ANALYTIC EXPRESSION OF MAGNETIC FIELD DISTRIBUTION OF RECTANGULAR PERMANENT MAGNETS

From the molecular current viewpoint,an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart's law. This expression is useful not only for the case of one rectangular permanent magnet bulk,but also for that of several rectangular permanent magnet bulks. By using this expression,the relations between magnetic field distribution and the size of rectangular permanent magnets as well as the magnitude of magnetic field and the distance from the point in the space to the top (or bottom) surface of rectangular permanent magnets were discussed in detail. All the calculating results are consistent with experimental ones. For transverse magnetic field which is a main magnetic field of rectangular permanent magnets,in order to describe its distribution,two quantities,one is the uniformity in magnitude and the other is the uniformity in distribution of magnetic field,were defined. Furthermore,the relations between them and the geometric size of the magnet as well as the distance from the surface of permanent magnets were investigated by these formulas. The numerical results show that the geometric size and the distance have a visible influence on the uniformity in magnitude and the uniformity in distribution of the magnetic field.

The Investigation of Round Billet Temperature and Magnetic Field Distribution and Variation During Induction Heating Process

Round billet temperature during induction heating was calculated with numerical simulation method in present work,the factors affect induction heating were studied,such as coil turns.using of magnetic material,the convective heat transfer between billet surface and surrounding environment,etc.It was found that coil turns played an important role in round billet temperature distribution,and it was necessary to choose reseaonable coil turns in order to get a relatively uniform temperature distribution.Using magnetic flux concentrator could greatly improve the billet end temperature,and the phenomena of low temperature in billet end would be elimiated.Besides,the billet temperature would be reduced by convective heat transfer in billet outsurface and air,longer time was cost to reache the target temperature.Meanwhile,the magnetic field during billet induction heating was calculated,it was used to explain billet temperature distribution and variation,the reasonable measures to control billet temperature during induction heating process were proposed.

Modeling of Fault-tolerant Flux-switching Permanent-magnet Machines for Predicting Magnetic and Armature Reaction Fields

The paper develops accurate analytical subdomain models for predicting the magnetic and armature reaction fields in fault-tolerant flux-switching permanent-magnet machines.The entire region is divided into five subdomains,followed by rotor slots,air-gap,stator slots,PM,and external air-gap imported to account for flux leakage.The coil turns and the remanence of magnets are adjusted by keeping the magnetic and electrical loading on the motor constant.The distance between the centers of two adjacent stator slots varies due to the introduction of faulttolerant teeth.According to the variable separation method,the general solution expression of each region can be determined by solving the partial differential systems of equations.The magnetic field distributions of subdomains are obtained by applying the continuity conditions between adjacent regions.Some analytical field expressions are represented as new forms under armature reaction field condition compared to those under no-load condition.Based on the developed analytical models,the flux density distribution and the electromagnetic performance can be calculated under no-load or armature reaction field condition separately.The finite element analysis is carried out to verify the validity of the proposed analytical model.

Three-Dimensional Analytical Modeling of Axial-Flux Permanent Magnet Drivers

In this paper, the axial-flux permanent magnet driver is modeledand analyzed in a simple and novel way under three-dimensional cylindricalcoordinates. The inherent three-dimensional characteristics of the deviceare comprehensively considered, and the governing equations are solved bysimplifying the boundary conditions. The axial magnetization of the sectorshapedpermanent magnets is accurately described in an algebraic form bythe parameters, which makes the physical meaning more explicit than thepurely mathematical expression in general series forms. The parameters of theBessel function are determined simply and the magnetic field distribution ofpermanent magnets and the air-gap is solved. Furthermore, the field solutionsare completely analytical, which provides convenience and satisfactoryaccuracy for modeling a series of electromagnetic performance parameters,such as the axial electromagnetic force density, axial electromagnetic force,and electromagnetic torque. The correctness and accuracy of the analyticalmodels are fully verified by three-dimensional finite element simulations and a15 kW prototype and the results of calculations, simulations, and experimentsunder three methods are highly consistent. The influence of several designparameters on magnetic field distribution and performance is studied and discussed.The results indicate that the modeling method proposed in this papercan calculate the magnetic field distribution and performance accurately andrapidly, which affords an important reference for the design and optimizationof axial-flux permanent magnet drivers.

Spatial distributions of magnetic field in the RHIC and LHC energy regions

Relativistic heavy-ion collisions can produce extremely strong magnetic fields in the collision regions. The spatial variation features of the magnetic fields are analyzed in detail for non-central Pb Pb collisions at LHC at √SNN= 900, 2760 and 7000 GeV and Au-Au collisions at RHIC at √SNN=62.4, 130 and 200 GeV. The dependencies of magnetic field on proper time, collision energies and impact parameters are investigated in this paper. It is shown that an enormous and highly inhomogeneous spatial distribution magnetic field can indeed be created in off-centre relativistic heavy-ion collisions in RHIC and LHC energy regions. The enormous magnetic field is produced just after the collision, and the magnitude of magnetic field of the LHC energy region is larger than that of the RHIC energy region at small proper time. It is found that the magnetic field in the LHC energy region decreases more quickly with the increase of proper time than that of the RHIC energy region.

Experimental Study and Numerical Visualization of Physical Fields of Electromagnetic Pumps Constructed on Permanent Magnets

Pumps with magnet systems constructed on permanent magnets and performed in two manners like two-disk type and the cylindrical rotor type are discussed.First,by way of example we consider the experimental study of disk pump with straight channel;second,we analyse the results of numerical simulation of cylindrical pump in two cases,namely,of straight and U-bend forms of pump channels.At a high speed of pump rotation when induced magnetic field becomes essential in as against the applied field,i.e.when the skin-effect takes place,the pump characteristics are analyzed.Visualization of physical fields of the pumps is reported.

Experimental investigation of a compact relativistic magnetron with axial TE_(11) mode radiation

As one of the relativistic electron tubes having compact configuration and high efficient output, the relativistic magnetron with direct axial radiation is very attractive in pulsed power and high power microwave fields for industrial and military applications. In this paper, the experimental investigation of a relativistic magnetron with axial TE11 mode radiation is reported. Under a total length of - 0.3 m, volume of - 0.014 m3, working at an applied voltage of 508 kV and a magnetic field of - 0.31 T, the relativistic magnetron radiates a microwave of 540 MW with the TE11 mode at 2.35 GHz in the axial direction. The power conversion efficiency is 15.0%. After a lot of shots, the detected amplitudes of microwaves are nearly the same. The fluctuations of wave amplitudes are less than 0.3 dB.

Experimental study of induction heating for steel plates

The temperature distribution of steel plates is affected by heating rates and heating curves in the process of induction heating.The magnetic flux density inside the induction furnace was measured,the distribution of magnetic flux density was analyzed and the uniform area of the induction heating temperature distribution was ascertained.The locations for measuring temperature were set and the temperature in different processes was measured.The influence of heating rates and heating curves on the temperature difference of steel plates was studied.The experimental results showed that the steel plates’ temperature difference increased with the increase of the heating rate.The temperature difference was obviously affected by different heating curves when the heating rate was the same.A suitable heating curve would be beneficial to reduction of steel plates’ temperature difference.

Elaboration of a Promising Design of the HTS Conductor for the Central Solenoid of a Compact Thermonuclear Reactor TRT

The results of the preliminary development of the HTS conductor based on the VS-type design and parallel stacks for the central solenoid of the compact thermonuclear reactor TRT are presented. One of the main problems that need to be solved for the successful implementation of such projects is the creation of high-current high-temperature superconducting (HTS) conductors for Toroidal Field coils (TF) and Central Solenoid (CS) sections. The conductor must have a high engineering current density of at least 90 A/mm2. The induction of the magnetic field in the central solenoid reaches 14 T, which leads to the occurrence of large mechanical stresses due to the influence of Lorentz forces. Like many large magnets, CS has a lot of stored energy. For the safe withdrawal of stored energy from the magnet, it requires the inclusion of elements in the conductor that provide an acceptable level of electrical voltage and heating of the conductor insulation. Thus, a sufficient amount of stabilizing and reinforcing materials should be placed in the conductor. In addition, the “cable-in-conduit” type of conductor must have channels for pumping the refrigerant. Two fundamentally different versions of the conductor based on radially arranged REBCO tapes and on the basis of pre-assembled tape packages are considered. Based on the analysis of the magnetic field distribution in the conductor by finite element method, the design characteristics of the proposed conductors under various operating modes of the electromagnetic system (EMS) of the tokamak TRT was evaluated. The results of the evaluation of the current carrying capacity of the conductor and the estimation of energy losses in a changing magnetic field in comparison with known methods are also presented.