Radial Field Component Research Articles

Analytical modelling of radial suspension force in bearingless surface‐mounted PM synchronous motors considering static rotor eccentricity

In this study, a new analytical model is provided in order to calculate the radial suspension force in bearingless surface-mounted permanent magnet synchronous motor with static rotor eccentricity. The proposed model is based on the harmonic analysis of magnetic flux density, and considers the influence of both radial and tangential air-gap field components on the computation of radial suspension force. This model can reveal the generation mechanism of the radial suspension force and identify the generation sources of the force ripples. Furthermore, the magnitudes and frequencies of radial suspension force harmonics, and the relationship between the radial suspension force and rotor eccentric displacements can be accurately predicted by the proposed model. However, this model cannot be used for saturated machines. The analytical model is verified by finite-element analyses and the result of static experimental study.

Influence of the Radial Electric Field Appraisal on Lightning-Induced Overvoltages Statistical Assessment

This paper analyzes the influence of the radial electric field radiated by return strokes on the lightning performance of an overhead distribution line. The calculation of the lightning electromagnetic pulse (LEMP) over a finitely conducting ground is performed by solving the Sommerfeld integral for the radial component of the electric field. The proposed method uses a trapezoidal scheme in which nodes are equidistant in logarithmic scale. The method is implemented in the LIOV-EMTP (lightning induced overvoltages-electromagnetic transient program) code that solves the field-to-multiconductor line coupling equations and calculates the lightning induced voltages in distribution networks having complex and realistic configuration. The results obtained by the proposed method for the LEMP calculation are compared with those obtained by using the Cooray-Rubinstein formula, which is the most commonly adopted approximation. Finally, the peak-amplitude probability distributions of the induced voltages obtained by using the two approaches are presented. It is shown that for ground conductivity values larger than 0.001 S/m, the Cooray-Rubinstein formula provides results in agreement with the accurate solution, while it significantly underestimates the lightning performance for lower conductivities and for lines with a high insulation level.

Selective excitation of a three-dimensionally oriented single plasmonic dipole

We experimentally demonstrate a scheme to deterministically excite a three-dimensionally oriented electric dipole in a single Au nanosphere by using a tightly focused radially polarized beam whose focal field possesses polarization states along three-dimensional (3D) orientations owing to the spatial overlap between longitudinal and radial electric field components. Experiment observations indicate that the orientation of an excited dipole moment gradually changes from out-of-plane to in-plane when the nanosphere is moved away from the beam center, which is reconfirmed by full-wave simulations. Moreover, rigorous calculation based on Mie theory reveals that a reduced effective ambient permittivity accompanies the rotation of the dipole moment, leading to a blue-shifted and narrowed resonance peak. We envision that our results could find applications in detecting the 3D orientation of isolated molecules and benefit the fine manipulation of light–matter interactions at the single-molecule level.

Design and commissioning of Brav measurement system for SC200 superconducting cyclotron

The SC200 proton therapy superconducting cyclotron was developed by ASIPP (Hefei, China) and JINR (Dubna, Russia). A measurement system was designed to assess the average radial component of the magnetic field (Brav) with 15 search coils in the median plane. The winding differences of the search coils affect the measurement accuracy of the Brav. Based on the electromagnetic induction principle, to measure the Brav accurately, this paper focuses on the design and commissioning of the Brav measurement system. The preliminary results confirm that the system design is reasonable and suitable. After testing the search coil at different speeds, the optimal speed was determined as 2.5 mm/s. The relative error was approximately 0.1% under the maximum radial component of the magnetic field Br of 7 G. The measurement precision was up to 1.0 × 10−3, which can provide the required measurement tolerance of 3–7 G for Br in the median plane. The commissioning of the Brav measurement system is an important step for Br measurement. It can check and adjust the asymmetry of the superconducting coils (SCs).

Multi‐frequency electromagnetic method for inductive measurement of ground induced polarization and resistivity

ABSTRACTA geophysical electromagnetic method to inductively measure the ground electrical resistivity and induced polarization has recently been tested. Its basic characteristics involve three major differences from other methods: the two electrical ground parameters are obtained through measuring magnetic field. For this purpose, a transmitter–receiver (T, R) electromagnetic system is used that operates in the frequency domain and consists of a horizontal loop as the transmitter for the perpendicular loops configuration on the ground surface; the measured function is the (T, R) inductive coupling main variation produced due to the presence of the earth, that is the magnetic field radial component; the measurements are conducted at a large number of frequencies (139 in the more advanced prototype), and the measured function is explored in the frequency interval 0.2 Hz to 1 kHz, a much broader frequency range of the induced polarization effect spectrum, than the one conventionally used in field exploration. Three major aspects are emphasized: (1) the existence of a small ‘main zone’ interior to a half‐space, which is responsible for most of the magnetic energy that the receiver measures on the half‐space surface. This permits to substitute the entire half‐space by the ‘main zone’ and, in a second step, to substitute the ‘main zone’ by an equivalent homogeneous half‐space with the electrical characteristics of such ‘main zone’; (2) the existence of a closed solution for the fields that the (T, R) system generates on the surface of a homogeneous isotropic half‐space, which provides exact functions with the two electrical parameters of interest as the variables (the apparent resistivity and relative polarization parameter); (3) the values of the electrical parameters so determined can be attributed to the central point of the ‘main zone’. Three‐horizontal layers half‐space and a conductive sphere in the free‐space are discussed as models. Four field surveys are analysed as examples and show a satisfactory performance of the method for detection of on‐shore hydrocarbon reservoirs, description of induced reservoir variations and structural features mapping at depths up to 2.5 km.

Mode symmetry in microstructured fibres revisited.

Motivated by the recent development of hollow-core, microstructured optical fibres without a translationally-periodic cladding structure, an analysis of the symmetry-induced properties of the modes of a uniform fibre with CMv point group symmetry is presented. Modes are classified according to the irreducible representations of the longitudinal components of the electric and magnetic fields; the radial component of the electric field and azimuthal component of the magnetic field share the symmetry of the longitudinal component of the electric field, while the radial component of the magnetic field and the azimuthal component of the electric field have the same symmetry as the longitudinal magnetic field. The symmetry class of the lowest order modes in fibres with point group CMv with M from 1 to 10 is given. The work is closely related to previous analyses, but clarifies the symmetry relationship between the two orthogonal modes in a degenerate pair and how the different symmetries of the longitudinal electric and magnetic field components emerge from the governing equations.

An Experimental Investigation of Cathode Spot Motion in a Magnetically Rotating Arc Plasma Generator at Atmospheric Pressure

Cathode spots present complex forms in magnetically rotating arc plasma generators due to the coupling effect of the plasma flow and electromagnetic fields. In this paper, a magnetically rotating arc plasma generator is built to study cathode spot motion at atmospheric pressure. Cathode spot configuration is observed and discussed for different magnetic fields, arc currents, gas flow rates and cathode lengths. Results show that cathode spots with a slow rotation speed (less than 1 Hz) and different rotation directions occur on the cathode end. For a low magnetic field, low arc current, high gas flow, short cathode rod, the rotation direction of the cathode spot is consistent with the arc column rotation. With an increase in the magnetic field, increase in the arc current, decrease in gas flow, or increase in the cathode rod length, the rotation speed declines, and the cathode spot can move in a reversed direction (i.e., against the arc column rotation). The cathode spot area also appears to expand gradually when the spot motion shifts from the normal direction to the reversed direction, resulting in less cathode erosion at the reversed motion. Further analysis indicates that the cathode spot motion is similar to the retrograde movement that occurs in a vacuum arc with an external magnetic field. The rotation of cathode spot may thus be induced by the radial component of the magnetic field. The cathode spot area that affects the self-magnetic field in the cathode spot is potentially a direct determinant of spot motion.

Faraday rotation maps of disc galaxies

Faraday rotation is one of the most widely used observables to infer the strength and configuration of the magnetic field in the ionised gas of the Milky Way and nearby spiral galaxies. Here we compute synthetic Faraday rotation maps at $z=0$ for a set of disk galaxies from the Auriga high-resolution cosmological simulations, for different observer positions within and outside the galaxy. We find that the strength of the Faraday rotation of our simulated galaxies for a hypothetic observer at the solar circle is broadly consistent with the Faraday rotation seen for the Milky Way. The same holds for an observer outside the galaxy and the observed signal of the nearby spiral galaxy M51. However, we also find that the structure and angular power spectra of the synthetic all-sky Faraday rotation maps vary strongly with azimuthal position along the solar circle. We argue that this variation is a result of the structure of the magnetic field of the galaxy that is dominated by an azimuthal magnetic field ordered scales of several kpc, but has radial and vertical magnetic field components that are only ordered on scales of 1-2 kpc. Because the magnetic field strength decreases exponentially with height above the disk, the Faraday rotation for an observer at the solar circle is dominated by the local environment. This represents a severe obstacle for attempts to reconstruct the global magnetic field of the Milky Way from Faraday rotation maps alone without including additional observables.

Incorporating Surface Convection into a 3D Babcock–Leighton Solar Dynamo Model

Abstract The convective flows observed on the photosphere (e.g., supergranulation, granulation) play a key role in the Babcock–Leighton (BL) process to generate large-scale polar fields from sunspot fields. In most surface flux transport (SFT) and BL dynamo models, the dispersal and migration of surface fields are modeled as an effective turbulent diffusion. Recent SFT models have incorporated explicit, realistic convective flows in order to improve the fidelity of convective transport but, to our knowledge, this has not yet been implemented in previous BL models. We present the first kinematic 3D Flux-Transport/BL model to explicitly incorporate realistic convective flows based on solar observations. Though we describe a means to generalize these flows to 3D, we find that the kinematic small-scale dynamo action they produce disrupts the operation of the cyclic dynamo. The cyclic solution is found by limiting the convective flow to act only on the vertical radial component of the magnetic field. The results obtained are generally in good agreement with the observed surface flux evolution and with non-convective models that have a turbulent diffusivity of the order of 3 × 1012 cm2 s−1 (300 km2 s−1). However, we find that the use of a turbulent diffusivity underestimates the dynamo efficiency, producing weaker mean fields and a shorter cycle than in the convective models. Also, the convective models exhibit bands of mixed polarity in the polar regions that have no counterpart in solar observations, and the poleward migration speed of poloidal flux is determined mainly by the meridional flow and the vertical diffusion.

A Compact Expression for Cogging Torque Considering Both Radial and Tangential Fields for Surface-Mounted PM Motors

Cogging torque is due to the interaction between a magnet’s magnetomotive force and a slotted stator or rotor structure. In this paper, a compact equation for cogging torque is presented for surface-mounted permanent magnet motors. This equation has four terms of field interactions involving tangential and radial components of airgap flux density. These four terms are considered as sources of cogging. Variations of these sources with pole embrace are examined. In earlier publications, closed-form expressions for pole embrace corresponding to the minimum cogging were presented considering only radial fields. In this paper, an attempt is made to recognize the influence of tangential fields in cogging. The compact form given here distinctly reflects the significance of both radial and tangential field components. Furthermore, to study the trends of cogging sources with pole number and airgap radius, simplified expressions for harmonic content of field components are derived using the first-order binomial approximation. The analysis on cogging presented in this paper helps in determining search domains in which optimum embrace for minimum cogging can be found when both the radial and tangential field components are considered.

Hypernatural inflation

We construct a model of natural inflation in the context of α-attractor supergravity, in which both the dilaton field and the axion field are light during inflation, and the inflaton may be a combination of the two. The T-model version of this theory is defined on the Poincaré disk with radius |Z| = 1. It describes a Mexican hat potential with the flat axion direction corresponding to a circle of radius |Z| < 1. The axion decay constant fa in this theory can be exponentially large because of the hyperbolic geometry of the Poincaré disk. Depending on initial conditions, this model may describe α-attractor inflation driven by the radial component of the inflaton field, natural inflation driven by the axion field, or a sequence of these two regimes. We also construct the E-model version of this theory, which have similar properties. In addition, we describe generalized α-attractor models where the potential can be singular at the boundary of the moduli space, and show that they can provide a simple solution for the problem of initial conditions for the models with plateau potentials.

Microwave-driven inductively coupled plasmas for analytical spectroscopy

New achievements in microwave-driven inductively coupled plasma (ICP) technology based on formation of homogeneous H-type field inside the plasma discharge tube by using both multi-helix and partial-turn couplers are discussed in detail. These couplers range from separate washers delivering longitudinal Ez and radial Er field components concentrated at the inner wall of the torch, through real multi-turn field shapers, which make the prevailing longitudinal Hz or hybrid EH field components, all the way to strait wires delivering a single radial Er field component with minimum at the axis. Two novel approaches utilizing either a ring washer coupler or a multi helix coupler are developed to generating atmospheric pressure annular-shaped microwave ICPs, suitable for analytical spectroscopy. They are stably operated with argon or helium at 1–2 L min−1 flow rates at a power level of 300 W while accepting up to 70 mg min−1 of water aerosol. For argon plasmas, rotational temperatures of OH (3300–4200 K) and electron number densities (1.9–2.2) × 1015 cm−3 are close to those measured in Ar ICP. Limits of detection for some metals were within the range of 0.006–0.035 mg L−1 using a portable OES detection system.

Imaging axial and radial electric field components in dielectric targets under plasma exposure

This work presents new ways to investigate the individual electric field components in a dielectric target induced by a non thermal atmospheric pressure plasma jet. Mueller polarimetry is applied to investigate electro-optic crystals under exposure of guided ionization waves produced by a plasma jet. Three different cases are examined to visualize the different electric field components induced in the crystals by charges deposited on the surface by impact of the ionization waves. Investigating a (BSO) crystal at normal incidence allows measurement and visualization of the axial field, while if the crystal is examined at 45° both radial and axial electric field components are combined. For the first time, a Fe:LiNbO3 (Felinbo) crystal is examined using Mueller polarimetry under influence of a plasma jet. In this case, exclusively the patterns and local values of the radial field are obtained and not the axial field. These unique imaging options in the target for the individual electric field components allow a new and more complete investigation of the dynamics of surface discharges on dielectric materials.

Numerical study on the time evolutions of the electric field in helium plasma jets with positive and negative polarities

This paper presents 2D simulations of atmospheric pressure discharges in helium with N2 and O2 admixtures, propagating in a dielectric tube between a point electrode and a grounded metallic target. For both positive and negative polarities, the propagation of the first ionization front is shown to correspond to a peak of the absolute value of the axial electric field inside the tube, but also outside the tube. After the impact on the metallic target, a rebound front is shown to propagate from the target to the point electrode. This rebound front is 2–3 times faster than the first ionization front. Close to the high voltage point, this rebound front corresponds to a second peak of the absolute value of the axial electric field. Close to the target, as the first ionization and rebound fronts are close in time, only one peak is observed. The dynamics of the absolute value of the radial component of electric field outside the tube is shown to present an increase during the first ionization front propagation and a fast decrease corresponding to the propagation of the rebound front. These time evolutions of the electric field components are in agreement with experiments. Finally, we have shown that the density of metastable He* in 99% He—1% N2 and 99% He—1% O2 atmospheric pressure discharges are very close. Close to the grounded target, the peak density of reactive species is significantly increased due to the synergy between the first ionization and rebound fronts, as observed in experiments. Similar results are obtained for both voltage polarities, but the peak density of metastable He* close to the target is shown to be two times less in negative polarity than in positive polarity.

Magnetic design and method of a superconducting magnet for muon [formula omitted]/EDM precise measurements in a cylindrical volume with homogeneous magnetic field

A magnetic field design method of magneto-motive force (coil block (CB) and iron yoke) placements for g−2/EDM measurements has been developed and a candidate placements were designed under superconducting limitations of current density 125 A/mm2 and maximum magnetic field on CBs less than 5.5 T. Placements of CBs and an iron yoke with poles were determined by tuning SVD (singular value decomposition) eigenmode strengths. The SVD was applied on a response matrix from magneto-motive forces to the magnetic fields in the muon storage region and two-dimensional (2D) placements of magneto-motive forces were designed by tuning the magnetic field eigenmode strengths obtained by the magnetic field. The tuning was performed iteratively. Magnetic field ripples in the azimuthal direction were minimized for the design.The candidate magnetic design had five CBs and an iron yoke with center iron poles. The magnet satisfied specifications of homogeneity (0.2 ppm peak-to-peak in 2D placements (the cylindrical coordinate of the radial position R and axial position Z) and less than 1.0 ppm ripples in the ring muon storage volume (0.318 m <R<0.348 m and -0.05 <Z< 0.05 m) with 3.0 T strength and a slightly negative BR (magnetic field radial component) at Z> 0.0 m) for the spiral muon injection from the iron yoke at top.

Van Allen Probes Observations of Second Harmonic Poloidal Standing Alfvén Waves

AbstractLong‐lasting second‐harmonic poloidal standing Alfvén waves (P2 waves) were observed by the twin Van Allen Probes (Radiation Belt Storm Probes, or RBSP) spacecraft in the noon sector of the plasmasphere, when the spacecraft were close to the magnetic equator and had a small azimuthal separation. Oscillations of proton fluxes at the wave frequency (∼10 mHz) were also observed in the energy (W) range 50–300 keV. Using the unique RBSP orbital configuration, we determined the phase delay of magnetic field perturbations between the spacecraft with a 2nπ ambiguity. We then used finite gyroradius effects seen in the proton flux oscillations to remove the ambiguity and found that the waves were propagating westward with an azimuthal wave number (m) of ∼−200. The phase of the proton flux oscillations relative to the radial component of the wave magnetic field progresses with W, crossing 0 (northward moving protons) or 180° (southward moving protons) at W ∼ 120 keV. This feature is explained by drift‐bounce resonance (mωd ∼ ωb) of ∼120 keV protons with the waves, where ωd and ωb are the proton drift and bounce frequencies. At lower energies, the proton phase space density ( ) exhibits a bump‐on‐tail structure with occurring in the 1–10 keV energy range. This is unstable and can excite P2 waves through bounce resonance (ω ∼ ωb), where ω is the wave frequency.

Plasma Response to Resonant Magnetic Perturbations in Large Aspect Ratio Tokamaks

In this paper, a plasma response model is investigated for large aspect ratio tokamaks, on the presence of external nonaxisymmetric resonant magnetic perturbations. To control plasma confinement, the plasma is perturbed by external resonant helical windings, similar to those introduced by an ergodic magnetic limiter. The plasma response to the perturbation is modeled as an additional magnetic perturbation, created by a current sheet on the main perturbed resonant surface, vanishing the radial component of the total magnetic field in the considered resonant surface. In order to show the influence of the plasma response on the field line topology, the field line differential equations are integrated numerically, showing the reduction of magnetic island sizes and the regularization of chaotic regions around the resonant surface where the response was introduced, in agreement with results observed in sophisticated simulation codes. Finally, the connection lengths indicate that, regarding their distribution, the plasma response introduces a homogenization effect which may affect the deposition patterns at the tokamak wall.

Observation of an Extremely Large-Density Heliospheric Plasma Sheet Compressed by an Interplanetary Shock at 1 AU

At 11:46 UT on 9 September 2011, the Wind spacecraft encountered an interplanetary (IP) fast-forward shock. The shock was followed almost immediately by a short-duration (∼ 35 minutes) extremely dense pulse (with a peak ∼ 94 cm−3). The pulse induced an extremely large positive impulse (SYM-H = 74 nT and Dst = 48 nT) on the ground. A close examination of other in situ parameters from Wind shows that the density pulse was associated with i) a spike in the plasma $\upbeta$ (ratio of thermal to magnetic pressure), ii) multiple sign changes in the azimuthal component of the magnetic field ( $B_{\phi}$ ), iii) a depressed magnetic field magnitude, iv) a small radial component of the magnetic field, and v) a large (> 90°) change in the suprathermal (∼ 255 eV) electron pitch angle across the density pulse. We conclude that the density pulse is associated with the heliospheric plasma sheet (HPS). The thickness of the HPS is estimated to be ${\sim}\,8.2\times10^{5}\ \mbox{km}$ . The HPS density peak is about five times the value of a medium-sized density peak inside the HPS (∼ 18 cm−3) at 1 AU. Our global three-dimensional magnetohydrodynamic simulation results (Wu et al. in J. Geophys. Res. 212, 1839, 2016) suggest that the extremely large density pulse may be the result of the compression of the HPS by an IP shock crossing or an interaction between an interplanetary shock and a corotating interaction region.

Directional analysis of cardiac motion field from gated fluorodeoxyglucose PET images using the Discrete Helmholtz Hodge Decomposition

ObjectivesExtract directional information related to left ventricular (LV) rotation and torsion from a 4D PET motion field using the Discrete Helmholtz Hodge Decomposition (DHHD). Materials and methodsSynthetic motion fields were created using superposition of rotational and radial field components and cardiac fields produced using optical flow from a control and patient image. These were decomposed into curl-free (CF) and divergence-free (DF) components using the DHHD. ResultsSynthetic radial components were present in the CF field and synthetic rotational components in the DF field, with each retaining its center position, direction of motion and diameter after decomposition. Direction of rotation at apex and base for the control field were in opposite directions during systole, reversing during diastole. The patient DF field had little overall rotation with several small rotators. ConclusionsThe decomposition of the LV motion field into directional components could assist quantification of LV torsion, but further processing stages seem necessary.

Transmission of electric fields due to distributed cloud charges in the atmosphere-ionosphere system

The transmission of electric fields in the lower atmosphere by thunder clouds with a suitable charge distribution profile has been modeled. The electromagnetic responses of the atmosphere are presented through Maxwell’s equations together with a time-varying source charge distribution. The conductivities are taken to be exponentially graded function of altitude. The radial and vertical electric field components are derived for isotropic, anisotropic and thundercloud regions. The analytical solutions for the total Maxwell’s current which flows from the cloud into the ionosphere under DC and quasi-static conditions are obtained for isotropic region. We found that the effect of charge distribution in thunderclouds produced by lightning discharges diminishes rapidly with increasing altitudes. Also, it is found that time to reach Maxwell’s currents a maximum is higher for higher altitudes.