Non-axisymmetric Field Research Articles

Tamed stability and transport using controlled non-axisymmetric fields in KSTAR

Meticulously orchestrated non-axisymmetric fields (δB) enabled KSTAR to explore various paths to tame plasma stability and transport in a very rigorous manner. Given an extremely low level of intrinsic non-axisymmetry, KSTAR has now established high-precision 3D field control capability that can not only robustly suppress edge localized modes (ELM) using resonant magnetic perturbation (RMP), but also exclusively alter plasma rotation without invoking particle and energy transport. In highly shaped plasmas (triangularity of δ ~ 0.6), we have secured low-n RMP-driven, ELM-crash suppressions in a wide range of edge safety factor at q95 = 3.4–6.4. One of the best n = 1 RMP-driven, ELM-crash suppressions has been sustained for more than 30 s (comparable to wall saturation time), satisfying a low edge collisionality (ν* ~ 0.2) at Zeff = 1, close to ITER-target. Besides a routinely used three-row RMP configuration, we have newly succeeded in suppressing ELM-crashes using n = 1 off-midplane RMPs only, whose helical structure in vacuum appears nearly orthogonal to a typical configuration. Nonetheless, when the plasma response is factored, the off-midplane RMP configuration remains dominantly resonant. With RMP configuration fixed, a gradual torque control between ‘perpendicular’ and tangential components of neutral beams probed the onset of ELM-crash-suppression, strongly endorsing the existence of ω⊥,e ~ 0 at pedestal top as necessary condition for ELM-crash-suppression, consistent with direct measurement of ECEI. In support of ITER, KSTAR has demonstrated broadened divertor heat fluxes during ELM-crash-suppression, as well as during ELM-crash-mitigation, using intentionally misaligned RMP configurations. However, we have found that such a misaligned configuration, as had effectively broadened the divertor heat fluxes during ELM-crash-mitigation, did not show a similar broadening during ELM-crash-suppression. This suggests that the divertor heat flux during ELM-crash-suppression, governed by a bifurcated state of δB, may not be appropriately projected, based on the results of ELM-crash-mitigation, in which the linear plasma response of δB prevails.

A Composite Neoclassical Toroidal Viscosity Model Incorporating Torques from both Axisymmetric and Nonaxisymmetric Tokamak Magnetic Fields

This paper combines the older neoclassical gyroviscous model for toroidal viscosity in the plasma core, which is based on an axisymmetric magnetic field and obtains reasonable agreement with experiment for toroidal rotation in the plasma core but not in edge plasma, with recent models for neoclassical toroidal viscosity (NTV) based on nonaxisymmetric “perturbation” magnetic field components present primarily in the edge plasma to obtain a composite toroidal viscosity model for toroidal velocity calculations in the tokamak core and edge plasma. This combination is facilitated by the fact that the same form of “drag frequency” representation of the viscous torque used in many of the new (NTV) torque models arising from toroidally nonaxisymmetric perturbation magnetic fields that are present mostly in the plasma edge can also be used to represent the old neoclassical toroidal viscous torques arising from toroidally axisymmetric magnetic fields.

The surface magnetic activity of the weak-line T Tauri stars TWA 9A and V1095 Sco

We present a detailed analysis of high-resolution spectropolarimetric observations of the weak-line T Tauri stars (wTTSs) TWA 9A and V1095 Sco as part of a wider sur- vey of magnetic properties and activity in weak-line T Tauri stars, called MaTYSSE (Magnetic Topologies of Young Stars and the Survival of close-in giant Exoplanets). Our targets have similar masses but differing ages which span the stage of radiative core formation in solar-mass stars. We use the intensity line profiles to reconstruct surface brightness maps for both stars. The reconstructed brightness maps for TWA 9A and V1095 Sco were used to model and subtract the activity-induced jitter, reducing the RMS in the radial velocity measurements of TWA 9A by a factor of $\sim$7, and for V1095 Sco by a factor of $\sim$3. We detect significant circular polarisation for both stars, but only acquired a high quality circular polarisation time-series for TWA 9A. Our reconstructed large-scale magnetic field distribution of TWA 9A indicates a strong, non-axisymmetric field. We also analyse the chromospheric activity of both stars by investigating their H$\alpha$ emission, finding excess blue-ward emission for most observations of V1095 Sco, and symmetric, double-peaked emission for TWA 9A, with enhanced emission at one epoch likely indicating a flaring event.

Conceptual design of extended magnetic probe set to improve 3D field detection in NSTX-U.

Adding toroidal arrays of magnetic probes at the top and bottom of NSTX-U would improve both the detection of the multimodal plasma response to applied magnetic perturbations and the identification of the poloidal structure of unstable plasma modes, as well as contribute to the validation of MHD models, improve the understanding of the plasma response to external fields, and improve the error field correction. In this paper, the linear MHD code MARS-F/K has been used to identify poloidal locations that would improve the capability to measure stationary or near-stationary 3D fields that may result from the plasma response to external sources of non-axisymmetric fields. The study highlighted 6 poloidal positions where new arrays of both poloidal and radial magnetic field sensors would improve the poloidal resolution. The proposed set of new arrays combined with the present ones is shown to be capable of measuring the poloidal structure of perturbations with n ≤ 6 and of detecting the multimodal plasma response. Assessment of the trade-off in the poloidal length of the probes leads to an ideal length between 10 cm and 30 cm. A method to configure the probes of a toroidal array based on the singular value decomposition condition number is proposed, and an ideal solution and a low-cost one are presented.

The magnetic field vector of the Sun-as-a-star – II. Evolution of the large-scale vector field through activity cycle 24

In the present work, we investigate how the large-scale magnetic field of the Sun, in its three vector components, has evolved during most of cycle 24, from 2010 Jan to 2018 Apr. To filter out the small-scale field of the Sun, present in high-resolution synoptic maps, we use a spherical harmonic decomposition method, which decomposes the solar field in multipoles with different l degrees. By summing together the low-l multipoles, we reconstruct the large-scale field at a resolution similar to observed stellar magnetic fields, which allows the direct comparison between solar and stellar magnetic maps. During cycle 24, the `Sun-as-a-star' magnetic field shows a polarity reversal in the radial and meridional components, but not in the azimuthal component. The large-scale solar field remains mainly poloidal with > 70% of its energy contained in the poloidal component. During its evolution, the large-scale field is more axisymmetric and more poloidal when near minima in sunspot numbers, and with a larger intensity near maximum. There is a correlation between toroidal energy and sunspot number, which indicates that spot fields are major contributors to the toroidal large-scale energy of the Sun. The solar large-scale magnetic properties fit smoothly with observational trends of stellar magnetism reported in See et al. The toroidal (Etor) and poloidal (Epol) energies are related as Etor ~Epol^{1.38 \pm 0.04}. Similar to the stellar sample, the large-scale field of the Sun shows a lack of toroidal non-axisymmetric field.

Quantitative measurement of ultrasonic pressure field using combination of optical phase contrast and nonlinear acoustic holography methods

Ultrasound has been widely used in medicine for both diagnosis and therapeutics. To assure its safety and efficacy, it is necessary to establish a fast and accurate method of measuring an ultrasonic field. Hydrophone scanning, which is a standard method for pressure measurement, requires a long measurement time and may disturb the field. In this study, an optical phase contrast method is combined with an acoustic holography method with nonlinear propagation simulation. The nonaxisymmetric pressure field of pulse ultrasound upstream of the focus was measured by the optical phase contrast method combined with a computed tomography (CT) algorithm, and the entire three-dimensional pressure field was reconstructed by acoustic holography. The result obtained by the proposed method agreed well with that by the hydrophone measurement without absolute pressure calibration and confirmed the markedly reduced required measurement time.

Magnetic polarization measurements of the multi-modal plasma response to 3D fields in the EAST tokamak

A multi-modal plasma response to applied non-axisymmetric fields has been found in EAST tokamak plasmas. Here, multi-modal means the radial and poloidal structure of an individually driven toroidal harmonic is not fixed. The signature of such a multi-modal response is the magnetic polarization (ratio of radial and poloidal components) of the plasma response field measured on the low field side device mid-plane. A difference in the 3D coil phasing (the relative phase of two coil arrays) dependencies between the two responses is observed in response to n = 2 fields in the same plasma for which the n = 1 responses are well synchronized. Neither the maximum radial nor the maximum poloidal field response to n = 2 fields agrees with the best applied phasing for mitigating edge localized modes, suggesting that the edge plasma response is not a dominant component of either polarization. GPEC modeling reproduces the discrepant phasing dependences of the experimental measurements, and confirms the edge resonances are maximized by the coil phasing that mitigates ELMs in the experiments. The model confirms the measured plasma response is not dominated by resonant current drive from the external field. Instead, non-resonant contributions play a large role in the diagnostic signal for both toroidal harmonics n = 1 and n = 2. The analysis in this paper demonstrates the ability of 3D modeling to connect external magnetic sensor measurements to the internal plasma physics and accurately predict optimal applied 3D field configurations in multi-modal plasmas.

Numerical Simulation of Temperature Fields in a Three-Dimensional SiC Crystal Growth Furnace with Axisymmetric and Spiral Coils

Three-dimensional numerical simulation platform for silicon carbide crystal growth furnace was established using C programing language, where a physical model of the furnace was built based on cylindrical coordinates; governing equations for electromagnetic and temperature fields were discretized by finite volume method; radiation characteristics were studied with the help of S2S model (surface to surface radiation model); and the least distance method was proposed to check radiation faces visibility efficiently. LU decomposition algorithm based on graphic processing unit (GPU) technology was developed to accelerate the solving process of surface to surface radiation. Then the radiation heat transfer in silicon carbide crystal (SiC) growth chamber and temperature field of silicon carbide growth furnace were studied quantificationally at I = 1250 A and F = 16 kHz. The effects of coil structures (axisymmetric and spiral) on temperature field and its gradient distributions were investigated by standard deviation method. The simulation results demonstrate that spiral electromagnetic coil generates non-axisymmetric temperature field easily; the radiation heat flux is 102~103 times more than conduction heat flux, radiation heat transfer is helpful to increase temperature evenness; the spiral temperature field on the SiC crystal cross-section reduces the poor homogeneity of temperature gradient, which will cause crystal to generate large defects.

Anelastic spherical dynamos with radially variable electrical conductivity

A series of numerical simulations of the dynamo process operating inside gas giant planets has been performed. We use an anelastic, fully nonlinear, three-dimensional, benchmarked MHD code to evolve the flow, entropy and magnetic field. Our models take into account the varying electrical conductivity, high in the ionised metallic hydrogen region, low in the molecular outer region. Our suite of electrical conductivity profiles ranges from Jupiter-like, where the outer hydrodynamic region is quite thin, to Saturn-like, where there is a thick non-conducting shell. The rapid rotation leads to the formation of two distinct dynamical regimes which are separated by a magnetic tangent cylinder - mTC. Outside the mTC there are strong zonal flows, where Reynolds stress balances turbulent viscosity, but inside the mTC Lorentz force reduces the zonal flow. The dynamic interaction between both regions induces meridional circulation. We find a rich diversity of magnetic field morphologies. There are Jupiter-like steady dipolar fields, and a belt of quadrupolar dominated dynamos spanning the range of models between Jupiter-like and Saturn-like conductivity profiles. This diversity may be linked to the appearance of reversed sign helicity in the metallic regions of our dynamos. With Saturn-like conductivity profiles we find models with dipolar magnetic fields, whose axisymmetric components resemble those of Saturn, and which oscillate on a very long time-scale. However, the non-axisymmetric field components of our models are at least ten times larger than those of Saturn, possibly due to the absence of any stably stratified layer.

Elastic Analysis of Nonhomogeneous Frozen Wall under Nonaxisymmetric Ground Stress Field and in State of Unloading

The mechanical analysis of frozen walls is a cornerstone technology of artificially frozen ground. The mechanical response of frozen walls is affected by heterogeneity, excavation unloading, uneven ground pressure, and the characteristics of surrounding rock. However, these factors are rarely taken into full consideration in existing analysis models. To address this shortfall, this study presents a plane‐strain model that considers the inhomogeneity of frozen walls, the unloaded state of the frozen‐wall inner edge, and the nonuniform ground stress field (abbreviated as “IF model”). The solution of the IF model is based on the superposition of thin concentric cylinders under two types of contact conditions: complete contact and smooth contact, and its validity is tested by a finite‐element calculation. The calculation indicates that the excavation reduces the radial force and increases the tangential force between the frozen wall and the surrounding earth mass; the ground principal stress is rotated after the excavation. If the radial unloading equals the tangential unloading at the inner edge of the frozen wall, the response of the radial stress differs from that of the tangential stress at the outer edge of the frozen wall. The circumferential stress and the radial displacement at the inner edge correlate linearly with the nonuniform coefficient of the ground press and the unloading ratio. If the nonuniform coefficient is relatively small, the inner edge of the frozen wall may incur tensile damage. Compared with the model of a homogeneous frozen wall (abbreviated as “HF model”), which has a uniform temperature distribution, the absolute value of the circumferential stress is lower (higher) for the IF model where the temperature is above (below) average. When the frozen wall is relatively thick, the circumferential stress of the inner edge of the frozen wall is lower for the IF model than for the HF model. The percent reduction is 8.12%∼9.32% for rock freezing and 13.41%∼18.03% for soil freezing. The IF model proposed herein thus reflects the characteristics of frozen walls and surrounding rock more clearly and accurately than the HF model and obtains stress states closer to the reality. Therefore, the IF model is recommended for the design and construction of frozen walls.

Trapping and displacement of liquid collars and plugs in rough-walled tubes

A liquid film wetting the interior of a long circular cylinder redistributes under the action of surface tension to form annular collars or occlusive plugs. These equilibrium structures are invariant under axial translation within a perfectly smooth uniform tube and therefore can be displaced axially by very weak external forcing. We consider how this degeneracy is disrupted when the tube wall is rough, and determine threshold conditions under which collars or plugs resist displacement under forcing. Wall roughness is modelled as a non-axisymmetric Gaussian random field of prescribed correlation length and small variance, mimicking some of the geometric irregularities inherent in applications such as lung airways. The thin film coating this surface is modelled using lubrication theory. When the roughness is weak, we show how the locations of equilibrium collars and plugs can be identified in terms of the azimuthally averaged tube radius; we derive conditions specifying equilibrium collar locations under an externally imposed shear flow, and plug locations under an imposed pressure gradient. We use these results to determine the probability of external forcing being sufficient to displace a collar or plug from a rough-walled tube, when the tube roughness is defined only in statistical terms.

Enhanced understanding of non-axisymmetric intrinsic and controlled field impacts in tokamaks

An extensive study of intrinsic and controlled non-axisymmetric field (δB) impacts in KSTAR has enhanced the understanding about non-axisymmetric field physics and its implications, in particular, on resonant magnetic perturbation (RMP) physics and power threshold (Pth) for L–H transition. The n = 1 intrinsic non-axisymmetric field in KSTAR was measured to remain as low as δB/B0 ~ 4 × 10−5 even at high-beta plasmas (βN ~ 2), which corresponds to approximately 20% below the targeted ITER tolerance level. As for the RMP edge-localized-modes (ELM) control, robust n = 1 RMP ELM-crash-suppression has been not only sustained for more than ~90 τE, but also confirmed to be compatible with rotating RMP. An optimal window of radial position of lower X-point (i.e. Rx = m) proved to be quite critical to reach full n = 1 RMP-driven ELM-crash-suppression, while a constraint of the safety factor could be relaxed (q95 = 5 0.25). A more encouraging finding was that even when Rx cannot be positioned in the optimal window, another systematic scan in the vicinity of the previously optimal Rx allows for a new optimal window with relatively small variations of plasma parameters. Also, we have addressed the importance of optimal phasing (i.e. toroidal phase difference between adjacent rows) for n = 1 RMP-driven ELM control, consistent with an ideal plasma response modeling which could predict phasing-dependent ELM suppression windows. In support of ITER RMP study, intentionally misaligned RMPs have been found to be quite effective during ELM-mitigation stage in lowering the peaks of divertor heat flux, as well as in broadening the ‘wet’ areas. Besides, a systematic survey of Pth dependence on non-axisymmetric field has revealed the potential limit of the merit of low intrinsic non-axisymmetry. Considering that the ITER RMP coils are composed of 3-rows, just like in KSTAR, further 3D physics study in KSTAR is expected to help us minimize the uncertainties of the ITER RMP coils, as well as establish an optimal 3D configuration for ITER and future reactors.

Measurement of scrape-off-layer current dynamics during MHD activity and disruptions in HBT-EP

We report scrape-off layer (SOL) current measurements during magnetohydrodynamic (MHD) mode activity, resonant magnetic perturbations (RMPs), and disruptions in the High Beta Tokamak—Extended Pulse (HBT-EP) device. Currents are measured via segmented plasma current Rogowski coils, jumpers running toroidally between otherwise-isolated vessel sections, and a grounded electrode in the scrape-off layer. These currents strongly depend on the plasma’s major radius, and amplitude and phase of non-axisymmetric field components. SOL currents connecting through the vessel are seen to reach ∼ of the plasma current during typical kink activity and RMPs. Plasma current asymmetries and scrape-off-layer currents generated during disruptions, which are commonly called halo currents, reach ∼ of Ip. Asymmetric toroidal currents between vessel sections rotate at tens of kHz through most of the current quench, then symmetrize once Ip reaches ∼ of its pre-disruptive value. Toroidal jumper currents oscillate between co- and counter-Ip, with co-Ip being dominant on average during disruptions. A relative increase in local plasma current measured by a segmented Ip Rogowski coil correlates with counter-Ip current in the nearest toroidal jumper. Measurements are interpreted in the context of two models that produce contrary predictions for the toroidal vessel current polarity during disruptions. Plasma current asymmetry measurements are consistent with both models, and SOL currents scale with plasma displacement toward the vessel wall. The design of an upcoming SOL current diagnostic and control upgrade is also briefly presented.

Evolution of the Sun’s non-axisymmetric toroidal field

Aims. We aim to infer the sub-surface distribution of the Sun's non-axisymmetric azimuthal magnetic flux from observable quantities, such as the surface magnetic field and the large scale plasma flows. Methods. We have built a kinematic flux transport model of the solar dynamo based on the Babcock-Leighton framework. We constructed the source term for the poloidal field using SOLIS magnetograms spanning three solar cycles. Based on this source we calculated the azimuthal flux below the surface. The flux transport model has two free parameters which we constrain using sunspot observations from cycle 22. We compared the model results with observations from cycle 23. Results. The structure of the azimuthal field is mainly axisymmetric. The departures from axisymmetry represent, on average, ~3% of the total azimuthal flux. Owing to its relative weakness, the non-axisymmetric structure of the azimuthal field does not have a significant impact on the location in which the emergences appear or on the amount of flux contained in them. We find that the probability of emergence is a function of the ratio between the flux content of an active region and the underlying azimuthal flux.

Experimental and analytical study of X-section cast-in-place concrete pile installation effect

A new type of displacement pile, the X-section cast-in-place concrete (XCC) pile, has been developed recently in China. Extensive field and laboratory experiments are being undertaken in order to evaluate the soil displacements during pile installation. The paper describes laboratory arrangements and results of transparent soil model tests aimed at capturing the non-axisymmetric soil displacement field. Results from model tests using the XCC pile are presented to reveal the complete soil displacement patterns (a) in the horizontal plane, and (b) in vertical planes of symmetry. Based on results from the transparent soil tests, a modified cavity expansion model (MCEM) is proposed to predict the radial displacements in any vertical plane induced by XCC pile installation. The radial displacements predicted by the MCEM are compared with data from the transparent soil test and the field experiment. The results show reasonable agreement for all cases, with the proposed MCEM proving more suitable than the conventional (axisymmetric) CEM for predicting the radial displacements induced by XCC pile installation. It may therefore provide a basis in the future for developing predictions of stress changes and, ultimately, shaft capacity of the XCC pile in comparison to displacement piles of circular cross-section.

Impact of toroidal and poloidal mode spectra on the control of non-axisymmetric fields in tokamaks

In several tokamaks, non-axisymmetric magnetic field studies show that applied magnetic fields with a toroidal harmonic n = 2 can lead to disruptive n = 1 locked modes. In Ohmic plasmas, n = 2 magnetic reconnection thresholds in otherwise stable discharges are readily accessed at edge safety factors q ∼ 3, low density, and low rotation. Similar to previous studies with n = 1 fields, the thresholds are correlated with the “overlap” field computed with the IPEC code. The overlap field quantifies the plasma-mediated coupling of the external field to the resonant field. Remarkably, the “critical overlap fields” at which magnetic islands form are similar for applied n = 1 and 2 fields. The critical overlap field increases with plasma density and edge safety factor but is independent of the toroidal field. Poloidal harmonics m > nq dominate the drive for resonant fields while m < nq harmonics have a negligible impact. This contrasts with previous results in H-mode discharges at high plasma pressure in which the toroidal angular momentum is sensitive to low poloidal harmonics. Together, these results highlight unique requirements for n > 1 field control including the need for multiple rows of coils to control selected plasma parameters for specific functions (e.g., rotation control or ELM suppression).

Nonlinear burn control using in-vessel coils and isotopic fueling in ITER

In future burning tokamaks, active control of the plasma temperature and density will be necessary to produce a determined amount of fusion power. Conventional actuation methods, such as auxiliary power modulation and fueling rate modulation, are usually employed to tackle this so-called burn control problem. Fueling rate modulation can be used not only to directly control the plasma density but also to indirectly control the plasma energy by means of isotopic fuel tailoring. Moreover, based on recent experiments, the in-vessel coil system arises as a possible actuation method to decrease the plasma energy by generating non-axisymmetric fields in the plasma that may reduce the energy confinement time. In this work, a nonlinear burn controller that integrates the three mentioned actuators is proposed. The controller performance is tested via simulations for an ITER-like scenario.

Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly for each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles.

Investigation of instabilities and rotation alteration in high beta KSTAR plasmas

H-mode plasma operation of the Korea Superconducting Tokamak Advanced Research (KSTAR) device has been expanded to significantly surpass the ideal MHD no-wall beta limit. Plasmas with high normalized beta, βN, up to 4.3 have been achieved with reduced plasma internal inductance, li, to near 0.7, exceeding the computed n = 1 ideal no-wall limit by a factor of 1.6. Pulse lengths at maximum βN were extended to longer pulses by new, more rapid control. The stability of the observed m/n = 2/1 tearing mode that limited the achieved high βN is computed by the M3D-C1 code, and the effect of sheared toroidal rotation to tearing stability is examined. As a method to affect the mode stability in high βN plasmas, the non-resonant alteration of the rotation profile by non-axisymmetric magnetic fields has been used, enabling a study of the underlying neoclassical toroidal viscosity (NTV) physics and stability dependence on rotation. Non-axisymmetric field spectra were applied using in-vessel control coils (IVCCs) with varied n = 2 field configurations to alter the plasma toroidal rotation profile in high beta H-mode plasmas and to analyze their effects on the rotation. The rotation profile was significantly altered with rotation reduced by more than 60% without tearing activity or mode locking. To investigate the physical characteristics and scaling of the measured rotation braking by NTV, changes in the rotation profile are analytically examined in steady state. The expected NTV scaling with the square of the normalized applied field perturbation agrees with the measured profile change δB2.1–2.3. The NTV is also found to scale as Ti2.1–2.4, in general agreement with the low collisionality “1/ν” regime scaling of the NTV theory (TNTV-(1/ν) ∝ Ti2.5).

Variation of magnetic braking by non-axisymmetric magnetic fields depending on the perturbed field structure in the KSTAR tokamak

The variation of a magnetic braking profile by non-axisymmetric magnetic fields has been experimentally demonstrated and numerically validated in the KSTAR tokamak. Two types of n = 2 non-resonant magnetic fields were applied by changing the relative phase of non-axisymmetric field coils. One is even parity, of which non-resonant fields deeply penetrate into the plasma core, and the other is odd parity localized at the plasma edge. The even and odd parity produced significantly different perturbed magnetic field structures, and thereby drove global and edge-dominant toroidal rotation damping, respectively. These distinct braking profiles are consistently reproduced by drift-kinetic particle simulations, indicating the possibility of the predictive utilization of non-resonant magnetic fields for rotation profile control.