Linear stability of viscoelastic Walters' liquid B in a channel in the presence of a magnetic field

The effects of transverse magnetic fields on a $J=1\ensuremath{\rightarrow}0$ laser transition are considered, and expressions for the macroscopic-atomic-polarization terms are derived. The contributions from the $\ensuremath{\sigma}$ modes are combined, and equations for the intensities and frequencies of the $\ensuremath{\pi}$ and $\ensuremath{\sigma}$ oscillations are deduced. Various coupling terms occur because of the common lower level of the transition, and a quenching of the initial $\ensuremath{\pi}$-mode oscillation with a change to the $\ensuremath{\sigma}$ mode is indicated as the magnetic field increases from zero. With increased field, both modes oscillate simultaneously, and a beat occurs whose frequency depends on the operating conditions, and which may become zero again at higher magnetic fields. At line center the beat frequency should remain zero with increasing magnetic field, representing a method of laser tuning. Similar equations for the circularly polarized $\ensuremath{\sigma}$ oscillations in axial magnetic fields are deduced. Here the conditions for stable two-frequency operation are more readily satisfied, and no such quenching is indicated. Again there are zero-beat-frequency regions of magnetic field in which a mutual synchronization of the oscillations should occur. Some experimental results with transverse magnetic fields on the 1.153-\ensuremath{\mu} He-Ne laser are given. These display the general features indicated by the theory. Thus a quenching of the initial $\ensuremath{\pi}$-mode oscillation occurs, with more or less abrupt changes to the $\ensuremath{\sigma}$ mode, depending on conditions. Similar single-beat-frequency variations with magnetic field occur, together with a region near the line center where the beat frequency, although finite, remains constant with increasing magnetic field.

The external bus and conductive rod of a vacuum circuit breaker form a “U” shaped circuit, which generates an external transverse magnetic field in the arc area of the arc extinguishing chamber, resulting in severe asymmetry of the transverse magnetic field in the arc area, reducing the breaking capacity and service life of the circuit breaker. In the paper, we use Maxwell to establish a transverse magnetic field model for single-phase short circuit arc region. The analysis revealed that transverse magnetic field in the arc region is severely asymmetric under the effect of the transverse magnetic field generated by the external bus. So as to eliminate the effect of external transverse magnetic field, this paper has constructed stainless steel and iron shield shields to shield the external transverse magnetic field. The results show that both stainless steel and iron shields can shield against transverse magnetic fields, but the effect of iron shields with high magnetic permeability is more obvious. The research results of this paper provide important basis and reference for eliminating the external transverse magnetic field in the arc region, improving the breaking capacity and service life of circuit breakers.

A transverse gauss shape magnetic field with wide width is proposed for collimating the fast relativistic electron beam in laser irradiating plasmas, which is highlighted by the two-dimensional particle-in-cell simulations, in particular, the effects of this magnetic field on the production and transport of fast electron beam. When the axial magnetic field is also present, it is found that the energy density of fast electrons can be enhanced greatly. For example, in the presence of 30 MG axial magnetic field, it is enhanced by 3–4 times when the amplitude of the applied transverse magnetic field lies within the optimal regime 200–300 MG comparable to that without the transverse magnetic field. Meanwhile, the divergence angle of the electron beam can be controlled and even decreased a little due to the better sandwich structure of the overall weakening magnetic field. The study implies that the proposed transverse magnetic field is helpful to obtain the high quality electron beam which is beneficial to the fast ignition in inertial confinement fusion.

Purpose– The purpose of this paper is to investigate the effects of thermal radiation and viscous dissipation on steady natural convection flow of a viscous incompressible fluid along a uniformly moving infinite vertical porous plate with Newtonian heating in the presence of transverse magnetic field. The governing non-linear boundary layer equations are solved by using homotopy analysis method (HAM). The effects of various system parameters on velocity and temperature fields are discussed graphically, and the numerical values for skin friction and Nusselt number are presented in tabular form.Design/methodology/approach– The problem is formulated using the Boussinesq approximation under the effects of thermal radiation and transverse magnetic field. The resulting coupled system of non-linear differential equations is solved using HAM with appropriate boundary conditions for Newtonian heating of the plate. HAM is a powerful method which provides rapidly converging series solution for the velocity and temperature fields. The effects of Prandtl number, Grashof number, suction parameter, magnetic field parameter, radiation parameter and Eckert number on the fluid velocity, temperature, skin friction and Nusselt number have been investigated.Findings– The HAM solution has been successfully applied to find the converging series solution for velocity and temperature fields in terms of pertinent system parameters. Comparison of the exact solution results agree well with the HAM solution results in the absence of Eckert number and this indicates that the HAM solutions are accurate. It is found that the velocity and temperature profiles decreases with the increase of thermal radiation and suction parameters. An increase in the magnetic field parameter leads to a rise in the fluid temperature and fall in the fluid velocity.Research limitations/implications– The present analysis is limited to steady state laminar natural convection flow only. Unsteady natural- /mixed-convection laminar flow in the presence of thermal radiation, chemical reaction and transverse magnetic field will be investigated in a future work.Practical implications– The study provides very useful information for heat transfer engineers to understand the heat transfer rate when the moving vertical porous surface temperature is not known a prior. The present results have immediate relevance in the design of nuclear reactors where vertical moving porous plates are using as control rods.Originality/value– The present research work is relatively original and illustrates the effects of thermal radiation, viscous dissipation and transverse magnetic field on natural convection flow past a uniformly moving infinite vertical porous plate with Newtonian heating.

Modal and non-modal linear stability analyses are employed to investigate the effect of internal and external heating on disturbance temporal growth for the Darcy–Bénard convection with throughflow. A matrix-forming approach is employed for both purposes, where the generalised eigenvalue problem is built using the generalised integral transform technique. Although the disturbance equations are not self-adjoint, the non-modal analysis indicates that there is no transient growth. Hence, any disturbance growth in time must be induced by modal mechanisms. An absolute instability analysis reveals that viscous dissipation has a destabilising effect and introduces new modes that are eventually destabilised by increasing the Péclet number. Beyond critical values of the Péclet number, where codimension-two absolutely unstable points exist, these modes become more unstable than the classical mode found in the absence of viscous dissipation, which is stabilised by an increasing Péclet number. This internal heating mechanism generated by viscous dissipation is so strong at high enough Péclet numbers that instability becomes possible through heating from above.

MR-Linac devices under development worldwide will require standard calibration, commissioning, and quality assurance. Solid state radiation detectors are often used for dose profiles and percent depth dose measurements. The dose response of selected solid state detectors is therefore evaluated in varying transverse and longitudinal magnetic fields for this purpose. The Monte Carlo code PENELOPE was used to model irradiation of a PTW 60003 diamond detector and IBA PFD diode detector in the presence of a magnetic field. The field itself was varied in strength, and oriented both transversely and longitudinally with respect to the incident photon beam. The long axis of the detectors was oriented either parallel or perpendicular to the photon beam. The dose to the active volume of each detector in air was scored, and its ratio to dose with zero magnetic field strength was determined as the "dose response" in magnetic field. Measurements at low fields for both detectors in transverse magnetic fields were taken to evaluate the accuracy of the simulations. Additional simulations were performed in a water phantom to obtain few representative points for beam profile and percent depth dose measurements. Simulations show significant dose response as a function of magnetic field in transverse field geometries. This response can be near 20% at 1.5 T, and it is highly dependent on the detectors' relative orientation to the magnetic field, the energy of the photon beam, and detector composition. Measurements at low transverse magnetic fields verify the simulations for both detectors in their relative orientations to radiation beam. Longitudinal magnetic fields, in contrast, show little dose response, rising slowly with magnetic field, and reaching 0.5%-1% at 1.5 T regardless of detector orientation. Water tank and in air simulation results were the same within simulation uncertainty where lateral electronic equilibrium is present and expectedly differed at the beam edge in transverse field orientations only. Due to the difference in design, the two detectors behaved differently. When transverse magnetic fields are present, great care must be taken when using diamond or diode detectors. Dose response varies with relative detector orientation, magnetic field strength, and between detectors. This response can be considerable (∼20% for both detectors). Both detectors in longitudinal fields exhibit little to no dose response as a function of magnetic field. Water tank simulations seem to suggest that the diode detector is better suited to general beam commissioning, and each detector must be investigated separately.

Monotectic Al-6.5wt%Bi alloy was directionally solidified in the presence of a transverse static homogeneous magnetic field up to 2.0 kG to determine if gravity-induced convection effects could be reduced or eliminated. Growth rate Vwas varied over the range 1 to 100 μm/s, while temperature gradient at the liquid-solid interface was 120 K/cm. The microstructures of Al-6.5wt%Bi alloy is characterized by regular, aligned Bi fibres or Bi droplets under given growth conditions. Morphological, thermal and magnetic analyses were carried out on sample grown with and without an applied magnetic field. Results indicated that spacing and diameter of Bi fibres decreased in a transverse magnetic field, and the microstructure became more homogeneous, which means that transverse static homogeneous magnetic field can effectively reduce or eliminate gravity-driven and thermal convection during directional solidification of Al-Bi monotectic alloy.

The drawn vacuum arc begins with a bridge column formed from the explosion of a liquid metal bridge after separating the contacts. The expansion process of the initial arc has an effect on arc motion or diffusion. In order to deeply study the influence of transverse magnetic field (TMF) and axial magnetic field (AMF) on the drawn arc characteristics in the initial expansion stage, in this article, arc ignition mode and appearance under two groups of contacts with different AMF and TMF components were experimentally studied. It was found that simultaneously reducing TMF and AMF components would end the expansion stage earlier, and the fluctuation of the arc column pressure during the expansion was larger. When TMF and AMF components were further reduced, the arc needs to take a longer time to extend across the slot gap due to insufficient Ampere force. When TMF was basically unchanged and AMF was reduced, the arc burned more intense, the diameter of the arc column was smaller, and the arc would merge earlier in multipoint ignition mode. The characteristics of arc voltage, pressure, and duration of expansion stage were analyzed, founding that the arc with a moderate TMF and AMF components had a smaller rising slope of arc voltage, a faster reducing speed of arc pressure, and a smaller range of the duration of expansion stage. In addition, the variation of magnetic field strength in different ignition modes and contact structures during the arc expansion stage was simulated to explain the mechanism of arc behavior.

To determine the relative dose response of a diamond detector and a ion chamber in a clinical photon beam within uniform magnetic fields, endeavoring to evaluate and refine reference dosimetry techniques for use in integrated MR-linac systems. The Monte Carlo code PENELOPE was used to model the structure and materials of the PTW60003 diamond detector and PR06 ion chamber in a 6MV beam in the presence of a homogeneous magnetic field. The magnetic field strength was varied from 0 to 1.5T, and both the parallel and transverse magnetic field orientations with respect to the beam central axis were simulated. The long axes of the detectors were oriented both perpendicular and parallel to the radiation beam direction for each magnetic field orientation. All simulations determined the detectors' signal in air. A small electromagnet was used to experimentally determine the detectors' response in transverse magnetic fields up to 0.2T to validate the simulations. The simulated response of both detectors matched to the experimental data within the estimation error. The relative response of PR06 and diamond detector varied up to ±8.5% (depending on chamber orientation) and >9% respectively with increasing transverse magnetic field strength. In contrast, both detectors were found to be relatively insensitive to the increasing magnetic fields irrespective of the detector orientation in parallel magnetic field. A maximum change of 2% in PR06 response was observed at 1.5T parallel magnetic field and in the parallel orientation of chamber. This work has significant impact on dosimetry protocols for integrated MR-linac systems, where detector response may be altered by the presence of a magnetic field. The need for a magnetic field dependent correction factor is strongly indicated for the transverse magnetic field cases, while such changes in detector response can be largely ignored in parallel magnetic fields < 1T. CIHR (Canadian Institutes of Health Research) - funding support Faculty of Medicine and Dentistry, University of Alberta - funding support.

In this study, the effect of the transverse magnetic field on the arc characteristics and droplet transfer behavior is investigated during Laser-MIG hybrid welding of Ti-6Al-4 V. Especially, transverse magnetic fields with 0 mT, 8 mT, 16 mT, 24 mT, and 32 mT are studied. Results indicate that an appropriate magnetic field can increase the stability of arc characteristics, improve the droplet detachment efficiency, and reduce the welding defects such as incomplete fusion and undercut. By applying 24-mT transverse magnetic field, the maximum arc area can decrease by 48.7% with its variance changing from 2.81 to 1.06 mm2, indicating that an appropriate transverse magnetic field can shrink the arc and improve its stability. The reason of arc shrinkage is that the electric streamline in the arc rotates away from the laser side to the droplet side due to the influence of external magnetic field. On the other hand, the droplet transfer process becomes more uniform under the appropriate magnetic field. This phenomenon is mainly attributed to the change of Lorentz force direction during droplet rotation, which resultantly increases effective detachment energy. This phenomenon leads to the reduction of the contact time between droplet and molten pool. The droplet transfer form changes from short-circuit transfer to meso-spray transfer under 24-mT magnetic field because of the reduction of the contact time. Therefore, the incomplete fusion and undercut disappears. At last, the appropriated magnetic field parameters during the laser-MIG parameters (2 kW, 160 A, 2 m/min) are concluded as B = 24 mT.

Purpose:Solid state radiation detectors are often used for dose profiles and percent depth dose measurements. The dose response of selected solid state detectors is evaluated in varying transverse and longitudinal magnetic fields for eventual use in MR‐Linac devices.Methods:A PTW 60003 and IBA PFD detector were modeled in the Monte Carlo code PENELOPE, incorporating a magnetic field which was varied in strength and oriented both transversely and longitudinally with respect to the incident photon beam. The detectors' long axis was in turn oriented either parallel or perpendicular to the photon beam. Dose to the active volume of each detector was scored, and its ratio to dose with zero magnetic field strength (dose response) was determined. Accuracy of the simulations was evaluated by measurements using both chambers taken at low field with a small electromagnet. Simulations were also performed in a water phantom to compare to the in air results.Results:Significant dose response was found in transverse field geometries, nearing 20% at 1.5T. The response is highly dependent on relative orientations to the magnetic field and photon beam, and on detector composition. Low field measurements confirm these results. In the presence of longitudinal magnetic fields, the detectors exhibit little dose response, reaching 0.5–1% at 1.5T regardless of detector orientation. Water tank simulations compared well to the in air simulations when not at the beam periphery, where in transverse magnetic fields only, the water tank simulations differed from the in air results.Conclusion:Transverse magnetic fields can cause large deviations in dose response, and are highly position orientation dependent. Comparatively, longitudinal magnetic fields exhibit little to no dose response in each detector as a function of magnetic field strength. Water tank simulations show longitudinal fields are generally easier to work with, but each detector must be evaluated separately.

The application of a strong transverse magnetic field to a volume undergoing irradiation by a photon beam can produce localized regions of dose enhancement and dose reduction. This study uses the PENELOPE Monte Carlo code to investigate the effect of a slice of uniform transverse magnetic field on a photon beam using different magnetic field strengths and photon beam energies. The maximum and minimum dose yields obtained in the regions of dose enhancement and dose reduction are compared to those obtained with the EGS4 Monte Carlo code in a study by Li et al (2001), who investigated the effect of a slice of uniform transverse magnetic field (1 to 20 Tesla) applied to high-energy photon beams. PENELOPE simulations yielded maximum dose enhancements and dose reductions as much as 111% and 77%, respectively, where most results were within 6% of the EGS4 result. Further PENELOPE simulations were performed with the Sheikh-Bagheri and Rogers (2002) input spectra for 6, 10 and 15 MV photon beams, yielding results within 4% of those obtained with the Mohan et al (1985) spectra. Small discrepancies between a few of the EGS4 and PENELOPE results prompted an investigation into the influence of the PENELOPE elastic scattering parameters C1 and C2 and low-energy electron and photon transport cut-offs. Repeating the simulations with smaller scoring bins improved the resolution of the regions of dose enhancement and dose reduction, especially near the magnetic field boundaries where the dose deposition can abruptly increase or decrease. This study also investigates the effect of a magnetic field on the low-energy electron spectrum that may correspond to a change in the radiobiological effectiveness (RBE). Simulations show that the increase in dose is achieved predominantly through the lower energy electron population.

Effect of assisted transverse magnetic field on distortion behavior of thin-walled components in WEDM process

Carbon nanomaterials have attracted vast attention due to the rising demand for various nanotechnology applications. The possibility of preparing multi-walled carbon nanotube (MWCNT) and graphene on large scale are demonstrated using direct current arc discharge with transverse magnetic field effect at low ambient pressure. In this work, we study, the effect of external transverse magnetic effect on structural perfection of graphene and multi-walled carbon nanotube. High quality carbon-nanotube were synthesized by arc discharge plasma in Hydrogen ambient at pressure 1 mbar in presence of external transverse magnetic field. The synthesized nanomaterials were characterized by electron microscopy, XRD and Raman Spectroscopy. A significant increase in the quantity and quality of carbon nanotube and graphene in the presence of transverse magnetic field during arc discharge process.

Thermocapillary flow and free-surface deformation of liquid bridge under different magnetic fields