Cusp Magnetic Field Research Articles

Numerical simulation of an external cusp magnetic field on the welding arc

A controlled welding arc is an up-and-coming research area for high-efficiency and high-precision wire arc additive manufacturing. This numerical simulation demonstrates that an alternating external cusp magnetic field (ECMF) can compress the arc. This is the result of the reversal of the Lorentz force direction caused by the reversal of the magnetic poles. The simulation results show that the solenoid current directly affects the arc section ellipticity, and the alternating frequency affects the arc contraction. The high-speed photos demonstrate the feasibility of ECMF.

The effect of anode axial position on the performance of a miniaturized cylindrical Hall thruster with a cusp-type magnetic field

A 200 W cylindrical Hall thruster with a cusp-type magnetic field was proposed, manifesting convergent plume and high specific impulse. In this paper, a series of ring-shaped anodes are designed and the influence of anode axial position on the performance of CHT with a cusp-type magnetic field is studied. The experimental results indicate that the thruster keeps stable operation at the condition of 140–270 W discharge power. When the anode moves axially towards the upstream cusp field, the thrust enhances from 6.5 mN to 7.6 mN and specific impulse enhances from 1658 s to 1939 s significantly. These improvements of thruster performance should be attributed to the enhancement of current utilization, propellant utilization and acceleration efficiency. According to the analyses on the discharge characteristics, it is revealed that as the anode moves upstream, the electron transport path could be extended, the magnetic field in this extended path could impede electron cross-field transport and facilitate the ionization intensity, yielding to the enhancement of current utilization and propellant utilization efficiency. Moreover, along with this enhancement of upstream ionization at the given anode flow rate, the main ionization region is thought to move upstream and then separate more apparently from the acceleration region, which has been demonstrated by the narrowing of ion energy distribution function shape. This change in acceleration region could decrease the ion energy loss and enhance acceleration efficiency. This work is beneficial for optimizing the electrode structure of thruster and recognize the ionization and acceleration process under the cusp magnetic field.

Measurement of plasma flow and electron energy probability function in radio frequency plasma thruster with a magnetic cusp

The use of a cusp magnetic field is studied to improve the thrust performance of small electrodeless radio frequency (RF) plasma thrusters based on a theoretical analysis of a magnetized inductively coupled plasma. In this type of thruster, electrons play a critical role in determining the thrust performance. The electron energy probability function (EEPF) and two-dimensional profiles of the plasma parameters in the cusp-type magnetic field RF thruster are investigated to characterize the plasma flow. Non-Maxwellian EEPFs were obtained, which correspond to the pressure and plasma potential profiles in the plasma plume. In addition, the axial ion velocity was measured, and the presence of ion flux in the downstream direction is revealed, indicating ideal ion acceleration.

On suitable experiments for demonstrating the feasibility of the beam-driven plasma neutraliser for neutral beam injectors for fusion reactors

Plasma neutralisers promise increased neutralisation efficiency of negative ion beams in neutral beam injection (NBI) beamlines compared with gas neutralisers. It has been suggested that, in the presence of an electron-confining magnetic cusp field along all neutraliser walls, the beam itself could ionise the neutraliser gas sufficiently to take advantage of this effect, avoiding the added complexity of external power coupling to the neutraliser. These predictions come from a zero-dimensional model by Surrey and Holmes (2013 AIP Conf. Proc. 1515 532) and Turner and Holmes (2019 Fusion Eng. Des. 149 111327). We have revisited and modified this model by introducing slowing-down energy distributions for stripped and Rudd electrons, including electron impact dissociation as an electron energy loss channel and taking into account dissociative recombination of molecular ions with electrons. Including the latter effect reduces the predicted plasma density by about a factor of four and the achievable neutralisation yield from to 68% in the case of a negative deuterium ion beam with an energy of 1 MeV and a current of 40 A. With this revised model we estimate the expected performance of potential beam-driven plasma neutralisers (BDPN) on a variety of existing negative ion beam test facilities for NBI. Based on these results, we conclude that the most suitable proof-of-principle experiment would be a dedicated chamber, ideally of the same dimensions and with the same magnetic cusp configuration as a BDPN for the DEMO NBI, in which the plasma is not created primarily by the fast electrons stripped from the beam ions, but by electrons of similar current and energy emitted from biased filaments.

Inhibition of Cusp magnetic field on stray-crystal formation in platform region during directionally solidified single-crystal superalloy

The stray crystal in the platform region is one of the common main defects in single-crystal superalloy blades. The simple and effective method to eliminate this defect is urgent to be explored. This work found that the Cusp magnetic field can effectively inhibit the stray-crystal formation in the platform. The tendency of stray-crystal formation decreases as the magnetic-field strength increases at a certain withdrawal rate and temperature-gradient. The suppressing effect decreases as the withdrawal rate or the temperature-gradient increases. Finally, the inhibiting mechanism on the stray-crystal formation from the Cusp magnetic field is proposed based on the experiments and the numerical simulation. The magnetic-field application strengthens the flow velocity and changes the flow structure near the liquid-solid interface, and further reduces the radial temperature difference. Accordingly, the secondary dendrites in the heat-conduction undercooled zone expands towards the corner in a faster speed, which reduces the stray-crystal formation in the platform corner. This study provides an effective and simple method for decreasing the stray-crystal formation during the preparation of single-crystal with platform region.

Mode transition of the cylindrical Hall thruster with the near-anode cusp magnetic field

There are two distinct discharge modes in a 200 W cylindrical Hall thruster with the near-anode cusp magnetic field. In mode I, a divergent plume is observed at a low discharge voltage. When the discharge voltage rises over 280 V, an apparent discharge mode transition occurs along with the sharp decreasing of discharge current (by 9.9%) and electron current (by 26%) and apparent narrowing of plume angle (by 12%), bringing a convergent plume (mode II). In mode I, the most probable ion energy of ion energy distribution function declines monotonically with the increasing of plume angle. However, a non-monotonic variation characteristic of most probable ion energy is indicated in mode II, which suggests that there are two ionization regions in this mode. These novel mode transition phenomena should be attributed to the unique near-anode cusp magnetic field. In low discharge voltage conditions (mode I), as the energies of the electron population are low, they are trapped in the near-axial magnetic mirror field, and a cylindrical ionization region along thruster axis is established. When the discharge voltage rises over the threshold voltage occurring mode transition, the energies of the electron population are enhanced and the energetic electrons could escape from the mirror field and reach the upstream crossed electric and magnetic fields. As a result, an additional ionization region related to E × B drift is formed in the upstream region. The competitive relationship between the upstream ionization related to E × B drift and the near-axial ionization related with magnetic mirror field should be the leading cause of mode transition.

Three-dimensional characteristics of turbulent flow and heat transfer in Czochralski silicon melt with different cusp magnetic field configurations

Three-dimensional unsteady simulations are performed for the turbulent flow and heat transfer in a Czochralski silicon melt for 300 mm crystal growth. The influence of the horizontal symmetry plane in the cusp magnetic field on the melt flow, temperature field, and crystal/melt interface is systematically analyzed. The numerical results show that the melt velocity and its fluctuation near the interface decrease, while the temperature and its fluctuation increase gradually with the downward horizontal symmetry plane position. For each horizontal symmetry plane position, the oscillation frequencies of melt temperature and velocity consist of a basic frequency and its integer multiple frequencies. Thermal waves with a regular shape rotate on the melt-free surface, and the rotational direction is consistent with the crucible rotation. The interface shape is strongly associated with the heat transfer near the interface, which depends on the melt flow direction and velocity magnitude as well as the temperature gradient below the crystal. In addition, the oscillation of interface temperature is affected by the melt flow below the crystal, changing from high-frequency small fluctuation to low-frequency large fluctuation with the horizontal symmetry plane moving down.

Measurement of electron density and temperature in an annular magnetically confined cold-cathode plasma of helium by optical emission spectroscopy

Magnetically confined cold-cathode plasmas in monatomic gases like helium can be used in a variety of devices and applications. In this paper, the radial distribution of electron temperature and electron density in cold-cathode helium plasmas constrained by an annular magnetic field were studied by optical emission spectroscopy. Helium plasma was generated under different pressures (7.5, 10, and 20 Pa) and values of current (23.5 and 33 mA). The spectral lines of He I 667.8 and He I 501.6 nm were studied and the Stark broadening method was applied to obtain the radial distributions of electron temperature and electron density. The results indicate that higher radial gradients or peak values of both electron density and electron temperature could be achieved with increasing operating pressures and discharge currents. It was found that the electrons were mainly concentrated in the area of the localized cusp magnetic field near the cathode surface and the electron density decreased rapidly as with the decrease in the magnetic field.

Effect of cusp magnetic field on the turbulent melt flow and crystal/melt interface during large-size Czochralski silicon crystal growth

The influences of cusp magnetic field on the turbulent melt flow and the crystal/melt interface are studied by three-dimensional unsteady simulations for 300 mm industrial Czochralski silicon crystal growth. Detailed comparisons are implemented for the melt flow pattern, temperature and velocity oscillations as well as the crystal/melt interface with and without magnetic field. It is found that the melt flow is complex and irregular in this system, accompanied with rich flow structures and large temperature and velocity fluctuations. Under the application of cusp magnetic field, the turbulent melt flow is significantly inhibited with the simple flow structure as well as the periodic temperature and velocity fluctuations. The anticlockwise periodical flow in the melt induced by cusp magnetic field can help to reduce the impurity in the crystal and suppress the crystal/melt interface deformation. In particular, the thermal waves on the melt free surface are firstly observed with cusp magnetic field for large-size Czochralski silicon crystal growth, traveling in the direction of crucible rotation.

Electric Potential in Volume Produced Negative Ion Sources with Magnetic Field Increasing toward a Wall

Distribution of electric potential near the wall in the volume produced negative ion source with the magnetic field increasing toward the wall such as the cusp magnetic field is investigated analytically. The plasma-sheath equation that gives the electric potential in the plasma region and the sheath region near the wall is derived analytically and the potential distribution near the wall is obtained by solving the plasma-sheath equation. Effects of the degree of increase of the magnetic field, the production amount of volume produced negative ion, and the ion temperature on the distributions of electric potential are shown.

Effects of different cusp magnetic ratios and crucible rotation conditions on oxygen transport and point defect formation during Cz silicon crystal growth

The effects of different crucible counter- and iso-rotation rates and cusp magnetic ratios (MRs) on the melt flow, temperature, oxygen content, and point defect formation during the growth of a 5-inch diameter silicon crystal are discussed numerically. In cases without a cusp magnetic field (CMF), the oxygen content gets smaller at a low crucible rotation speed than at a high one, for both counter- and iso-rotation conditions. This trend is reversed under a CMF. The flow field is controlled by the crucible rotation rate, the rotation direction between the crucible and the crystal, and the MR. Since the melt flow motion is retarded by the Lorentz force at a high MR, diffusion has a greater effect on oxygen transport in the bulk melt. It promotes the transport of oxygen atoms from the crucible wall towards the melt surface and the growth interface. The point defect density is quite dependent on the thermal field arising from changes in the growth interface shape. Microdefects in the silicon crystal can be reduced in density and enhanced in the radial uniformity using a high crucible iso-rotation rate and high unbalanced MR. A flatter shape of growth interface can be obtained under these growth conditions.

Magnetic cusp confinement in low-β plasmas revisited

Magnetic cusps have been used for more than 50 years to limit charged particle losses to the walls and confine the plasma in a large variety of plasma sources or ion sources. Quantification of the effective loss area has been the subject of many experimental as well as theoretical investigations in the 1970s–1990s. In spite of this effort, there is no fully reliable expression of the effective wall loss as a function of cusp magnetic field, electron temperature, ion mass, gas pressure, etc. We describe in this paper a first attempt at obtaining scaling laws for the effective loss width of magnetic cusps based on two-dimensional particle-in-cell Monte Carlo collision simulations. The results show that the calculated leak width follows a 1/B scaling in the collisionless low B limit, is approximately proportional to the hybrid gyroradius with an ion velocity equal to the Bohm velocity, and is proportional to the square root of gas pressure in the collisional limit.

Numerical Investigation of Effect of Temperature Profile Imposed on the Crucible Surface on Oxygen Incorporated at the Crystal Melt Interface for 450 mm Diameter Silicon Single Crystal Growth in Presence of CUSP Magnetic Field Using Czochralski Technique

Numerical investigation has been carried out to study the effect of thermal boundary condition on turbulent melt flow and oxygen transfer inside a crucible used to grow 450 mm diameter silicon single crystal using Czochralski method. Two types of thermal boundary conditions, namely, isothermal crucible surface and experimentally measured temperatures on the crucible surface have been imposed on the crucible wall and crucible bottom. Melt motion owing to buoyancy, surface tension variation at the free melt surface as well as crystal and crucible rotation has been considered. Effect of CUSP magnetic field has also been investigated. Melt having aspect ratio of 1 and 0.5, representing high and moderate level of melt inside the crucible have been considered. K-epsilon turbulent model with low Reynolds number formulation has been used for turbulence modelling. Melt motion governed by natural convection, Marangoni convection and crystal as well as crucible rotation shows higher oxygen concentration at melt crystal interface for aspect ratio of 1, when experimental temperature profile is imposed at the crucible wall. For melt aspect ratio of 0.5, natural convection and Marangoni convection dependent melt show higher oxygen concentration for isothermal crucible wall boundary condition. Marangoni convection in absence of rotation of crystal and crucible leads to low oxygen concentration zone near the crystal outer surface, the size of which is larger for melt aspect ratio of 0.5. Maximum turbulent viscosity values for aspect ratio of 1, in case of experimental temperature at the crucible are higher compared to isothermal case, which is just the opposite of the trend for aspect ratio of 0.5. Imposing a CUSP magnetic field leads to similar distribution of turbulent viscosity for both types of thermal boundary conditions, irrespective of the type of thermal boundary condition. Oxygen concentration at the melt crystal interface is found to be higher in presence of CUSP magnetic field. Value of maximum turbulent viscosity for the two boundary condition are similar for melt aspect ratio of 1.0. Crucible surface temperature profile for aspect ratio of 1, on actual melt aspect ratio of 0.5 predicts lower oxygen concentration at melt crystal interface. Values and distribution of turbulent viscosity is however the same for both temperature profiles.

E × B electron drift current across the aperture of an ion source surrounded by a cusped magnetic field profile

In negative ion sources, a cusped magnetic field is generated by magnets placed around each aperture of the extraction grid in order to limit the co-extracted electron current. In spite of this suppression magnetic field, the co-extracted electron current is large, on the same order as the negative ion current extracted from the plasma. In this paper, we study the mechanisms of electron extraction from the plasma through a cusped aperture in a simplified situation, in the absence of negative ions, with the help of a three-dimensional Particle-In-Cell Monte Carlo Collisions model. The calculation results show that the electron current extracted from the plasma is small for an infinite slit aperture with a suppressed (cusped) magnetic field and significantly increases in the case of finite slit or circular grid apertures. We find that the E×B electron drift plays an important role in the extraction of electrons through a finite slit grid aperture and that current driven micro instabilities are present in the aperture region. This work is relevant to negative ion sources and micro-ECR neutralizers designed for space propulsion.

Influence of near-anode cusped magnetic field on the performance of a miniaturized cylindrical Hall thruster

A near-anode cusped magnetic field topology is proposed for a 3 cm cylindrical Hall thruster (CHT), and its performance characteristics are investigated. The experimental results indicate that on imposing an anode voltage of 400 V, the thruster achieves a 2071 s specific impulse with a highly collimated plume. Compared with a conventional direct magnetic field, its thrust and anode efficiency are improved by 10.8% and 27.9%, respectively, which is due to the dramatic increase in the plume divergence efficiency (28.9%) and voltage utilization efficiency (6.7%). According to the analyses on the distribution characteristics of ion current density and ion energy, these performance improvements should be attributed to the downstream shift of both the ionization and acceleration regions. This work provides some design ideas on the magnetic field optimization of CHTs.

Nondestructive effect of the cusp magnetic field on the dendritic microstructure during the directional solidification of Nickel-based single crystal superalloy

The mechanical-property improvement of directionally-solidified Nickel-based single crystal (SC) superalloy with the single-direction magnetic fields is limited by their destructiveness on the dendritic microstructure. Here, the work present breaks through the bottleneck. It shows that the application of the cusp magnetic field (CMF) ensures that the dendrites are not destroyed. This feature embodies that the primary dendrite trunks arrange regularly and orderly, as well the secondary dendrite arms grow symmetrically. By contrast, both the unidirectional transverse and longitudinal magnetic field destroy the dendrite morphology, and there are a number of stray grains near the totally-remelted interface. The nondestructive effect is achieved mainly by the combined action of the thermoelectromagnetic force on the dendrites and thermoelectromagnetic convection in the melt during directional solidification. The investigation should contribute a new route for dramatically and effectively improving the crystal quality and mechanical properties of the directionally-solidified alloys.

Theoretical research on the annular intensive relativistic electron motion focused by coaxial cusped periodic permanent magnetic field

This paper theoretically investigates the motion characteristics of an annular intensive relativistic electron beam (IREB) in a coaxial, smooth waveguide under a cusped periodic permanent magnetic (CPPM) field. The motion of the electron beam clearly exhibits a periodic oscillation in a CPPM. For the effective transmission of an IREB, the structural parameters of the CPPM must be chosen carefully. Based on theoretical analysis, stability conditions are suggested. The influence of the magnetic field phase, strength, and period on the oscillation amplitude of the beam envelope is analyzed, and the criteria for minimal oscillation amplitude are proposed accordingly. Notably, the theoretical formula, used to predict the oscillation period of the beam envelope, is proposed and verified by single-particle and particle-in-cell simulation results.

Influence of cusp magnetic field configuration on K-TIG welding arc penetration behavior

Experiments have been carried out to test the improving effect of the cusp magnetic field to K-TIG arc penetration ability. The cusp magnetic field was generated with permanent magnets, the configuration parameters, including pole angle and field direction, were changed. Stationary welding experiments were carried out to measure the melting zone and the melting depth. After compressed with the cusp magnetic field, the anode melting zone changed from a circular shape to an ellipse shape, and the melting zone area was reduced. When the magnetic field direction was perpendicular to the arc column, the constraint effect was better than that when the magnetic field direction was parallel. Arc pressure distributions were experimental measured. Magnetic field with smaller pole angle has better constraint effect to the arc in the aspects of smaller melting zone area, increased melting depth, arc voltage and peak value of the arc pressure. These results indicated that the additional cusp magnetic field with less pole angle could further improve the penetration ability of the K-TIG arc.

Characterization of argon plasma in a variable multi-pole line cusp magnetic field configuration

This paper presents a detail characterization of argon plasma confined by a multi-pole line cusp magnetic field (MMF) over a large cylindrical volume (1 m axial length and 40 cm diameter) (Patel et al 2018 Rev. Sci. Instrum. 89 043510) and various magnetic field scaling with magnet current obtained from the magnetic field simulation in the vacuum. From the experimental results, it has been observed that in this field configuration the confinement of the primary electrons increases and leak width (plasma escaping through the cusp) of plasma decreases with increasing the magnetic field. As a result the mean density, particle confinement time and the stability of the plasma increase with increasing magnetic field values. In addition to this, it has been also observed that the radial uniformity of the plasma density across the magnetic field explicitly depends on the magnetic field values of MMF. Moreover, the nature of turbulence in a quiescent argon plasma has been identified.

Effects of crystal-crucible iso-rotation and a balanced/unbalanced cusp magnetic field on the heat, flow, and oxygen transport in a Czochralski silicon melt

• Melt flow pattern is varied by crystal-crucible rotation rates and magnetic ratios. • CMF insignificantly affects oxygen content at low crystal iso-rotation rates. • Iso-rotating crystal faster than crucible enhances oxygen content under a CMF. • Iso-rotating crystal faster than crucible increases the uniformity of oxygen content under a CMF. The effects of using a balanced/unbalanced cusp magnetic field (CMF) along with crystal-crucible counter-/iso-rotation on the heat, flow, and oxygen distributions during Czochralski (Cz) growth of an 8-inch silicon crystal are numerically investigated. One counter-rotation example is compared to iso-rotation cases. In both rotation modes, the vertical flow in the central melt region is strengthened while the buoyancy-driven melt flow is weakened under a cusp field. The CMF has a stronger effect on the oxygen content when there is a large difference in rotation rate between the crystal and the crucible (n S − n C ). This is because a higher value of (n S − n C ) induces stronger melt convection and hence, the Lorentz force has a more significant effect on a fast melt flow than a slow one. Although diffusion significantly influences oxygen transport in the melt at low crystal iso-rotation rates, different flow patterns and local melt velocities induced by different crystal iso-rotation speeds will modify the oxygen distribution. There is a slight change in the oxygen content at a low ingot iso-rotation rate with a CMF. In cases of iso-rotation, the radial oxygen content is enhanced more by an unbalanced CMF than a balanced one. Greater uniformity of the radial oxygen concentration is achieved applying iso-rotation with n S > n C under a CMF.