Ray-tracing simulations of whistler-mode wave propagation in different rescaled dipole magnetic fields

Kinetic simulation is a powerful tool to study the excitation and propagation of whistler-mode waves in the Earth’s inner magnetosphere.This method typically applies a scaled-down dipole magnetic field to save computational time.However,it remains unknown whether whistler wave propagation in the scaled-down dipole field is consistent with that in the realistic dipole field.In this work,we develop a ray-tracing code with a scalable dipole magnetic field to address this concern.The simulation results show that parallel whistler waves at different frequencies gradually become oblique after leaving the equator and propagate in different raypaths in a dipole magnetic field.During their propagation,the higher frequency waves tend to have larger wave normal angles at the same latitude.Compared with the wave propagation in a realistic dipole field,the wave raypath and wave normal remain the same,whereas the wave amplification or attenuation is smaller because of the shorter propagation time in a scaled-down dipole field.Our study provides significant guidance for kinetic simulations of whistler-mode waves.

Numerical Analysis of the Magnetic Dipole Effect on a Radiative Ferromagnetic Liquid Flowing over a Porous Stretched Sheet

The effects of a magnetic dipole on a nonlinear thermally radiative ferromagnetic liquidflowing over a stretched surface in the presence of Brownian motion and thermophoresis are investigated.By means of a similarity transformation,ordinary differential equations are derived and solved afterwards using a numerical(the BVP4C)method.The impact of various parameters,namely the velocity,temperature,concentration,is presented graphically.It is shown that the nanoparticles properties,in conjunction with the magnetic dipole effect,can increase the thermal conductivity of the engineered nanofluid and,consequently,the heat transfer.Comparison with earlier studies indicates high accuracy and effectiveness of the numerical approach.An increase in the Brow-nian motion parameter and thermophoresis parameter enhances the concentration and the related boundary layer.The skin-friction rises when the viscosity parameter is increased.A larger value of the ferromagnetic para-meter results in a higher skin-friction and,vice versa,in a smaller Nusselt number.

Impact of a Magnetic Dipole on Heat Transfer in Non-Conducting Magnetic Fluid Flow over a Stretching Cylinder

The thermal behavior of an electrically non-conducting magnetic liquid flowing over a stretching cylinder under the influence of a magnetic dipole is considered.The governing nonlinear differential equations are solved numerically using a finite element approach,which is properly validated through comparison with earlier results available in the literature.The results for the velocity and temperature fields are provided for different values of the Reynolds number,ferromagnetic response number,Prandtl number,and viscous dissipation parameter.The influence of some physical parameters on skin friction and heat transfer on the walls of the cylinder is also investigated.The applicability of this research to heat control in electronic devices is discussed to a certain extent.

Binding Energy, Root-Mean Square Radius and Magnetic Dipole Moment of the Nucleus 6Li

In this work, we have applied the translation invariant shell model with number of quanta of excitations N=2,4,6,8and 10 to define the ground-state eigenenergies and their corresponding normalized eigenstates, the root mean-square radius, and the magnetic dipole moment of the nucleus 6Li. We have computed the necessary two-particle orbital fractional parentage coefficients for nuclei with mass number A=6and number of quanta of excitations N=10, which are not available in the literature. In addition, we have used our previous findings on the nucleon-nucleon interaction with Gaussian radial dependencies, which fits the deuteron characteristics as well as the triton binding energy, root-mean square radius and magnetic dipole moment. The numerical results obtained in this work are in excellent agreement with the corresponding experimental data and the previously published theoretical results in the literature.

First observation of laser–beam interaction in a dipole magnet

As a new-generation light source,free-electron lasers(FELs)provide high-brightness x-ray pulses at the angstrom-femtosecond space and time scales.The fundamental physics behind the FEL is the interaction between an electromagnetic wave and a relativistic electron beam in an undulator,which consists of hundreds or thousands of dipole magnets with an alternating magnetic field.We report the first observation of the laser–beam interaction in a pure dipole magnet in which the electron beam energy modulation with a 40-ke V amplitude and a 266-nm period is measured.We demonstrate that such an energy modulation can be used to launch a seeded FEL,that is,lasing at the sixth harmonic of the seed laser in a high-gain harmonic generation scheme.The results reveal the most basic process of the FEL lasing and open up a new direction for the study and exploitation of laser–beam interactions.

Design and end chamfer simulation of PEFP beam line curved dipole magnets

The design, fabrication and field measurement of 11 DC curved dipole magnets for the PEFP Beam Line have been completed. In this paper, a design method for a complex end chamfer using OPERA-3D is proposed. The conventional method for estimating chamfer shape is extended and applied to a curved dipole magnet by a coordinate transformation. Using the interface with CAD software, the complex end chamfer is modeled and fully determined by 3D simulation to meet the field uniformity requirement. The magnetic field measurement results are in good agreement with the simulation. The design considerations, field simulation results, end chamfer development process and measurement results are presented in detail.

Development of dipole magnet power supply for BEPC-II energy upgrading project

Purpose In order to make BEPC-II to run at a higher energy,the Institute of High Energy Physics undertook an upgrading project.One of the important factors limiting the energy boost is the power and performance of the dipole magnet power supplies;therefore,these four magnet power supplies are developed for the BEPC-II upgrading.Methods The power supplies adopt topologies of thyristor rectifiers to realize a high-power output.In the control unit of each power supply,a digital current closed loop is adopted,and the key components in the feedback loop are thermostatically controlled.In order to improve the performances of the power supplies,analog voltage regulators are added to the inner control loops.Results These four power supplies have been tested and have already been officially used in BEPC-II,and their powers have reached the requirements of the upgrading.The test results of the current stability are described and shown in this paper,which testifies that the stabilities meet the design parameters.Conclusions A digital control is applied to each SCR rectifier control.The performances of the power supplies are improved by the combination of digital current control loops and the analog voltage control loops,which makes the performances of the dipole magnet power supplies meet the requirements of the upgrading project.

Collaborative Simulation and Testing of the Superconducting Dipole Prototype Magnet for the FAIR Project

The superconducting dipole prototype magnet of the collector ring for the Facility for Antiproton and Ion Research （FAIR） is an international cooperation project. The collaborative simulation and testing of the developed prototype magnet is presented in this paper. To evaluate the mechanical strength of the coil case during quench, a 3-dimensional （3D） electromagnetic （EM） model was developed based on the solid97 magnetic vector element in the ANSYS commercial software, which includes the air region, coil and yoke. EM analysis was carried out with a peak operating current at 278 A. Then, the solid97 element was transferred into the solid185 element, the coupled analysis was switched from electromagnetic to structural, and the finite element model for the coil case and glass-fiber reinforced composite （G10） spacers was established by the ANSYS Parametric Design Language based on the 3D model from the CATIA V5 software. However, to simulate the friction characteristics inside the coil case, the conta173 surface-to-surface contact element was established. The results for the coil case and G10 spacers show that they are safe and have sufficient strength, on the basis of testing in discharge and quench scenarios.

Accurate calculation of field quality in conventional straight dipole magnets

Purpose In the standard design method of straight dipole magnets,the good field region is symmetric to the magnet mechanical center both in 2D and in 3D,so the obtained field quality is not the actual one because the field integration lines are not consistent with the curved beam paths.In this paper,an improved method for straight dipole magnets aiming at obtaining accurate field quality is proposed.Methods The field quality is calculated by taking into account the relationship of the good field region to the magnet straight geometry.General description of the improved method is introduced,and two application examples of straight dipole magnets are presented to investigate the detailed field quality difference between the improved and traditional methods.The result of the improved method is also compared with the field quality calculated along particle trajectory in OPERA-3D.Results It is shown that the difference in field quality between the improved and traditional methods cannot be neglected,and the field quality in the improved method is very close to the one calculated along real beam paths.Conclusion The field quality in the improved method is accurate enough for practical application in a straight dipole magnet.

Shim coil design for Halbach magnet by equivalent magnetic dipole method

Low-field nuclear magnetic resonance magnet（2 MHz） is required for rock core analysis. However, due to its low field strength, it is hard to achieve a high uniform B0 field only by using the passive shimming. Therefore, active shimming is necessarily used to further improve uniformity for Halbach magnet. In this work, an equivalent magnetic dipole method is presented for designing shim coils. The minimization of the coil power dissipation is considered as an optimal object to minimize coil heating effect, and the deviation from the target field is selected as a penalty function term. The lsqnonlin optimization toolbox of MATLAB is used to solve the optimization problem. Eight shim coils are obtained in accordance with the contour of the stream function. We simulate each shim coil by ANSYS Maxwell software to verify the validity of the designed coils. Measurement results of the field distribution of these coils are consistent with those of the target fields.The uniformity of the B0 field is improved from 114.2 ppm to 26.9 ppm after using these shim coils.

3-D Magnetic Sensor Module for Locating and Tracking MEMS Swallowable Capsule Based on Scalar Form of Magnetic Dipole Model

MEMS swallowable capsule is a novel technology in the non-invasive surgery. This technology provides a way to diagnose directly into the deep intestinal where the traditional invasive technology implemented, such as X-Ray, endoscopy. It is a key for us to locate and track the position of a MEMS capsule in clinical applications. To solve this problem, we implemented a magnetic sensor module based on the scalar form of the magnetic dipole model,which was designed with very small size （5.2 ＊ 2. 1 ＊ 1.2 em） and easy to assemble to satisfy the system requirement. Here we discuss in detail the principle of magnetic dipole model, rules of selecting sensor and functions of the module. Some trials are established to test the characteristic of the module. The results of the Cm experiment demonstrates that the module follows the rules of the new magnetic dipole model form.

Angular dependence of vertical force and torque when magnetic dipole moves vertically above flat high-temperature superconductor

The interaction between a permanent magnet(PM)assumed as a magnetic dipole and a flat high-temperature superconductor(HTS)is calculated by the advanced frozen-image model.When the dipole vertically moves above the semiinfinite HTS,the general analytical expression of vertical force and that of torque are obtained for an arbitrary angle between the magnetization direction of the PM and the c axis of the HTS.The variations of the force and torque are analyzed for angle and vertical movements in both zero-field cooling(ZFC)condition and field cooling(FC)condition.It is found that the maximum vertical repulsive or attractive force has the positive or negative cosine relation with the angle.However,the maximum torque has the positive or negative sine relation.From the viewpoint of the rotational equilibrium,the orientation of the magnetic dipole with zero angle is deemed to be an unstable equilibrium point in ZFC,but the same orientation is considered as a stable equilibrium point in FC.In addition,both of the variation cycles of the maximum force and torque with the angle areπ.

Equivalent magnetic dipole method used to design gradient coil for unilateral magnetic resonance imaging

The conventional magnetic resonance imaging(MRI)equipment cannot measure large volume samples nondestructively in the engineering site for its heavy weight and closed structure.In order to realize the mobile MRI,this study focuses on the design of gradient coil of unilateral magnet.The unilateral MRI system is used to image the local area above the magnet.The current density distribution of the gradient coil cannot be used as a series of superconducting nuclear magnetic resonance gradient coils,because the region of interest(ROI)and the wiring area of the unilateral magnet are both cylindrical side arc surfaces.Therefore,the equivalent magnetic dipole method is used to design the gradient coil,and the algorithm is improved for the special case of the wiring area and the ROI,so the X and Y gradient coils are designed.Finally,a flexible printed circuit board(PCB)is used to fabricate the gradient coil,and the magnetic field distribution of the ROI is measured by a Gauss meter,and the measured results match with the simulation results.The gradient linearities of x and y coils are 2.82%and 3.56%,respectively,less than 5%of the commercial gradient coil requirement.

Energy levels and magnetic dipole transition parameters for the nitrogen isoelectronic sequence

Theoretical calculations of the energy levels and magnetic dipole transition parameters for the 1s^(2)2s^(2)2p^(3) and 1s^(2)2p^(5) configurations of nitrogen isoelectronic sequence with Z=21-30 are performed using multi-congfiguration Dirac-Fock(MCDF)method.Based on the relativistic computational code GRASP2k compiled within the framework of MCDF method,the electron correlations,Breit interaction and QED effects are well treated in detail.The energy levels,line strengths and transition rates of magnetic dipole transition are obtained and compared with the experimental data avail-able.For most cases,good agreements are achieved and the relative differences of them are less than 0.114%,8.43% and 9.80%,respectively.The scaling laws of the fine structure splitting and transition rate are obtained on the isoelec-tronic sequence and the corresponding physical mechanisms are discussed.The data sets for tables are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00022.

Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation

A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.

An equivalent magnetic dipoles model for quantitative damage recognition of broken wire

By simplifying saturatedly magnetized wire-rope to magnetic dipoles of the same magnetic field strength, an equivalent magnetic dipoles model is developed and the measuring principle for recognising damage of broken wire was presented. The relevant calculation formulas were also deduced. A composite solution method about nonlinear optimization was given. An example was given to illustrate the use of the equivalent magnetic dipoles method for quantitative damage recognition, and demonstrates that the result of this method is consistent with the real situation, so the method is valid and practical. wire-rope, damage of broken wires, quantitative recognition, equivalent magnetic dipoles, simulate

Observation of Magnetic Dipole Forbidden Transitions in LHD and Its Application to Burning Plasma Diagnostics

Magnetic dipole forbidden （M1） transition was studied in large helical device （LHD） and F-, Si- and Ti-like M1 transitions are successfully observed for highly ionized Ar, Kr, Mo and Xe ions. The wavelengths measured in visible range for the heavy elements, which are carefully determined with extremely small uncertainties of 0.02 - 0.05 A as a standard wavelength of usual electric dipole （El） plasma emissions, are compared with theoretical predictions. The result shows a good agreement with recent Hatree-Fock calculation including semi-empirical adjustment. The M1 intensity for the F-like ions is examined by analyzing the intensity ratio of M1 to El. Density dependence of the ratio is experimentally verified by comparing with collisional- radiative model calculation on level population. The M1/E1 line ratio for the F-like ions is applied to the α （He^2＋） particle diagnostics in ITER, in which a steady-state operation of burning plasmas based on D-T fusion reaction is expected with α particle heating. Unfortunately, the present estimation suggests a negative result for the α particle measurement because the ratio is largely enhanced by the collisional excitation with bulk ions due to high ion temperature of ITER of 10 keV as assumed and the resultant effect of the collisional excitation with α particles becomes less. Meanwhile, the M1 transition, in particular, Ti-like WLIII （W^52＋） transition （3627 A） emitted in visible range, is very useful for diagnostics of the impurity behavior and the core plasma parameters in ITER.

Quantification of the Diminishing Earth’s Magnetic Dipole Intensity and Geomagnetic Activity as the Causal Source for Global Warming within the Oceans and Atmosphere

Quantitative analyses of actual measurements rather than modeling have shown that “global warming” has been heterogeneous over the surface of the planet and temporally non-linear. Residual regression analyses by Soares (2010) indicated increments of increased temperature precede increments of CO2 increase. The remarkably strong negative correlation (r = -0.99) between the earth’s magnetic dipole moment values and global CO2-temperature indicators over the last ~30 years is sufficient to be considered causal if contributing energies were within the same order of magnitude. Quantitative convergence between the energies lost by the diminishing averaged geomagnetic field strength and energies gained within the ocean-atmosphere interface satisfy the measured values for increased global temperature and CO2 release from sea water. The pivotal variable is the optimal temporal unit employed to estimate the total energies available for physical-chemical reactions. The positive drift in averaged amplitude of geomagnetic activity over the last 100 years augmented this process. Contributions from annual CO2 from volcanism and shifts in averaged geomagnetic activity, lagged years before the measured global temperature-CO2 values, are moderating variables for smaller amplitude perturbations. These results indicated that the increase in CO2 and global temperatures are primarily caused by major geophysical factors, particularly the diminishing total geomagnetic field strength and increased geomagnetic activity, but not by human activities. Strategies for adapting to climate change because of these powerful variables may differ from those that assume exclusive anthropomorphic causes.

Quantification of the Diminishing Earth’s Magnetic Dipole Intensity and Geomagnetic Activity as the Causal Source for Global Warming within the Oceans and Atmosphere

Quantitative analyses of actual measurements rather than modeling have shown that “global warming” has been heterogeneous over the surface of the planet and temporally non-linear. Residual regression analyses by Soares (2010) indicated increments of increased temperature precede increments of CO2 increase. The remarkably strong negative correlation (r = -0.99) between the earth’s magnetic dipole moment values and global CO2-temperature indicators over the last ~30 years is sufficient to be considered causal if contributing energies were within the same order of magnitude. Quantitative convergence between the energies lost by the diminishing averaged geomagnetic field strength and energies gained within the ocean-atmosphere interface satisfy the measured values for increased global temperature and CO2 release from sea water. The pivotal variable is the optimal temporal unit employed to estimate the total energies available for physical-chemical reactions. The positive drift in averaged amplitude of geomagnetic activity over the last 100 years augmented this process. Contributions from annual CO2 from volcanism and shifts in averaged geomagnetic activity, lagged years before the measured global temperature-CO2 values, are moderating variables for smaller amplitude perturbations. These results indicated that the increase in CO2 and global temperatures are primarily caused by major geophysical factors, particularly the diminishing total geomagnetic field strength and increased geomagnetic activity, but not by human activities. Strategies for adapting to climate change because of these powerful variables may differ from those that assume exclusive anthropomorphic causes.

Moments of Inertia, Magnetic Dipole Moments, and Electric Quadrupole Moments of the Lithium Isotopes

The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes 6Li, 7Li, 8Li, 9Li, 10Li, and 11Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus 6Li may be assumed to be deformed and has an axis of symmetry.