Vertical Field Gradient Research Articles

Deformation and necking of liquid droplets in a magnetic field

Pendant droplets of water and paramagnetic solutions are studied in the presence of uniform and nonuniform magnetic fields produced by small permanent magnet arrays, both in static conditions and during dynamic pinch-off. Static measurements of the droplet shape are analyzed in terms of an apparent surface tension γapp or an effective density ρeff. The change of surface tension of deionized water in a uniform field of 450 mT is insignificant, 0.19 ± 0.21 mNm−1. Measurements on droplets of compensated zero-susceptibility solutions of Cu2+, Mn2+, and Dy3+, where the shape is unaffected by any magnetic body force, show changes of surface tension of about −1% in 500 mT. Magnetic field gradients of up to 100 T2 m−1 deform the droplets and lead to changes of ρeff that are negative for diamagnetic solutions (buoyancy effect) and positive for paramagnetic solutions. The droplet profile of strongly paramagnetic 0.1 molar DyCl3 solution is analyzed, treating the nonuniform vertical field gradient as a spatial variation of gravity. The influence of Maxwell stress on the droplet shape is discussed. In dynamic measurements, the droplet shape at pinch-off is recorded by high-speed photography and analyzed in terms of a relative change of dynamic surface tension in the presence of a magnetic field. The surface-tension-dependent prefactor of the scaling law that governs the pinch-off dynamics shows no difference for pure water or 0.11 M DyCl3 solutions in the field. The nonuniform field has no influence in the pinch-off region because the filament diameter is much less than the capillary length.

Quantitative assessment of finite-element models for magnetostatic field calculations

We present quantitative means for assessing the numerical accuracy of static magnetic field calculations in finite-element models. Our calculations use the three-dimensional Opera simulation software suite of Dassault Systèmes. Our need to assess the effects of fringe fields requires such a 3D algorithm. While we do discuss and compare our approach to a method of accuracy estimation used in the Opera post-processor, our methods are generally applicable to any model using relaxation techniques in finite-element systems. For purposes of illustration, we present modeling and analysis of two types of quadrupole electromagnets presently in operation in the south arc of the Cornell Electron Storage Ring (CESR). Calculations of field multipole expansion coefficients and numerical deviations from Maxwell’s equations in source-free regions are discussed, with emphasis on the dependence of their accuracy on changes to the finite-element model. Successive refinement steps in the finite-element model for the non-extraction type of CESR south arc quadrupole achieve a reduction in the RMS value of the longitudinal component of the curl vector on the magnet axis by a factor of nearly 70 from 4.38×10−2 T/m to 6.36×10−4 T/m, which is 0.0021% of the field gradient. An accuracy of 2.9% is achieved for a dodecapole coefficient of 2.4×10−4 of that of the quadrupole in the longitudinal integral of the vertical field gradient at a radius of 1 cm.

Phase-merging enhanced harmonic generation free-electron laser with a normal modulator.

A phase-merging enhanced harmonic generation free-electron laser (FEL) was proposed to increase the harmonic conversion efficiency of seeded FELs and promote the radiation wavelength towards the X-ray spectral region. However, this requires a specially designed transverse gradient undulator (TGU) as the modulator to couple the transverse and longitudinal phase space of the electron beam. In this paper, the generation of the phase-merging effect is explored using the natural field gradient of a normal planar undulator. In this method, a vertical dispersion on the electron beam is introduced and then the dispersed beam travels through a normal modulator in a vertical off-axis orbit where the vertical field gradient is selected properly in terms of the vertical dispersion strength and modulation amplitude. The phase-merging effect will be generated after passing through the dispersive chicane. Theoretical analysis and numerical simulations for a seeded soft X-ray FEL based on parameters of the Shanghai Soft X-ray FEL project are presented. Compared with a TGU modulator, using the natural gradient of a normal planar modulator has the distinct advantage that the gradient can be conveniently tuned in quite a large range by adjusting the beam orbit offset.

Normal planar undulators doubling as transverse gradient undulators

The transverse gradient undulator (TGU) has important application in the short-wavelength high-gain free electron lasers (FELs) driven by laser-plasma accelerators. However, the usual transversely tapered TGUs need special design and manufacture, and the transverse gradient cannot be tuned arbitrarily. In this paper we explore a new and simple method of using the natural transverse gradient of a normal planar undulator to compensate the beam energy spread effect. In this method, a vertical dispersion on the electron beam is introduced, then the dispersed beam passes through a normal undulator with a vertical off-axis orbit where the vertical field gradient is selected properly related to the dispersion strength and the beam energy spread. Theoretical analysis and numerical simulations for self-amplified spontaneous emission FELs based on laser plasma accelerators are presented, and indicate that this method can greatly reduce the effect of the beam energy spread, leading to a similar enhancement on FEL performance as the usual transversely tapered TGU, but with the advantages of economy, tunable transverse gradient and no demand of extra field for correcting the orbit deflection induced by the field gradient.Received 21 December 2016DOI:https://doi.org/10.1103/PhysRevAccelBeams.20.020707Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsSynchrotron radiation & free-electron lasersAccelerators & Beams

Evidence for a cephalic site of action of high magnetic fields on the behavioral responses of rats

Static high magnetic fields (MFs) from 7 T to 9 T can elicit behavioral responses in rodents such as suppression of rearing, locomotor circling, and acquisition of a conditioned taste aversion (CTA). MF exposure also induces c-Fos expression in the visceral and vestibular nuclei of the brainstem, suggesting the stimulation of some sensory pathways. It is not clear, however, if the effects of the MF are caused by exposure to the uniform maximal field at the center of the magnet, or by exposure to the steep field gradients along the bore of the magnet during the rat's placement. In addition, the site of action within the rat is unknown. In an attempt to limit MF exposure to rostral or caudal portions of the rats' body, we exposed male and female rats at different positions within the bore of a 14.1-T superconducting magnet ranging from 2 cm (1.6 T at the head) to 155 cm (0.05 T at the head), with the center of the bore at 65 cm (14.1 T across the whole body). This approach also allowed us to expose rats to the maximal field strength (14.1 T) vs. the maximal field gradients (54 T/m). To assess both immediate and delayed behavioral effects, locomotor and CTA responses were recorded. A small but significant CTA was seen after exposure of the head to the lowest MF tested (0.05 T at 155 cm). Graded effects were seen, however, with greater circling and CTA acquisition as the MF strength increased at the rostral end of the rat. This suggests a cephalic site of action. Furthermore, maximal circling and CTA were induced after exposure to the uniform center field, and not after exposure to high field gradients on either side of the center. This suggests that the behavioral responses seen after MF exposure are a consequence of the uniform static field at the center of the magnet, and are not caused by passage through, or exposure to, the vertical field gradients. Female rats responded similarly to male rats, although magnet-induced CTA appeared resistant to extinction in female rats.

An Improved Virial Estimate of Solar Active Region Energy

The MHD virial theorem may be used to estimate the magnetic energy of active regions on the basis of vector magnetic fields measured at the photosphere or chromosphere. However, the virial estimate depends on the measured vector magnetic field being force-free. Departure from the force-free condition leads to an unknown systematic error in the virial energy estimate and an origin dependence of the result. We present a method for estimating the systematic error by assuming that magnetic forces are confined to a thin layer near the photosphere. If vector magnetic field measurements are available at two levels in the low atmosphere (e.g., the photosphere and the chromosphere), the systematic error may be directly calculated using the observed horizontal and vertical field gradients, resulting in an energy estimate that is independent of the choice of origin. If (as is generally the case) measurements are available at only one level, the systematic error may be approximated using the observed horizontal field gradients together with a simple linear force-free model for the vertical field gradients. The resulting improved virial energy estimate is independent of the choice of origin but depends on the choice of the model for the vertical field gradients, i.e., the value of the linear force-free parameter α. This procedure is demonstrated for five vector magnetograms, including a chromospheric magnetogram.

Three dimensional structure of a regular sunspot from the inversion of IR Stokes profiles

The magnetic, thermal and velocity structure of a regular sunspot, observed close to solar disk center is pre- sented. Spectropolarimetric data obtained with the Tenerife Infrared Polarimeter (TIP) in two infrared Fe I lines at 15 648.5 A and 15 652.8 A are inverted employing a technique based on response functions to retrieve the atmospheric stratification at every point in the sunspot. In order to improve the results for the umbra, profiles of Zeeman split OH lines blending the Fe I 15 652.8 A are also consistently fit. Thus we obtain maps of temperature, line-of-sight velocity, magnetic field strength, inclination, and azimuth, as a function of both location within the sunspot and height in the atmosphere. We present these maps for an optical depth range between log τ5 = 0 and log τ5 = −1.5, where these lines provide accurate results. We find decreasing magnetic field strength with increasing height all over the sunspot, with a particularly large vertical field gradient of ∼− 4Gk m −1 in the umbra. We also observe the so called spine structures in the penumbra, i.e. extended radial features with a stronger and more vertical magnetic field than the surroundings. Also we found that the magnetic field zenith angle increases with height. From the velocity map it is clear that the Evershed flow avoids the spines and mostly concentrates in the more inclined intervening field. The field inclination at a few locations in the outer penumbra in lower layers goes beyond 90 ◦ . These locations coincide with the strongest flows in the velocity map.

Active magnetic shielding for biomagnetic measurement using spatial gradient fields

Biomagnetic measurement performed outside a magnetically shielded room is subject to distortion by strong magnetic fields. Reducing such disturbances can enhance and stabilize biomagnetic measurement conditions in the absence of passive shielding. We have developed an active magnetic shielding system that produces both homogeneous and spatial gradient magnetic fields. The system is composed of anisotropic magnetoresistive sensors, a digital signal processor controller and two different coil systems. In order to improve the measurement environment for a first-order gradient coil SQUID system, the disturbing vertical magnetic fields and vertical field gradients are reduced, thus achieving a shielding factor of approximately 6 at 100 Hz. Our system provides a more flexible and less costly alternative to magnetically shielded rooms.

Amplitude and orientation of prominence magnetic fields from constant-αmagnetohydrostatic models

We analyze outputs from three-dimensional models for three observed filaments, which belong to the quiescent, intermediate and plage class respectively. Each model was calculated from a constant- magnetohydrostatic extrapolation, as- suming that the prominence material is located in magnetic dips, so that the field is nearly horizontal throughout the prominence body and feet. We calculate the spatial distribution of the magnetic field amplitude B and orientation with respect to the fila- ment axis, neither of which were imposed a priori in the models. In accordance with past magnetic field measurements within prominence bodies, we also obtain nearly homogeneous magnetic fields, respectively of about B 3; 14 and 40 G for the qui- escent, intermediate and plage prominence, with a systematic weak vertical field gradient of @B=@z 0:1 1:5 10 4 Gk m 1 . We also find that the inverse polarity configuration is dominant with 20 to 0, which is slightly smaller than in some observations. We also report some other properties, which have either rarely or never been observed. We find at prominence tops some localized normal polarity regions with<+10. At prominence bottoms below 20 Mm in altitude, we find stronger field gradients @B=@z 1 10 10 4 Gk m 1 and a wider range of field directions 90 to 0. These properties can be interpreted by the perturbation of the prominence flux tube by strong photospheric polarities located in the neighborhood of the prominence. We also report some full portions of prominences that have the normal polarity. The latter are simply due to the local curvature of the filaments with respect to their average axis, which was used to define . These results could either be used as predictions for further testing of this class of models with new observations, or as quantitative tools for the interpretation of observations which show complex patterns.

Line-integral corrections in Larmor-precession devices

Larmor-precession devices need homogeneous line integrals of the magnetic field along the neutron trajectories over the beam cross section. Line-integral inhomogeneities must be homogenized or corrected in order not to spoil the initial polarization. They can be corrected by two sets of coils. The first set of coils generates a vertical field gradient opposite to the precession-field gradient. Actually, these coils transform a gradient of the line integral in the field direction to a direction perpendicular to it. This last gradient is corrected by the second set of coils, which has a homogenous field in the vertical direction and a parabolic shape in the perpendicular direction. The corrected beam has a polarization of 0.82 for a beam cross section of 10×15 mm2 whereas, for the uncorrected beam, the polarization is 0.20.

Prominence height and vertical gradient in magnetic field

The existence of a critical height for quiescent prominences and its relationship to parameters of the magnetic field of photospheric sources are discussed. In the inverse-polarity model, stable equilibrium of a filament with a current is possible only in the region where the external field decreases with height no faster than ∼1/h. Calculations of the potential magnetic field above the polarity-inversion line are compared with the observed prominence height. The prominence height is shown to actually depend on the vertical field gradient and does not exceed the level at which the exponent of field decrease is equal to unity.

Interfacial instabilities in aluminium reduction cells

This paper extends the analysis of Sneyd (1985) on interfacial instabilities in aluminium reduction cells. The cell model consists of a plane fluid layer of relatively low electrical conductivity, sandwiched between an upper rigid wall and lower fluid layer, both of high conductivity. A steady current passes through the layers, and the magnetic field is assumed to be a linear function of position. The principal new effects introduced are (i) a horizontal current component in the aluminium; (ii) vertical magnetic field components, and vertical field gradients; (iii) an aluminium pool of finite depth; and (iv) uniform zeroth-order flow in the fluid layers, and mechanical dissipation. A dispersion relation for small-amplitude waves is derived and discussed. The destabilizing Kelvin—Helmholtz mechanism and electromagnetic forces compete with gravity, surface tension and mechanical dissipation. Electromagnetic destabilization is likely to occur in practice at wavelengths of 1 m or more, and becomes more intense with decreasing layer depths. The most dangerous mechanism appears to be driven by vertical gradients of the horizontal field.

Magnetosedimentation of particles in heterogeneous colloids

When binary mixtures of colloidal particles settle under gravity the structure of the sediment is a function of the relative dimensions and densities of the particles. All this is changed if the colloids are allowed to settle in an attractive vertical field gradient. Here, the particles acquire a contribution to the effective density which results in selective magnetosedimentation. A description is given of exploratory settling experiments of this type, using binary mixtures of paramagnetic materials. In certain of these experiments clear evidence of sediment bands is found.

Magnetic field and electric current structure in the chromosphere

Three dimensional vector magnetic field structure throughout the chromosphere above an active region is deduced by combining high resolution Hα filtergrams with a simultaneous digital magnetogram. An analog model of the field is made with 400 metal wires representing fieldlines which are assumed to outline the Hα structure. The height extent of the field is determined from vertical field gradient observations around sunspots, from observed fibril heights and from an assumption that the sources of the field should be largely local. After digitization the magnetic field H matrix is retrieved. Electric current densities j are computed from j=curl H. The currents (typically 10 mA m−2) flow in patterns not similar to observed features and not parallel to magnetic fields. Lorentz forces are computed from {ie0323-01}. The force structures correspond to observed solar features and a series of observed dynamics may be expected: downward motion in bipolar areas in lower chromosphere, an outflow of the outer chromosphere into the corona with radially outward flow above bipolar plage regions (where coronal streamers are observed) and motions of arch filament systems. Observed current structure and magnitude agree well with previous vector magnetograph observations but disagree with theoretical current-free or force-free concepts. A dynamic chromosphere with electromagnetic forces in action is thus inferred from observations.