Transverse Homogeneous Magnetic Field Research Articles

Energy stability of magnetohydrodynamic flow in channels and ducts

We study the energy stability of pressure-driven laminar magnetohydrodynamic flow in a rectangular duct with a transverse homogeneous magnetic field and electrically insulating walls. For sufficiently strong fields, the laminar velocity distribution has a uniform core and convex Hartmann and Shercliff boundary layers on the walls perpendicular and parallel to the magnetic field. The problem is discretized by a double expansion in Chebyshev polynomials in the cross-stream coordinates. The linear eigenvalue problem for the critical Reynolds number depends on the streamwise wavenumber, Hartmann number and the aspect ratio. We consider the limits of small and large aspect ratios in order to compare with stability models based on one-dimensional base flows. For large aspect ratios, we find good numerical agreement with results based on the quasi-two-dimensional approximation. The lift-up mechanism dominates in the limit of a zero streamwise wavenumber and provides a linear dependence between the critical Reynolds and Hartmann numbers in the duct. As the aspect ratio is reduced away from unity, the duct results converge to Orr's original energy stability result for spanwise uniform perturbations imposed on the plane Poiseuille base flow. We also examine different possible symmetries of eigenmodes as well as the purely hydrodynamic case in the duct geometry.

Magnetic Properties of A Cavity‐Embedded Square Lattice of Quantum Dots or Antidots

AbstractQuantum electrodynamical density functional theory is applied to obtain the electronic density, spin polarization, as well as orbital and spin magnetizations of square periodic arrays of quantum dots or antidots subjected to the influence of a far‐infrared cavity photon field. A gradient‐based exchange‐correlation functional adapted to a 2D electron gas in a transverse homogeneous magnetic field is used in the theoretical framework and calculations. The obtained results predict a non‐trivial effect of the cavity field on the electron distribution in the unit cell of the superlattice, as well as on the orbital and spin magnetizations. The number of electrons per unit cell of the superlattice is shown to play a crucial role in the modification of the magnetization via the electron–photon coupling. The calculations show that cavity photons strengthen the diamagnetic effect in the quantum dot structure, while they weaken the paramagnetic effect in the antidot structure. As the number of electrons per unit cell of the lattice increases, the electron–photon interaction reduces the exchange forces that will otherwise promote strong spin splitting for both the dot and the antidot arrays.

The spin-one DKP oscillator in the plane with an external magnetic field

We successfully obtained the complete exact solution of the Duffin–Kemmer–Petiau oscillator (DKPO) for spin-1 bosons in (1+2)-dimensional space time using a 10×10 representation of the beta-matrices. We show that the problem can be decoupled into three independent subproblems, each of which is assigned with one of the spin-projection numbers ms=0 and ms=±1. Moreover, the solutions such that ms=0 and those for which ms=±1 are found to be respectively associated with (−1)J and (−1)J+1 parities. In addition, we investigate the effect of the presence of an external transverse homogeneous magnetic field on the dynamics of the oscillator: different settings, as well as interesting particular cases, are considered and the non-relativistic limit of the model is also discussed.

Design of a Curved Canted-Cosine-Theta Superconducting Magnet for a Laser Proton Radiotherapy System

Proton therapy (PT) is a precise and efficient radiotherapy method in modern medical treatment, which can be focused on the lesion location to kill the tumor cells with little affection on the normal tissues and thus largely reduce the potential side effects. However, the proton therapy instrument is usually very huge with a large occupation in the space. In order to reduce the instrument scale, a petawatt level laser proton accelerator project is being conducted in China. This paper will report a curved Canted-Cosine-Theta (CCT) magnet which is a critical component in the proposed laser proton accelerator system. The CCT superconducting magnet was designed with a curved dipole magnet that had an equivalent arc π/4 with radius 1 m, and two short quadrupole magnets were nested symmetrically at the dipole magnet ends. The warm bore of the magnet was 72 mm, where a homogeneous transverse magnetic field that amounted to 2.5 T was required along the magnet bore and homogeneous magnetic field gradients 25 T/m were required at the magnet inlet and outlet. NbTi superconducting wire will be used on the coil winding and immersed in liquid helium environment. The structural design of the magnet will be emphatically introduced in this paper.

Heat and mass transfer on MHD convective flow over an infinite vertical porous plate with the heat source and chemical reaction

AbstractIt is considered that the magnetohydrodynamic free convective flow of an incompressible electrically conducting fluid through a porous medium past a vertical absorbent surface. The homogeneous transverse magnetic field is considered in the existence of heat source and chemical reaction in the rotating frame. The accurate solutions of the velocity, temperature, and concentration are acquired systematically making use of the perturbation method. The consequences of a variety of governing flow parameters on the velocity, temperature, and concentration are analyzed through graphical profiles. Computational outcomes for the skin friction, Nusselt number, and Sherwood number through the tabular format were also examined.

Hall current impacts on unsteady MHD free convective flow past an infinite vertical porous surface

AbstractIn this paper, the magnetohydrodynamic free convective flow of an incompressible electrically conducting fluid over a vertical plate embedded in a porous medium is considered. A homogeneous transverse magnetic field is applied in the presence of a heat source and chemical reaction in a rotating frame, taking Hall current effects into account. The momentum equations for the fluid flow in a porous medium were determined by Brinkman modeling. At the undisturbed state, both the plate and fluid have an rigid body rotation due to the constant angular velocity, perpendicular to the infinite vertical plane surface. The vertical surface is subject to the homogeneous constant suction and the heat on the surface vary by time about a nonzero constant rate whereas the temperature of free stream is engaged to be constant. The accurate solutions for the velocity, temperature, and concentration distributions were acquired systematically using the perturbation method. The consequences of an assortment of governing flow parameters on the velocity, temperature, and concentration were analyzed through graphical profiles. The computational results for the skin friction, Nusselt number, and Sherwood number in a tabular format were also examined.

Recent Progress in Birdcage RF Coil Technology for MRI System.

The radio frequency (RF) coil is one of the key components of the magnetic resonance imaging (MRI) system. It has a significant impact on the performance of the nuclear magnetic resonance (NMR) detection. Among numerous practical designs of RF coils for NMR imaging, the birdcage RF coil is the most popular choice from low field to ultra-high field MRI systems. In the transmission mode, it can establish a strong and homogeneous transverse magnetic field B1 for any element at its Larmor frequency. Similarly, in the reception mode, it exhibits extremely high sensitivity for the detection of even faint NMR signals from the volume of interest. Despite the sophisticated 3D structure of the birdcage coil, the developments in the design, analysis, and implementation technologies during the past decade have rendered the development of the birdcage coils quite reasonable. This article provides a detailed review of the recent progress in the birdcage RF coil technology for the MRI system.

PIV mapping of pressure and velocity fields in the plane magnetohydrodynamic Couette flow

We present the first simultaneous mapping of two-dimensional, time-dependent velocity and pressure fields in a plane Couette flow pervaded by a transverse magnetic field. While electromagnetic forces are strongest in fluids of high electric conductivity such as liquid metals, their opacity excludes optical optical measurement methods. We circumvent this difficulty using a transparent electrolyte (Sulfuric acid), whose weaker conductivity is offset by higher magnetic fields. We describe an experimental rig based on this idea, where the Couette flow is entrained by a tape immersed in sulfuric acid and positioned flush onto the bore of large superconducting magnet, so that most of the flow is pervaded by a sufficiently homogeneous transverse magnetic field. Velocity and pressure fields are obtained by means of a bespoke PIV system, capable of recording the fluid's acceleration as well as its velocity. Both fields are then fed into a finite difference solver that extracts the pressure field from the magnetohydrodynamic governing equations. This method constitutes the first implementation of the pressure PIV technique to an MHD flow. Thanks to it, we obtain the first experimental velocity and pressure profiles in an MHD Couette flows and show that the transitional regime between laminar and turbulent states is dominated by near-wall, isolated, anisotropic perturbations.

Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho3Mg2Sb3O14.

A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material Ho3Mg2Sb3O14 unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to . These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In Ho3Mg2Sb3O14, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial role played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.

Equivalence between the Dirac oscillator and a spin-1/2 fermion embedded in a transverse homogeneous magnetic field: movement in a (2 + 1)-dimensional world

Abstract It is shown that the Dirac oscillator in a (2+1)-dimensional spacetime can be interpreted as a spin-1/2 fermion embedded in a transverse homogeneous magnetic field.

Near-threshold photodetachment microscopy in the presence of a transverse magnetic field

Near-threshold photodetachment microscopy of mononegative ions is theoretically studied when a homogeneous transverse magnetic field $\mathrm{B}$ is superimposed to the static electric field $\mathrm{E}$. The electron flux distribution is obtained using two different approaches: the quantum source theory with the energy-Green function evaluated by means of the stationary phase approximation and the closed-orbit theory. Here we describe the physical ideas while developing the theory in detail. Both theoretical methods yield consistent descriptions for all field intensities and angular momentum of the detached electrons we have investigated and also reproduce reported experimental results. From our calculations, we have found that the presence of the transverse magnetic field leads to a global displacement of the recorded electron flux distribution along the $\mathrm{E}\ifmmode\times\else\texttimes\fi{}\mathrm{B}$ direction. Furthermore, we found that the shape of the recorded interference pattern changes from circular to elliptical as the magnetic field increases. We have theoretically characterized and quantified those effects on the interference pattern due to the presence of the transverse magnetic field.

Equivalence between the planar Dirac oscillator and a spin-1/2 fermion embedded in a transverse homogeneous magnetic field

Abstract It is shown that a spin-1/2 fermion coupled to the axially symmetric electromagnetic vector potential has the same matrix structure as that one for the planar Dirac oscillator. In particular, the planar Dirac oscillator can be interpreted as a charged particle minimally coupled to a transverse homogeneous magnetic field.

Microwave preparation of two-dimensional fermionic spin mixtures

We present a method for preparing a single two-dimensional sample of a two-spin mixture of fermionic potassium in a single antinode of an optical lattice, in a quantum-gas microscope apparatus. Our technique relies on spatially-selective microwave transitions in a magnetic field gradient. Adiabatic transfer pulses were optimized for high efficiency and minimal atom loss and heating due to spin-changing collisions. We have measured the dynamics of those loss processes, which are more pronounced in the presence of a spin mixture. As the efficient preparation of atoms in a single antinode requires a homogeneous transverse magnetic field, we developed a method to image and minimize the magnetic field gradients in the focal plane of the microscope.

Edge modes in the Hofstadter model of interacting electrons

We provide a detailed analysis of a realization of chiral gapless edge modes in the framework of the Hofstadter model of interacting electrons. In a transverse homogeneous magnetic field and a rational magnetic flux through a unit cell the fermion spectrum splits into topological subbands with well-defined Chern numbers and contains gapless edge modes in the gaps. It is shown that the behavior of gapless edge modes is described within the framework of the Kitaev chain where the tunneling of Majorana fermions is determined by effective hopping of Majorana fermions between chains. The proposed approach makes it possible to study the fermion spectrum in the case of an irrational flux, to calculate the Hall conductance of subbands that form a fine structure of the spectrum. In the case of a rational flux and a strong on-site Hubbard interaction U, (Δ is a gap), the topological state of the system, which is determined by the corresponding Chern number and chiral gapless edge modes, collapses. When the magnitude of the on-site Hubbard interaction changes, at the point a topological phase transition is realized, i.e., there are changes in the Chern numbers of two subbands due to their degeneration.

Chern insulator with large Chern numbers. Chiral Majorana fermion liquid

In the framework of Hofstadter’s approach we provide a detailed analysis of a realization of exotic topological states such as the Chern insulator (CI) with large Chern numbers. In a transverse homogeneous magnetic field a one-particle spectrum of fermions transforms to an intricate spectrum with a fine topological structure of the subbands. In a weak magnetic field H for a rational magnetic flux, a topological phase with a large Chern number is realized near the half filling. There is an abnormal behavior of the Hall conductance . At half-filling, the number of chiral Majorana fermion edge states increases sharply forming a new state, called the chiral Majorana fermion liquid.

Temperature fluctuations in a liquid metal MHD-flow in a horizontal inhomogeneously heated tube

The investigation of heat transfer characteristics during liquid metal flow in a horizontal tube with one-sided heating of the lower half of the tube is carried out. Experimental investigations are conducted using the mercury MHD complex of the Moscow Power Engineering Institute and the Joint Institute for High Temperatures, Russian Academy of Science, in the context of a long-term collaboration program. The characteristics of the averaged and fluctuation temperatures are considered in different sections over the length of the heating zone in the area of a homogeneous transverse magnetic field. The laminar liquid metal flow revealed the occurrence and development of a low-frequency quasi-harmonic temperature fluctuation with great intensity.

Monte Carlo simulations of patient dose perturbations in rotational-type radiotherapy due to a transverse magnetic field: a tomotherapy investigation.

Several groups are exploring the integration of magnetic resonance (MR) image guidance with radiotherapy to reduce tumor position uncertainty during photon radiotherapy. The therapeutic gain from reducing tumor position uncertainty using intrafraction MR imaging during radiotherapy could be partially offset if the negative effects of magnetic field-induced dose perturbations are not appreciated or accounted for. The authors hypothesize that a more rotationally symmetric modality such as helical tomotherapy will permit a systematic mediation of these dose perturbations. This investigation offers a unique look at the dose perturbations due to homogeneous transverse magnetic field during the delivery of Tomotherapy(®) Treatment System plans under varying degrees of rotational beamlet symmetry. The authors accurately reproduced treatment plan beamlet and patient configurations using the Monte Carlo code geant4. This code has a thoroughly benchmarked electromagnetic particle transport physics package well-suited for the radiotherapy energy regime. The three approved clinical treatment plans for this study were for a prostate, head and neck, and lung treatment. The dose heterogeneity index metric was used to quantify the effect of the dose perturbations to the target volumes. The authors demonstrate the ability to reproduce the clinical dose-volume histograms (DVH) to within 4% dose agreement at each DVH point for the target volumes and most planning structures, and therefore, are able to confidently examine the effects of transverse magnetic fields on the plans. The authors investigated field strengths of 0.35, 0.7, 1, 1.5, and 3 T. Changes to the dose heterogeneity index of 0.1% were seen in the prostate and head and neck case, reflecting negligible dose perturbations to the target volumes, a change from 5.5% to 20.1% was observed with the lung case. This study demonstrated that the effect of external magnetic fields can be mitigated by exploiting a more rotationally symmetric treatment modality.

Dose response of selected solid state detectors in applied homogeneous transverse and longitudinal magnetic fields.

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.

SU‐E‐J‐51: Dose Response of Common Solid State Detectors in Homogeneous Transverse and Longitudinal Magnetic Fields

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.

SU-E-T-503: Exploiting the Rotational Symmetry of Tomotherapy to Reduce Dose Perturbations From MRI-Guided Radiotherapy: A Monte Carlo Investigation

Purpose: There is growing excitement over new treatment modalities that integrate magnetic resonance (MR) image guidance with radiotherapy delivery systems. The therapeutic gain from reducing tumor position uncertainty using intra‐fraction MR imaging during radiotherapy will only be achieved by adequately accounting for impact of the magnetic field on dose distributions during treatment delivery. We propose that integrating MR‐image guidance with a more rotationally symmetric modality such as helical Tomotherapy delivery might reduce or even eliminate dose perturbations due to magnetic fields. The purpose of this study was to investigate the magnetic field effect on clinical Tomotherapy dose distributions in two disparate patient geometries using Monte Carlo methods. Methods: The Monte Carlo code Geant4 was used for all simulations performed in this study. To simulate magnetic resonance imaging guided radiation therapy (MRIgRT), we investigated dose distributions from Tomotherapy patient plans subjected to homogeneous transverse magnetic fields of varying field strengths. For this study, perturbations in the dose distributions from a prostate and lung case are presented. Results: Results show that perturbations in the overall dose profile due the magnetic field can increase the dose heterogeneity to the target volume when a transverse magnetic field was applied to the patient geometry. The perturbations were dependent on the heterogeneity of the patient geometry, symmetry of the primary beam fluence, and magnetic field strength. The heterogeneous lung geometry demonstrated a significant impact to the tumor volume due to the magnetic field, whereas relatively homogeneous prostate geometry showed minimal dose perturbations. Conclusion: This study demonstrated that the effect of external magnetic fields can be mitigated by exploiting a more rotationally symmetric treatment modality.