DIII-D

Calculations of the plasma response to applied non-axisymmetric fields in several DIII-D discharges show that predicted displacements depend strongly on the edge current density. This result is found using both a linear two-fluid-MHD model (M3D-C1) and a nonlinear ideal-MHD model (VMEC). Furthermore, it is observed that the probability of a discharge being edge localized mode (ELM)-suppressed is most closely related to the edge current density, as opposed to the pressure gradient. It is found that discharges with a stronger kink response are closer to the peeling–ballooning stability limit in ELITE simulations and eventually cross into the unstable region, causing ELMs to reappear. Thus for effective ELM suppression, the RMP has to prevent the plasma from generating a large kink response, associated with ELM instability. Experimental observations are in agreement with the finding; discharges which have a strong kink response in the MHD simulations show ELMs or ELM mitigation during the RMP phase of the experiment, while discharges with a small kink response in the MHD simulations are fully ELM suppressed in the experiment by the applied resonant magnetic perturbation. The results are cross-checked against modeled 3D ideal MHD equilibria using the VMEC code. The procedure of constructing optimal 3D equilibria for diverted H-mode discharges using VMEC is presented. Kink displacements in VMEC are found to scale with the edge current density, similar to M3D-C1, but the displacements are smaller. A direct correlation in the flux surface displacements to the bootstrap current is shown.

Overview of recent pedestal studies at ASDEX Upgrade

New or upgraded diagnostics of the edge transport barrier allow investigations of the dominant transport mechanisms in the pedestal. The density build-up after the L–H transition can be explained with a mainly diffusive edge transport barrier. A small inward convection term improves the agreement between modelling and experiment, but its existence cannot be confirmed due to the uncertainty in the neutral sources. Measurements of the impurity ion flow asymmetry as well as the edge current density are in agreement with neoclassical modelling. The inter-ELM pedestal recovery was traced with ideal peeling–ballooning modelling, which shows that the stability boundary moves closer to the operational point as the pedestal becomes wider. Gyrokinetic modelling of the different phases reveal that density gradient driven trapped electron modes are dominant during the early recovery, while electron temperature gradient modes or kinetic ballooning modes determine the temperature gradient in the final phase. Microtearing modes are modelled and also experimentally determined at the top of the pedestal. Non-linear coupling between modes could explain the failure of ideal linear MHD modelling.

Test of bootstrap current models using high-βp EAST-demonstration plasmas on DIII-D

Magnetic measurements together with kinetic profile and motional Stark effect measurements are used in full kinetic equilibrium reconstructions to test the Sauter and NEO bootstrap current models in a DIII-D high- EAST-demonstration experiment. This aims at developing on DIII-D a high bootstrap current scenario to be extended on EAST for a demonstration of true steady-state at high performance and uses EAST-similar operational conditions: plasma shape, plasma current, toroidal magnetic field, total heating power and current ramp-up rate. It is found that the large edge bootstrap current in these high- plasmas allows the use of magnetic measurements to clearly distinguish the two bootstrap current models. In these high collisionality and high- plasmas, the Sauter model overpredicts the peak of the edge current density by about 30%, while the first-principle kinetic NEO model is in close agreement with the edge current density of the reconstructed equilibrium. These results are consistent with recent work showing that the Sauter model largely overestimates the edge bootstrap current at high collisionality (Belli et al 2014 Plasma Phys. Control. Fusion 56 045006).

Impact of Te and ne on edge current density profiles in ELM mitigated regimes on ASDEX Upgrade

ELM resolved edge current density profiles are reconstructed using the CLISTE equilibrium code. As input, highly spatially and temporally resolved edge electron temperature and density profiles are used in addition to data from the extensive set of external poloidal field measurements available at ASDEX Upgrade, flux loop difference measurements, and current measurements in the scrape-off layer. Both the local and flux surface averaged current density profiles are analysed for several ELM mitigation regimes. The focus throughout is on the impact of altered temperature and density profiles on the current density. In particular, many ELM mitigation regimes rely on operation at high density. Two reference plasmas with type-I ELMs are analysed, one with a deuterium gas puff and one without, in order to provide a reference for the behaviour in type-II ELMy regimes and high density ELM mitigation with external magnetic perturbations at ASDEX Upgrade. For type-II ELMs it is found that while a similar pedestal top pressure is sustained at the higher density, the temperature gradient decreases in the pedestal. This results in lower local and flux surface averaged current densities in these phases, which reduces the drive for the peeling mode. No significant differences between the current density measured in the type-I phase and ELM mitigated phase is seen when external perturbations are applied, though the pedestal top density was increased. Finally, ELMs during the nitrogen seeded phase of a high performance discharge are analysed and compared to ELMs in the reference phase. An increased pedestal pressure gradient, which is the source of confinement improvement in impurity seeded discharges, causes a local current density increase. However, the increased Zeff in the pedestal acts to reduce the flux surface averaged current density. This dichotomy, which is not observed in other mitigation regimes, could act to stabilize both the ballooning mode and the peeling mode at the same time.