Radial Field Research Articles

Cattaneo-Christov heat flux model in radiative flow of (Fe3O4– TiO2/Transformer oil) and (Cu– TiO2/Transformer oil) magnetized hybrid nanofluids past through double rotating disks

Recent progresses in nanotechnologies and nanoscience have led to the creation of hybrid nanofluids, which are a complicated category of fluids with superior thermal features to regular nanofluids. The current framework demonstrates the importance of a two-dimensional steady incompressible axisymmetric flow of Maxwell hybrid nanofluid over double disks with thermal radiation. This investigation analyzes a novel idea regarding the execution of the Cattaneo-Christov heat theory and melting phenomenon by considering transformer oil as a base fluid. Two dissimilar classes of hybrid nanofluid, Iron–Titanium oxide/Transformer oil (Fe3O4–TiO2/TO) and Copper–Titanium oxide/Transformer oil (Cu–TiO2/TO) have been taken into our research work. The main equations (PDEs)are translated into a present set of ODEs using the necessary similarity variables. In MATLAB, the shooting scheme is utilized to evaluate the numerical and graphical outcomes of physical flow parameters. The radial velocity rose as the volume fraction of nanoparticles increased. The radial velocity field is increased as the porosity parameter is enhanced. The temperature profile is decreased with increasing the values of the thermal redaction parameter. Furthermore, because of the higher compactness of the copper nanoparticles, the addition of the volume fraction of nanoparticles slows the flow profile, and because copper is an excellent conductor of heat, it raises the fluid temperature throughout the domain. The mathematical fallouts also tackle the idea of employing magnetized spinning discs in space engines and nuclear propulsion, and such a model carries useful applications in heat transfer enhancement in a wide range of industrial thermal management devices and renewable energy generation systems.

Swirling flow analysis of Eyring–Powell fluid between coaxial disks with variable property

Abstract The main objective of this study is to examine an unsteady swirling flow of a non-Newtonian Eyring–Powell fluid between two coaxial disks. The lower and upper disks are considered to rotate with different angular velocities. The three-dimensional axisymmetric flow phenomenon and heat transfer mechanism are observed with the consequences of the magnetic field and variable thermal conductivity of the fluid. The variable thermal conductivity is taken to be dependent on the fluid temperature. The implementation of the Von Karman similarity transformations on the constituting equations of the flow phenomenon yields the dimensionless system of the non-linear equations. An optimal homotopy analysis technique is adopted to obtain analytical solutions for highly non-linear equations. In view of the same and opposite directions of disks rotation, the various aspects of the flow system corresponding to the pertinent parameters are discussed with physical significance. The obtained results indicate that both radial and axial fields are the escalating functions of the Eyring–Powell fluid parameter. Moreover, the heat transfer rate enhances with the improving variable thermal conductivity parameter.

Extracting Spatial–Temporal Coherent Patterns in Geomagnetic Secular Variation Using Dynamic Mode Decomposition

AbstractRapid growth of magnetic‐field observations through SWARM and other satellite missions motivate new approaches to analyze it. Dynamic mode decomposition (DMD) is a method to recover spatially coherent motion with a periodic time dependence. We use this method to simultaneously analyze the geomagnetic radial field and its secular variation from CHAOS‐7 at high latitudes. A total of five modes are permitted by noise levels in the observations. One mode represents a slowly evolving background state, whereas the other four modes describe a pair of waves; each wave is comprised of a complex DMD mode and its complex conjugate. The waves have periods of T1 = 19.1 and T2 = 58.4 years and quality factors of Q1 = 11.0 and Q2 = 4.6, respectively. A 60‐year wave is consistent with previous predictions for zonal waves in a stratified fluid. The 20‐year wave is also consistent with previous reports at high latitudes, although its nature is less clear.

Coupling resonance correction and avoidance for the TRIUMF 500 MeV cyclotron

The linear coupling resonance νr - νz = 1 in a cyclotron is driven by the first harmonic in the radial gradient of the radial magnetic field. In the TRIUMF 500 MeV cyclotron, this resonance is encountered multiple times. When the circulating beam is off-centred radially passing through the resonance, the radial betatron oscillation can be converted into vertical oscillation, which can cause beam losses and radio-activation. We investigated this resonance with goal to correct it by using the available harmonic correction coils. Moreover, we improved the cyclotron vertical tune measurement by using trim coils to create a flat-top radial field, and thus confirmed an extra νr - νz = 1 coupling resonance passage as this is unexpected from the historical tune diagram. To avoid this passage, the local vertical tune is adjusted to stay farther away from the resonance line by using the trim coils axial field, but at the cost of a local excursion in isochronism. After the correction and the avoidance of this resonance, both the coherent and incoherent vertical oscillations are decreased, thus helping to reduce the machine tank spills under high intensity operation. In this paper, we present the results of calculations and simulations as well as measurements that we undertook.

Redundant field survey data of cyclotron with imperfect median plane

An accurate and detailed field map is important for cyclotron beam dynamics studies. During the long history of cyclotron studies, many techniques have been developed by cyclotron pioneers for the treatment of median plane field map. In this paper, we take the TRIUMF 500 MeV cyclotron as an example to study the asymmetric field resulting from imperfect median plane symmetry. The “Gordon approach” and a highly accurate compact finite differentiation method are used to investigate the historical field survey data. The redundancy in the survey data is revealed by the expansion method, which also makes it possible to correct the error in the measurement. Finally, both the azimuthal field Bθ and the axial gradient of the axial field dBz /dz in the median plane are corrected using the radial field map Br . The influence of the correction is examined by recalculating the equilibrium orbit properties of the TRIUMF cyclotron. The result shows significantly increased vertical centering errors of the closed orbits. A further simulation study suggests that these centering errors can be reduced to below 1.5 cm by adjusting the trim coils' Br field within the output limits of our trim coils' power supplies. The error in the measurement field data may explain why the calculated trim coils' settings during the cyclotron commissioning in 1974 encountered difficulty.

Unified Picture of the Local Interstellar Magnetic Field from Voyager and IBEX

Prior to the Voyagers’ heliopause crossings, models and the community expected the magnetic field to show major rotations across the boundary. Surprisingly, the field showed no significant change in direction from the heliospheric Parker Spiral at either Voyager location. Meanwhile, a major result from the IBEX mission is the derived magnitude and direction of the interstellar field far from the Sun (∼1000 au) beyond the influence of the heliosphere. Using a self-consistent model fit to IBEX ribbon data, Zirnstein et al. reported that this “pristine” local interstellar magnetic field has a magnitude of 0.293 nT and direction of 227° in ecliptic longitude and 34.°6 in ecliptic latitude. These values differ by 27% (51%) and 44° (12°) from what Voyager 1 (2) currently observes (as of ∼2022.75). While differences are to be expected as the field undrapes away from the heliosphere, the global structure of the draping across hundreds of astronimcal units has not been reconciled. This leads to several questions: How are these distinct sets of observations reconcilable? What is the interstellar magnetic field’s large-scale structure? How far out would a future mission need to go to sample the unperturbed field? Here, we show that if realistic errors are included for the difficult-to-calibrate radial field component, the measured transverse field is consistent with that predicted by IBEX, allowing us to answer these questions through a unified picture of the behavior of the local interstellar magnetic field from its draping around the heliopause to its unfolding into the pristine interstellar medium.

Potential Singularity Formation of Incompressible Axisymmetric Euler Equations with Degenerate Viscosity Coefficients

In this paper, we present strong numerical evidence that the incompressible axisymmetric Euler equations with degenerate viscosity coefficients and smooth initial data of finite energy develop a potential finite-time locally self-similar singularity at the origin. An important feature of this potential singularity is that the solution develops a two-scale traveling wave that travels toward the origin. The two-scale feature is characterized by the scaling property that the center of the traveling wave is located at a ring of radius surrounding the symmetry axis while the thickness of the ring collapses at a rate . The driving mechanism for this potential singularity is due to an antisymmetric vortex dipole that generates a strong shearing layer in both the radial and axial velocity fields. Without the viscous regularization, the three-dimensional Euler equations develop a sharp front and some shearing instability in the far field. On the other hand, the Navier–Stokes equations with a constant viscosity coefficient regularize the two-scale solution structure and do not develop a finite-time singularity for the same initial data.

Angle of polarization calibration for omnidirectional polarization cameras.

Polarization cameras quantify one of the fundamental properties of light and capture intrinsic properties of the imaged environment that are otherwise omitted by color sensors. Many polarization applications, such as underwater geolocalization and sky-based polarization compass, require simultaneous imaging of the entire radial optical field with omnidirectional lenses. However, the reconstructed angle of polarization captured with omnidirectional lenses has a radial offset due to redirection of the light rays within these lenses. In this paper, we describe a calibration method for correcting angle of polarization images captured with omnidirectional lenses. Our calibration method reduces the variance of reconstructed angle of polarization from 76.2 ∘ to 4.1 ∘. Example images collected both on an optical bench and in nature, demonstrate the improved accuracy of the reconstructed angle of polarization with our calibration method. The improved accuracy in the angle of polarization images will aid the development of polarization-based applications with omnidirectional lenses.

Exploring the origin of turbulent Taylor rolls.

Since Taylor's seminal paper, the existence of large-scale quasi-axisymmetric structures has been a matter of interest when studying Taylor-Couette flow. In this article, we probe their formation in the highly turbulent regime by conducting a series of numerical simulations at a fixed Reynolds number [Formula: see text] while varying the Coriolis parameter to analyse the flow characteristics as the structures arise and dissipate. We show how the Coriolis force induces a one-way coupling between the radial and azimuthal velocity fields inside the boundary layer, but in the bulk, there is a two-way coupling that causes competing effects. We discuss how this complicates the analogy of narrow-gap Taylor-Couette to other convective flows. We then compare these statistics with a similar shear flow without no-slip boundary layers, showing how this double coupling causes very different effects. We finish by reflecting on the possible origins of turbulent Taylor rolls. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical Transactions paper (part 1)'.

Impact of β n and spectrum of n = 1 applied fields on fast ion losses in DIII-D

The effect of n = 1 magnetic perturbations (MPs) on prompt fast ion losses in DIII-D has been investigated using the light ion beam probe technique. The effect of normalized beta, β n , and the plasma response to the MPs is studied for several MP spectra. Magnetics data show a strong dependence of plasma response to β n that depends on the phase difference in perturbation coils, . For most phases, the response increases with β n , however, the response is suppressed for phases between 180∘ and 240∘. Experimental data from scintillator based fast ion loss detectors shows that relative fluctuation of lost ions (20%–30% of the steady signal) does not diminish across the L- to H-mode transition for , despite the 34% decrease in radial response field and 50% decrease in poloidal response field. Simulations of the DIII-D discharges using M3D-C1 and ASCOT5 find that prompt losses from neutral beam injection in each investigated case hit the first wall at several concentrated locations: the vessel floor, midplane diagnostic ports, vessel ceiling, and inner wall. Simulated losses from co-injection neutral beams are born outside the last closed flux surface, corresponding to radial orbit displacements of 3–6 cm due to the MPs.

Thermal Convection in a Central Force Field Mediated by Sound

Convection in radial force fields is a fundamental process behind weather on Earth and the Sun, as well as magnetic dynamo action in both. Until now, benchtop experiments have been unable to study convection in radial force fields due to the inability to generate radial forces of sufficient strength. Recently, it has been appreciated that sound, when averaged over many cycles, exerts a force on density gradients in the gas it travels through. The acoustic radiation pressure on thermal gradients draws cooler gas to regions with large time-averaged acoustic velocity and can be modeled as an effective acoustic gravity. We have constructed a system which generates a high amplitude, spherically symmetric acoustic wave in a rotating spherical bulb containing weakly ionized sulfur gas. Without sound, the gas stratifies itself into an initial state with the warmest gas near the center of the bulb, and the coolest gas near the bulb surface. When the sound is initiated, the acoustic radiation pressure is not balanced and a convective instability is triggered. With high speed videography, we observe the initial shape and growth rate of the most unstable mode at various acoustic amplitudes. Acoustic and rotational forces both contribute to the detailed mode shape, which changes qualitatively at low amplitudes where acoustic forces no longer surpass rotational ones everywhere in the bulb.

Maximum likelihood kinetic Sunyaev-Zel’dovich velocity reconstruction

The kinetic Sunyaev Zel'dovich (kSZ) effect, cosmic microwave background (CMB) temperature anisotropies induced by the scattering of CMB photons from free electrons, will be measured by near-term CMB experiments at high significance. By combining CMB temperature anisotropies with a tracer of structure, such as a galaxy redshift survey, previous literature introduced a number of techniques to reconstruct the radial velocity field. This reconstructed radial velocity field encapsulates the majority of the cosmological information contained in the kSZ temperature anisotropies, and can provide powerful new tests of the standard cosmological model and theories beyond it. In this paper, we introduce a new estimator for the radial velocity field based on a coarse-grained maximum likelihood fit for the kSZ component of the temperature anisotropies, given a tracer of the optical depth. We demonstrate that this maximum likelihood estimator yields a higher fidelity reconstruction than existing quadratic estimators in the low-noise and high-resolution regime targeted by upcoming CMB experiments. We describe implementations of the maximum likelihood estimator in both harmonic space and map space, using either direct measurements of the optical depth field or a galaxy survey as a tracer. We comment briefly on the impact of biases introduced by imperfect reconstruction of the optical depth field.

Study on transport phenomena and performance of proton exchange membrane fuel cell with radial flow fields

The radial flow field structure, which has the advantages of low pressure drop, good water removal and good mass transfer, is an emerging structure for proton exchange membrane fuel cell (PEMFC) flow fields. However, optimization work on the design the structure is scarce for a complex structure that is difficult to manufacture. A comprehensive three-dimensional, non-isothermal and single-phase mathematical model is developed to describe the flow and heat, mass and charge transfer processes in a PEMFC. The transport phenomena and cell performance of radial flow fields with different gradient channels and parallel flow fields are studied and compared using the commercial computational fluid dynamics (CFD) software Fluent®. The distribution of oxygen concentration, pressure drop and temperature with different radial lengths is obtained. The effects of gradient channels, gas supply modes and radial lengths on cell performance are investigated. The results show that radial flow fields could offer more uniform oxygen distributions and lower pressure drops compared with parallel flow fields. Larger gradient channel sizes contribute to larger transfer volumes and higher gas molar concentrations in the catalyst layers and lower pressures in channels. The counter-flow supply mode is superior to the co-flow supply mode because it can enable a higher oxygen velocity and hence a higher current density.

Electrically Tunable Gyrohelitrons with Crossed Fields

The generation frequency is ω ≈ k ω н in classical gyrotrons, where ω н = е B 0 / m is the electron cyclotron rotation frequency in a uniform longitudinal magnetic field with induction B 0 , e is the electron charge, m is the electron mass, k = 1, 2, 3… is the cyclotron frequency working harmonic number. Thus, the generation frequency ω being tuned is possible only by changing B 0 . This way is very inconvenient. It’s necessary a solenoid additional (control) winding. That difficulty can be eliminated in gyrotrons with crossed fields - electric 0 and magnetic 0 , here 0 ⊥ 0 . The frequency can be tuned by changing E 0 . This possibility can be realized at least two ways: a gyrotron based on a coaxial resonator with radial field E 0 ; a four-mirror gyrotron on traveling Т -waves with transverse in respect the traveling wave direction to uniform crossed fields – electric 0 and magnetic 0 . The single-screw electron flow has a rotation frequency , for the first gyrotron type, where , , Δ V is the potential difference between the inner (radius b 1 ) and outer (radius b 2 ) coaxial conductors, r 0 is the electron flow rotation radius. Thus, the generation frequency ω ≈ k ω н is determined by both B 0 and Δ V . Moreover, at Δ V = 0 the device becomes a classical high-orbit gyrotron, at B 0 = 0 a classical helitron. Therefore, at B 0 ≠ 0 and Δ V ≠ 0 it should be called a gyrohelitron, the generation frequency of which is tuned electrically - by changing Δ V . The article presents the design schemes of a gyrohelitron and a two-beam four-mirror gyrotron. In both cases, piezoelectric devices realize synchronous tuning of the frequency, just it allows the devices becoming fully electrically controllable. The following results were obtained for the gyrohelitron. Resonator field – H 211 , interaction on the second harmonic ω s ; a) narrow-band tuning 10 %: maximum efficiency – 55 %, minimum efficiency – 25 %; β 0 = v 0 / c = 0.27; q = v 0 ⊥ / v || = 2; b) broadband tuning 58 %: maximum efficiency – 18 %, minimum efficiency – 14 %; β 0 = v 0 / c = 0.2; q = v 0 ⊥ / v || = 2. The given results for the gyrohelitron indicate that it is promising to use electrical frequency tuning in a coaxial gyro-BWT and the amplification band in a gyro-TWT, since these devices do not require piezoelectric tuning of electrodynamic structures.

Development of Vacuum Tube Well Dewatering Test Device and Study on Vacuum Degree Transfer Law

Vacuum tube well dewatering technology has gradually become an effective means to deal with low-permeability soil groundwater. The vacuum degree transfer law is an important element in the study of the mechanism of deep foundation pit vacuum tube well dewatering. To further study the transfer law of vacuum degree in vacuum tube well dewatering, a laboratory test setup for vacuum tube well dewatering was developed, and vacuum tube well dewatering tests were conducted under various in-well vacuum values, tube diameter, depth of tube well, and other factors. The variation law of vacuum degree under various working condition coupling was thoroughly analyzed in this research. The results show that with the increase of vacuum value in the well, the radial vacuum degree and vertical vacuum degree have about 14.9~47.7% and 14.9~32.4% increase, respectively, and transmission attenuation of radial vacuum degree, transmission attenuation of vertical vacuum degree, and the range of the vacuum field all increase to some extent. With the outward transmission of the vacuum degree, the transmission attenuation of the radial vacuum degree decreases rapidly and then tends to be stable, and the transmission attenuation of the vertical vacuum degree decreases gradually. The radial vacuum degree, the transmission attenuation of the radial vacuum degree, and the range of the radial vacuum field are not affected by the buried depth of the tube well. The study’s conclusions can serve as a foundation and point of reference for projects involving the design and implementation of deep foundation pit vacuum tube well dewatering.

Issue Information

International Journal of Applied Glass ScienceVolume 14, Issue 1 p. 1-2 ISSUE INFORMATIONFree Access Issue Information First published: 02 December 2022 https://doi.org/10.1111/ijag.16586AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Graphical Abstract Cover Photograph: (a) Snapshot of molecular model of a 0.1Na2O-0.9SiO2 sodium silicate glass structure with a loaded slit crack simulated with the ReaxFF forcefield. Bonds along a half plane (depicted with a dashed line) were severed to create the initial slit crack. The displacements of atoms in an outer annulus were prescribed by an external boundary condition to generate far-field loading conditions. Atom colors: Si (yellow), O (red), Na (blue). (b) The same sodium silicate molecule model demonstrating the radial displacement field generated by the far field loading conditions. As the distance from the crack tip increases so does the total displacement, consistent the classical linear elastic fracture mechanics continuum solution for a semi-infinite slit crack under mode I loading. Volume14, Issue1Special Issue: Glasses for tomorrowJanuary 2023Pages 1-2 RelatedInformation

Solar Polar Magnetic Fields: Comparing Full-disk and High-resolution Spectromagnetograph Data

This is the first systematic comparison between photospheric polar magnetic field data from a full-disk synoptic observing program, the National Solar Observatory’s Synoptic Optical Long-term Investigations of the Sun Vector Spectromagnetograph (SOLIS/VSM), and a high-resolution vector spectromagnetograph, the Hinode Solar Optical Telescope Spectropolarimeter (SOT/SP). Polar magnetic fluxes derived from longitudinal magnetic field measurements from both telescopes and from SOT/SP full-Stokes vector data are all compared in the form of polar synoptic maps. Measurements taken over 35 day periods with advantageous rotation axis tilt angle are used; observations extend to the poles, and no synthetic pole-filling is needed. Polar fluxes are derived from longitudinal data assuming an approximately radial field, whereas those derived from vector data are based on measured vector magnitude and direction. However, the full-vector measurements may have a detection problem: polar fields are observed as mostly transverse from (near) Earth, and Zeeman sensitivity to transverse fields is significantly lower than for longitudinal fields. Accordingly, the SOT/SP vector-based polar fluxes are lower than the longitudinal-based fluxes from both telescopes, a result driven by pixels without sufficient Q and U signals for the full-Stokes inversions to detect significant radial field but with good Stokes V signal implying a significant field. Furthermore, the SOT/SP longitudinal-based fluxes are significantly higher than their VSM counterparts because of superior seeing-free spatial resolution and longer observation time. The SOT/SP longitudinal-based polar fluxes appear large enough to account for radial interplanetary field measurements whereas the SOT/SP vector-based and the VSM ones are generally too low.

The Imprint of Intermittent Interchange Reconnection on the Solar Wind

The solar wind is known to be highly structured in space and time. Observations from Parker Solar Probe have revealed an abundance of so-called magnetic switchbacks within the near-Sun solar wind. In this Letter, we use a high-resolution, adaptive-mesh, magnetohydrodynamics simulation to explore the disturbances launched into the solar wind by intermittent/bursty interchange reconnection and how they may be related to magnetic switchbacks. We find that repeated ejection of plasmoid flux ropes into the solar wind produces a curtain of propagating and interacting torsional Alfvénic waves. We demonstrate that this curtain forms when plasmoid flux ropes dynamically realign with the radial field as they are ejected from the current layer and that this is a robust effect of the 3D geometry of the interchange reconnection region. Simulated flythroughs of this curtain in the low corona reveal an Alfvénic patch that closely resembles observations of switchback patches, but with relatively small magnetic field deflections. Therefore, we suggest that switchbacks could be the solar wind imprint of intermittent interchange reconnection in the corona, provided an in situ process subsequently amplifies the disturbances to generate the large deflections or reversals of radial field that are typically observed. That is to say, our results indicate that a combination of low-coronal and inner-heliospheric mechanisms may be required to explain switchback observations.

Multiphase magnetic fields in the galaxy NGC 3627

ABSTRACT Magnetic fields play an important role in the formation and evolution of a galaxy, but it is challenging to measure them by observation. Here, we study the Seyfert galaxy NGC 3627’s magnetic field orientations measured from the synchrotron polarization observed with the Very Large Array and from the Velocity Gradient Technique (VGT) using spectroscopic data. The latter employs the magnetohydrodynamical turbulence’s anisotropy to probe the magnetic fields. Being applied to the CO (2–1) and H α emission lines obtained from the PHANGS-ALMA and PHANGS-MUSE surveys, it reveals the magnetic field orientation globally consistent with the polarization. The agreement of the VGT-CO and polarization suggests that the magnetic fields associated with synchrotron emission also percolate through star-forming regions. The VGT-H α measurement reveals the magnetic fields in the warm ionized medium that permeates the disc and disc’s vicinity so that it exhibits less agreement with polarization. We find prominent radial fields measured by synchrotron polarization appear in the transition regions from the spiral arms to the galactic bar, while such morphology is less apparent in the VGT-CO and VGT-H α measured magnetic fields. The radial fields suggest that the magnetic torque is important in removing orbiting gas’ angular momentum. We notice that magnetic fields inferred from the dust polarization, VGT-CO, and synchrotron polarization are different in the east arm. We interpret this difference as arising from the fact that the three measurements are tracing the magnetic fields associated with pre-collision, the mixture of pre-collision and post-collision, and post-collision flows, respectively.

Toroidal modeling of 3D perturbations generated by current filaments in scrape-off layer in tokamak with biased divertor targets

The divertor biasing technique offers a promising alternative to control the edge localized mode (ELM) as well as the divertor heat load in tokamaks, as compared to the resonant magnetic perturbation (RMP) generated by magnetic coils. The linear resistive MHD code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) is employed to study the plasma response to the n = 2 (n is the toroidal mode number) field perturbation in HL-2A, produced by the divertor biasing current filaments flowing in the scrape-off layer region. The response field due to biasing currents is compared with the RMP field utilized for ELM control in HL-2A. The strength of the radial resonant field perturbation, produced by the biasing currents of 100 A level, is found to be comparable with RMP generated by several kA of ELM control coil currents for the reference plasma. The plasma normal displacement near the X-point and the associated neoclassical toroidal viscosity torque are also computed to be similar between these two techniques. The modeling results thus strongly suggest that the biasing technique can be applied to control ELMs. Moreover, the biasing currents produce field perturbations, including the plasma response, that are localized more near the plasma edge (compared to the RMP counterpart), thus reducing the chance of mode locking associated with core perturbations. Particle orbit tracing also reveals that the biasing current produced magnetic perturbation tends to widen the heat deposition region and induce the strike point splitting of the ion saturation flow on the outer divertor surface, consistent with experimental observations in HL-2A. These toroidal modeling results confirm the possibility of ELM control and plasma exhaust solution by the divertor biasing technique.