# Biblio

This paper presents an analytical method for predicting the electromagnetic performance in permanent magnet (PM) machine with the spoke-type rotor (STR) and a proposed hybrid rotor structure (HRS), respectively. The key of this method is to combine magnetic field analysis model (MFAM) with the magnetic equivalent circuit model. The influence of the irregular PM shape is considered by the segmentation calculation. To obtain the boundary condition in the MFAM, respectively, two equivalent methods on the rotor side are proposed. In the STR, the average flux density of the rotor core outer-surface is calculated to solve the Laplace's equation with considering for the rotor core outer-surface eccentric. In the HRS, based on the Thevenin's theorem, the equivalent parameters of PM remanence BreB and thickness hpme are obtained as a given condition, which can be utilized to compute the air-gap flux density by conventional classic magnetic field analysis model of surface-mounted PMs with air-gap region. Finally, the proposed analytical models are verified by the finite element analysis (FEA) with comparisons of the air-gap flux density, flux linkage, back-EMF and electromagnetic torque, respectively. Furthermore, the performance that the machine with the proposed hybrid structure rotor can improve the torque density as explained.

To decouple the multi-axis motion in the 6 degrees of freedom magnetically levitated actuators (MLAs), this paper introduces a numerical method to model the force and torque distribution. Taking advantage of the Gaussian quadrature, the concept of coil node is developed to simplify the Lorentz integral into the summation of the interaction between each magnetic node in the remanence region and each coil node in the coil region. Utilizing the coordinate transformation in the numerical method, the computation burden is independent of the position and the rotation angle of the moving part. Finally, the experimental results prove that the force and torque predicted by the numerical model are rigidly consistent with the measurement, and the force and torque in all directions are decoupled properly based on the numerical solution. Compared with the harmonic model, the numerical wrench model is more suitable for the MLAs undertaking both the translational and rotational displacements.

The understanding of measured jitter is improved in three ways. First, it is shown that the measured jitter is not only governed by written-in jitter and the reader resolution along the cross-track direction but by remanence noise in the vicinity of transitions and the down-track reader resolution as well. Second, a novel data analysis scheme is introduced that allows for an unambiguous separation of these two contributions. Third, based on data analyses involving the first two learnings and micro-magnetic simulations, we identify and explain the root causes for variations of jitter with write current (WC) (write field), WC overshoot amplitude (write-field rise time), and linear disk velocity measured for heat-assisted magnetic recording.

Micromagnetic simulations of coercivity as a function of external magnetic field direction were performed for a hexagonal array of hemispherical Permalloy nanocaps. The analysis was based on hysteresis loops for arrangements of nanocaps of variable thickness (5 nm and 10 nm). The angular dependence of coercivity had a maximum at about 80° with respect to the arrangement plane. An increase in coercivity with nanocap thickness is related to the magnetization reversal mechanism, where the dipole energy of individual caps generates an effective intermediate axis, locking the magnetic moments. The coercivity has maximum values of 109 Oe for 5 nm and 156 Oe for 10 nm thickness. The remanence decreases monotonically with angle. This is associated with the influence of shape anisotropy, where the demagnetizing field in the plane of the array is much smaller than the demagnetizing field perpendicular to the plane.

One method to increase bit density in magnetic memory devices is to use multi-state structures, such as a ferromagnetic nanoring with multiple domain walls (DWs), to encode information. However, there is a competition between decreasing the ring size in order to more densely pack bits and increasing it to make multiple DWs stable. This paper examines the effects of ring geometry, specifically inner and outer diameters (ODs), on the formation of 360° DWs. By sequentially increasing the strength of an applied circular magnetic field, we examine how DWs form under the applied field and whether they remain when the field is returned to zero. We examine the relationships between field strength, number of walls initially formed, and the stability of these walls at zero field for different ring geometries. We demonstrate that there is a lower limit of 200 nm to the ring diameter for the formation of any 360° DWs under an applied field, and that a high number of 360° DWs are stable at remanence only for narrow rings with large ODs.

In order to study the stress detection method on long-distance oil and gas pipeline, the distribution characteristics of the surface remanence signals in the stress concentration regions must be known. They were studied by using the magnetic domain model in the non-magnetic saturation state. The finite element method was used herein with the aim to analyse the static and mechanical characteristics of a ferromagnetic specimen. The variation law of remanence signal in stress concentration regions was simulated. The results show that a residue signal in the stress concentration region exists. In addition, a one-to-one correspondence in the non-magnetic saturation environment is evident. In the case of magnetic saturation, the remanence signal of the stress concentration region is covered and the signal cannot be recognised.

The process of release of a single domain wall from the closure domain structure at the microwire ends and the process of nucleation of the reversed domain in regions far from the microwire ends were studied using the technique that consists in determining the critical parameters of the rectangular magnetic field pulse (magnitude-Hpc and length-τc) needed for free domain wall production. Since these processes can be influenced by the magnitude of the magnetic field before or after the application of the field pulse (Hi, τ), we propose a modified experiment in which the so-called three-level pulse is used. The three-level pulse starts from the first level, then continues with the second measuring rectangular pulse (Hi, τ), which ends at the third field level. Based on the results obtained in experiments using three-level field pulses, it has been shown that reversed domains are not present in the remanent state in regions far from the microwire ends. Some modification of the theoretical model of a single domain wall trapped in a potential well will be needed for an adequate description of the depinning processes.