Effects of geometric parameters and axial magnetic field on buoyant-thermocapillary convection during detached solidification

In order to understand the effect of geometric parameters and axial magnetic field on buoyant-thermocapillary convection during detached solidification, a series of threedimensional numerical simulations were conducted by the finite-difference method. The results indicate that the stable flow is observed when the Marangoni number （Ma） is small; however, when the value of Ma increases and exceeds a threshold value, the stable steady flow transits to be unstable flow. As the height of the melt increases, the flow is enhanced at first and then gets weakened. As the width of gap decreases gradually, the strength of flow is enhanced. The approach of using axial magnetic field is an effective way to suppress the buoyant-thermocapillary convection. As the magnetic field strength increases, the inhibition is enhanced. The critical Marangoni number increases slightly with a greater melt height, a narrower width of gap, and a more strength of magnetic field.

Effect of an axial magnetic field on a DC argon arc

In this paper a commercial CFD （computational fluid dynamics） code FLUENT has been used and modified for the axisymmetric swirl and time-dependent simulation of an atmospheric pressure argon arc in an external axial magnetic field （AMF）. The computational domain includes the arc itself and the anodic region. Numerical results demonstrate that the AMF substantially increases the tangential component of the plasma velocity. The resulting centrifugal force for the plasma rotation impels it to travel to the arc mantel and as a result, a low-pressure region appears at the arc core. With the AMF, the arc presents a hollow bell shape and correspondingly, the maximal values of the temperature, pressure and current density on the anode surface are departing from the arc centreline.

Arc Behaviours in Vacuum Interrupters with Axial Magnetic Field Electrodes

To improve the limiting current interruption capability and minimizing vacuum interrupter with axial magnetic field （AMF） electrodes, it is significant to investigate the vacuum arc behaviours between the contacts. AMF distributions of the slot type electrodes were studied by both numerical analysis and experiments. Furthermore, the behaviours of vacuum arcs for different parameters of the slot type AMF electrodes were investigated by using high-speed CCD camera. The influences of gap distance, contact diameter and phase shift time between AMF and arc current on the vacuum arc were investigated. The results provide a reference for research and development of vacuum interrupters with slot type or other types of AMF electrode.

Simulation Research of Magnetic Constriction Effect and Controlling by Axial Magnetic Field of Vacuum Arc

Based on magnetohydrodynamic (MHD) model of vacuum arc, the computer simulation of vacuum arc was carried out in this paper. In the MHD model, mass conservation equation, momentum conservation equations, energy conservation equations, generalized ohm's law and Maxwell equation were considered. MHD equations were calculated by numerical method, and the distribution of vacuum arc plasma parameters and current density were obtained. Simulation results showed that the magnetic constriction effect of vacuum arc is primarily caused by the Hall effect. In addition, the inhibition of axial magnetic field (AMF) on constriction of vacuum arc was calculated and analyzed.

Influence of the axial magnetic field on sheath development after current zero in a vacuum circuit breaker

After current zero,which is the moment when the vacuum circuit breaker interrupts a vacuum arc,sheath development is the first process in the dielectric recovery process.An axial magnetic field（AMF） is widely used in the vacuum circuit breaker when the high-current vacuum arc is interrupted.Therefore,it is very important to study the influence of different AMF amplitudes on the sheath development.The objective of this paper is to study the influence of different AMF amplitudes on the sheath development from a micro perspective.Thus,the particle in cell-Monte Carlo collisions（PIC-MCC） method was adopted to develop the sheath development model.We compared the simulation results with the experimental results and then validated the simulation.We also obtained the speed of the sheath development and the energy density of the ions under different AMF amplitudes.The results showed mat the larger the AMF amplitudes are,the faster the sheath develops and the lower the ion energy density is,meaning the breakdown is correspondingly more difficult.

Investigation of Vacuum Arc Voltage Characteristics Under Different Axial Magnetic Field Profiles

Characteristics of the arc voltage under different profiles of axial magnetic field were investigated experimentally in a detachable vacuum chamber with five pairs of specially designed electrodes generating both bell-shaped and saddle-shaped magnetic field profile. The arc column and cathode spot images were photographed by a high speed digital camera. The dependence of the arc voltage on arcing evolution is analyzed. It is indicated that the axial magnetic field profile could affect the arc behaviors significantly, and the arc voltage is closely related to the arc light intensity.

Cogging Torque Reduction in Axial Flux PMSM with Different Permanent Magnet Combination

With the increasing requirement for the mechanical vibration and acoustic noise of the permanent magnet synchronous motor(PMSM)drive system,the demand for cogging torque reduction of PMSM has been considerably increased.To solve the problem of oversized cogging torque of axial flux PMSM,a rotor topology with hybrid permanent magnet is proposed to weaken the cogging torque.Firstly,the expression of the cogging torque of the axial flux motor is derived,and the influence of the pole-arc ratio of the permanent magnet on the cogging torque is analyzed.Secondly,the rotor structure with hybrid permanent magnet is adopted to reduce the cogging torque.According to the analytical analysis,the constraints of the size and pole-arc ratio between the hybrid permanent magnets are obtained,and the two permanent magnets related to the minimum cogging torque are determined.And the analysis results are verified by the finite element simulation.Furthermore,the motor performance with and without the hybrid permanent magnet is compared with each other.Finally,the cogging torque is significantly reduced by adopting a rotor structure with hybrid permanent magnets.

Dynamic Stiffness Analysis and Experimental Verification of Axial Magnetic Bearing Based on Air Gap Flux Variation in Magnetically Suspended Molecular Pump

Current and displacement stiffness are important parameters of axial magnetic bearing(AMB)and are usually considered as constants for the control system.However,in actual dynamic work situations,time-varying force leads to time-varying currents and air gap with a specific frequency,which makes the stiffness of appear decrease and even worsens control performance for the whole system.In this paper,an AMB dynamic stiffness model considering the flux variation across the air gap due to frequency is established to obtain the accurate dynamic stiffness.The dynamic stiffness characteristics are analyzed by means of the dynamic equivalent magnetic circuit method.The analytical results show that the amplitude of current and displacement stiffness decreases with frequency increasing.Moreover,compared with the stiffness model without considering the variation of flux density across the air gap,the improved dynamic stiffness results are closer to the actual results.Through the dynamic stiffness measurement method of AMB,experiments of AMB in magnetically suspended molecular pump(MSMP)are carried out and the experimental results are consistent with theoretical analysis results.This paper proposes the dynamic stiffness model of axial magnetic bearing considering the variation of flux density across the air gap,which improves the accuracy of the AMB stiffness analysis.

Dynamic Analysis of Axial Magnetic Forces for DVD Spindle Motors

The axial magnetic force, induced by the complicated flux linkage distribution from rotor magnet and stator slotted, is constructed by different relative heights and calculated by 3D finite element method (FEM) to analyze the dynamic characteristics for a DVD spindle motor. The axial magnetic force is designed to provide an axial stiffness, and govern the natural frequency of the dynamic performance. According to the simulation results and experimental measurements, the dynamic behaviors are significantly improved with a variation of relative height of rotor magnet and stator slotted on a DVD spindle motor.

Design and Performance Analysis of Axial Flux Permanent Magnet Machines with Double-Stator Dislocation Using a Combined Wye-Delta Connection

Conventional fractional slot concentrated winding three-phase axial flux permanent magnet machines have an abundance of armature reaction magnetic field harmonics which deteriorate the torque performance of the machine.This paper presents a double-stator dislocated axial flux permanent magnet machine with combined wye-delta winding.A wye-delta(Y-△)winding connection method is designed to eliminate the 6 th ripple torque generated by air gap magnetic field harmonics.Then,the accurate subdomain method is adopted to acquire the no-load and armature magnetic fields of the machine,respectively,and the magnetic field harmonics and torque performance of the designed machine are analyzed.Finally,a 6 k W,4000 r/min,18-slot/16-pole axial flux permanent magnet machine is designed.The finite element simulation results show that the proposed machine can effectively eliminate the 6 th ripple torque and greatly reduce the torque ripple while the average torque is essentially identical to that of the conventional three-phase machines with wye-winding connection.

Comparative Study of Novel Axial Flux Magnetically Geared and Conventional Axial Flux Permanent Magnet Machines

In this paper,a performance comparison between the novel axial flux magnetically geared machines(AFMG)and the conventional axial flux YASA machine is presented.The AFMG and YASA machines have the same stator construction in which segments are equipped with concentrated windings to form the stator.However,the AFMG machine has two rotors with different pole-pair numbers.Magnetic gear effect can be obtained to increase the torque density.The performance comparisons at no-load and on-load conditions are then studied by 3D-finite element analysis(FEM).Moreover,both machines are prototyped,tested and compared.

Electron-Cyclotron Laser Using Free-Electron Two-Quantum Stark Radiation in a Strong Uniform Axial Magnetic Field and an Alternating Axial Electric Field in a Voltage-Supplied Pill-Box Cavity

We consider the radiation from the beam electrons traveling in a strong uniform axial magnetic field and an axial alternating electric field of wavelength Aw generated by a voltage-supplied pill-box cavity. The beam electrons emit genuine laser radiation that propagates only in the axial direction through free-electron two- quantum Stark radiation. We find that laser radiation takes place only at the expense of the axial kinetic energy when Aw 〈〈 c/（ωc/γ）, where ωc/γ is the relativistic electron--cyclotron frequency. We formulate the laser power based on quantum-wiggler electrodynamics, and envision a laser of length lore with estimated power 0.1 GW/（kA） in the 10-4 cm wavelength range.

Modulation of absorption manner in helicon discharges by changing profile of low axial magnetic field

The modulation of absorption manner in helicon discharge by changing the profile of low axial magnetic field is explored experimentally in this work. The experiments are carried out in Boswell-type antenna driven by 13.56-MHz power source in 0.35-Pa argon environment. The peak of the external non-uniform magnetic field （Bex） along the axis is observed in a range from 0 Gs to 250 Gs （1 Gs=10^-4 T）, where the electron density varies from 0.5×10^16 m^-3 to 9×10^16 m^-3. When Bex is located near the tube upper end sealed by a dielectric plate, or near the tube bottom end connected with a diffusion chamber, the plasmas are centralized in the tube in the former case while the strong luminance appears between the edge of the tube and the axial line in the latter case. When Bex is located in the middle of the antenna, moreover, an effective resistance （Reff） peak appears apparently with increasing magnetic field. The glow moves toward first the edge of the tube and then the two antenna legs as the magnetic field increases. The discharge in this case is caused by the absorption of Trivelpiece-Gould （TG） wave. It is suggested that Bex is located in the middle of the antenna to obtain a higher efficiency of power transfer.

Axial Magnetic Field Effects on Xenon Short-Arc Lamps

The effect of an axial magnetic field （AMF） on an old xenon short-arc lamp is experimentally investigated in this work. As the AMF increases up to 18 roT, the visible radiation power and electric power ascend more than 80% and 70% respectively, and the radiation efficiency is improved by 23% for the best increment at 12 mT AMF. The measurement of radiation intensity shows that the increment of radiation intensity comes mostly from the plasma area close to the cathode tip, and partially from the other area of the arc column. Successive images of the arc indicate that the arc column not only rotates about its axis, but revolves around the axis of electrodes with the AMF. The arc column structure is constricted, distorted and elongated as the AMF increases. It is suggested that the improvements of the radiation intensity and radiation efficiency are attributed to the constriction of the arc column, which is mainly induced by the enhanced cathode jet.

Axial magnetic field effect in numerical analysis of high power Cherenkov free electron laser

Cherenkov free electron laser(CFEL) is simulated numerically by using the single particle method to optimize the electron beam. The electron beam is assumed to be moving near the surface of a flat dielectric slab along a growing radiation. The set of coupled nonlinear differential equations of motion is solved to study the electron dynamics. For three sets of parameters, in high power CFEL, it is found that an axial magnetic field is always necessary to keep the electron beam in the interaction region and its optimal strength is reported for each case. At the injection point, the electron beam’s distance above the dielectric surface is kept at a minimum value so that the electrons neither hit the dielectric nor move away from it to the weaker radiation fields and out of the interaction region. The optimal electron beam radius and current are thereby calculated. This analysis is in agreement with two previous numerical studies for a cylindrical waveguide but is at odds with analytical treatments of a flat dielectric that does not use an axial magnetic field. This is backed by an interesting physical reasoning.

Build Axial Gradient Field by Using Axial Magnetized Permanent Rings

Axial magnetic field produced by an axial magnetized permanent ring was studied. For two permanent rings, if they are magnetized in the same directions, a nearly uniform axial field can be produced. If they are magnetized in opposite direction, an axial gradient magnetic field can be generated, with the field range changing from-Bo to Bo- A permanent magnet with a high axial gradient field was fabricated, the measured results agree with the PANDIRA calculation very well. For wider usage, it is desirable for the field gradient to be changed. Some methods to produce the variable gradient field are presented. These kinds of axial gradient magnetic field can also be used as a beam focusing for linear accelerator if the periodic field can be produced along the beam trajectory. The axial magnetic field is something like a solenoid, large stray field will leak to the outside environment if no method is taken to control them. In this paper, one method is illustrated to shield off the outside leakage field.

Experimental Investigation on the Inf1uence of Axial Magnetic Field Distribution on Resisting the Constriction of a High-Current Vacuum Arc

Effect of the axial magnetic field （AMF） on resisting the constriction of a highcurrent vacuum arc is studied in this paper. Two typical AMF distributions were investigated, i.e., the traditional bell-shaped AMF, and the saddle-shaped AMF. Experiments were conducted in a detachable vacuum chamber with arms arc current in the range of 10 kA to 25 kA. The arc column was photographed by a high-speed digital camera with an exposure time of 2 microseconds. The constriction of the vacuum arc was compared by processing the images of the arc column under the two different field configurations and numerically determining the dimensions of the arc column near the electrodes. It was also confirmed that the AMF distribution had a significant influence on its effectiveness in resisting arc constriction. of the arc is more influential than that at the Furthermore, the AMF strength near the periphery centre of the electrodes in resisting arc constriction.

Distribution of Cathode Spots in Vacuum Arc Under Nonuniform Axial Magnetic Fields

Recent results on the distribution of vacuum arc cathode spots （CSs） in nonuniform axial magnetic field （AMF） are presented. Based on previous studies, we deem that two contrary influences of AMF, inward effect and outward effect, are attributed to CSs distribution. With this notion, we have analyzed the controlling effectiveness of nonuniform AMF on CSs distribution. Experiments were conducted in a detachable vacuum chamber with iron-style AMF electrodes. Images of vacuum arc column and the distribution of CSs were photographed with a high-speed charge coupled device （CCD） camera. Experimental results agreed well with the theoretical analysis.

Numerical simulation of low-current vacuum arc jet considering anode evaporation in different axial magnetic fields

As the main source of the vacuum arc plasma,cathode spots(CSs)play an important role on the behaviors of the vacuum arc.Their characteristics are affected by many factors,especially by the magnetic field.In this paper,the characteristics of the plasma jet from a single CS in vacuum arc under external axial magnetic field(AMF)are studied.A multi-species magneto-hydro-dynamic(MHD)model is established to describe the vacuum arc.The anode temperature is calculated by the anode activity model based on the energy flux obtained from the MHD model.The simulation results indicate that the external AMF has a significant effect on the characteristic of the plasma jet.When the external AMF is high enough,a bright spot appears on the anode surface.This is because with a higher AMF,the contraction of the diffused arc becomes more obvious,leading to a higher energy flux to the anode and thus a higher anode temperature.Then more secondary plasma can be generated near the anode,and the brightness of the‘anode spot’increases.During this process,the arc appearance gradually changes from a cone to a dumbbell shape.In this condition,the arc is in the diffuse mode.The appearance of the plasma jet calculated in the model is consistent with the experimental results.

Interruption Phenomenon in Intermediate-Frequency Vacuum Arc

In the condition of the 3 mm gap, experiments for 360 Hz intermediate-frequency vacuum arc are carried out in interrupters with the diameters being 41 mm and with the contact materials being CuCr50 and Cu-W-WC alloy respectively. The results indicate that the contacts material is closely related to the breaking capacity of the vacuum interrupters and characteristics of an intermediate-frequency vacuum arc. For contacts with the same diameter, the breaking capacity of CuCr50 is better than that of Cu-W-WC. When the current fails to be interrupted, the arcs overflow the gap and present irregular performances in the first half wave. Consequently a voltage spike appears. More macroscopic metal droplets can be seen in the arc column between CuCr50 contacts because of the lower melting point. It is observed that the droplet emission is much more severe during arc reignition than that in the first half wave. It is much more conspicuous that the high frequency arc voltage noises appear in Cu-W-WC contacts when the vacuum arcs reignite, for higher temperature and stronger electronic emission ability of Cu-W-WC contacts.