Arbitrary Orientation Of Magnetic Field Research Articles

An exact analytical solution for the weakly magnetized flow around an axially symmetric paraboloid, with application to magnetosphere models

Rotationally symmetric bodies with longitudinal cross sections of parabolic shape are frequently used to model astrophysical objects, such as magnetospheres and other blunt objects, immersed in interplanetary or interstellar gas or plasma flows. We discuss a simple formula for the potential flow of an incompressible fluid around an elliptic paraboloid whose axis of symmetry coincides with the direction of incoming flow. Prescribing this flow, we derive an exact analytical solution to the induction equation of ideal magnetohydrodynamics for the case of an initially homogeneous magnetic field of arbitrary orientation being passively advected in this flow. Our solution procedure employs Euler potentials and Cauchy's integral formalism based on the flow's stream function and isochrones. Furthermore, we use a particular renormalization procedure that allows us to generate more general analytical expressions modeling the deformations experienced by arbitrary scalar or vector-valued fields embedded in the flow as they are advected first toward and then past the parabolic obstacle. Finally, both the velocity field and the magnetic field embedded therein are generalized from incompressible to mildly compressible flow, where the associated density distribution is found from Bernoulli's principle.

Magnetohydrodynamic Richtmyer–Meshkov instability under an arbitrarily oriented magnetic field

The effect of an initially uniform magnetic field of arbitrary orientation on the Richtmyer–Meshkov instability in Hall-magnetohydrodynamics (MHD) and ideal MHD is considered. Attention is restricted to the case where the initial density interface has a single-mode sinusoidal perturbation in amplitude and is accelerated by a shock traveling perpendicular to the interface. An incompressible Hall-MHD model for this flow is developed by solving the relevant impulse-driven linearized initial value problem. The ideal MHD theory is naturally obtained by taking the limit of vanishing ion skin depth. It is shown that the out-of-plane magnetic field component normal to both the impulse and the interface perturbation does not affect the evolution of the flow. For all field orientations other than strictly out-of-plane, the growth of interface perturbations is suppressed. However, the suppression is most effective for near tangential fields but becomes less effective with increasing ion skin depth and Larmor radius. The modeled suppression mechanism is transport of vorticity along magnetic field lines via Alfvén fronts in ideal MHD, and via a dispersive wave system in Hall-MHD. Oscillation of the interface growth rate is caused by a continuous phase change of the induced velocities at the interface due to vorticity transport parallel to the perturbation direction in ideal MHD, while it can also result from interfacial vorticity production associated with the ion cyclotron effect in Hall-MHD with a finite Larmor radius. The limiting flow behavior of a large ion-skin-depth is explored. To assess the accuracy and appropriateness of the incompressible model, its ideal MHD predictions are compared to the results of the corresponding shock-driven nonlinear compressible simulations.

Numerical simulations of 3D magnetohydrodynamic flows in dual-coolant lead lithium blankets

In the dual coolant lead lithium blanket (DCLL) the liquid metal PbLi is used as coolant to remove the volumetrically generated heat. This requires higher flow velocities than in separately cooled blanket concepts, where the liquid metal serves exclusively as breeder, neutron multiplier and shield against high neutron radiation. The relatively fast movement of the electrically conducting fluid in the strong magnetic field confining the fusion plasma induces electric currents, which are responsible for strong Lorentz forces, high magnetohydrodynamic (MHD) pressure drop, and substantial modifications of velocity profiles compared with hydrodynamic flows. In order to support the design activities of a DCLL blanket, 3D numerical MHD simulations for one column of such a blanket module have been performed. The simulations take into account, that currents may close along the inner conducting sheet of sandwich-type flow channel inserts that are foreseen for pressure drop reduction. The applied numerical code has been carefully validated. It applies for magnetic fields of arbitrary orientation and is capable of simulating the liquid metal MHD flow in the blanket in the parameter range relevant for fusion applications.

The dynamic resistance of YBCO coated conductor wire: effect of DC current magnitude and applied field orientation

Dynamic resistance, which occurs when a HTS coated conductor carries a DC current under an AC magnetic field, can have critical implications for the design of HTS machines. Here, we report measurements of dynamic resistance in a commercially available SuperPower 4 mm-wide YBCO coated conductor, carrying a DC current under an applied AC magnetic field of arbitrary orientation. The reduced DC current, It/Ic0, ranged from 0.01 to 0.9, where It is the DC current level and Ic0 is the self-field critical current of the conductor. The field angle (the angle between the magnetic field and the normal vector of the conductor wide-face) was varied between 0° and 90° at intervals of 10°. We show that the effective width of the conductor under study is ∼12% less than the physical wire width, and we attribute this difference to edge damage of the wire during or after manufacture. We then examine the measured dynamic resistance of this wire under perpendicular applied fields at very low DC current levels. In this regime we find that the threshold field, Bth, of the conductor is well described by the nonlinear equation of Mikitik and Brandt. However, this model consistently underestimates the threshold field at higher current levels. As such, the dynamic resistance in a coated conductor under perpendicular magnetic fields is best described using two different equations for each of the low and high DC current regimes, respectively. At low DC currents where It/Ic0 ≤ 0.1, the nonlinear relationship of Mikitik and Brandt provides the closest agreement with experimental data. However, in the higher current regime where It/Ic0 ≥ 0.2, closer agreement is obtained using a simple linear expression which assumes a current-independent penetration field. We further show that for the conductor studied here, the measured dynamic resistance at different field angles is dominated by the perpendicular magnetic field component, with negligible contribution from the parallel component. Our findings now enable the dynamic resistance of a single conductor to be analytically determined for a very wide range of DC currents and at all applied field angles.

Benchmark Solutions for Magnetic Fields in the Presence of Two Superconducting Spheres

A complete solution is presented for the boundary value problem of two perfect conductor spheres in a uniform magnetic field of arbitrary orientation. Expressions are given for the scalar magnetic potential and for the field intensity. They can readily be applied for calculating the forces between the spheres. Benchmark numerical results of specified accuracy are generated, which are also useful for validating various approximate numerical methods.

Landau level spectrum for bilayer graphene in a tilted magnetic field

We consider a graphene bilayer in a constant magnetic field of arbitrary orientation, i.e., tilted with respect to the graphene plane. In the low energy approximation to the tight-binding model with Peierls substitution, we find the Landau level spectrum analytically in terms of spheroidal functions and the respective eigenvalues. We compare our result to the perpendicular and purely in-plane field cases. In the limit of perpendicular field we reproduce the known equidistant spectrum for Landau levels. In the opposite limit of large in-plane field this spectrum becomes two-fold degenerate, which is a consequence of Dirac point splitting induced by the in-plane field.

Upwinding Meshfree Point Collocation Method for Unsteady Magnetohydrodynamic Flow at High Hartmann Numbers

In this paper, a meshfree point collocation method, with an upwinding scheme, is presented to obtain the numerical solutions of the coupled equations in the velocity field for the unsteady magnetohydrodynamic (MHD) flow through a straight duct of rectangular section with insulated walls. Computations have been carried out for the unsteady MHD flow, which is under the external applied magnetic field of arbitrary orientation, of different Hartmann number from 5 to 106 and at various time levels. As the adaptive upwinding local support domain is introduced in the meshless collocation method, numerical results show that the method can compute MHD problems with Hartmann numbers up to 106 with good accuracy. The results also show that as Hartmann number increases, the time needed to reach the steady state decreases.

Magneto-optical coupling in ferromagnetic thin films investigated by vector-magneto-optical generalized ellipsometry

We performed generalized Mueller matrix ellipsometry measurements in a magnetic field of arbitrary orientation and magnitude up to 400 mT at room temperature and probed the magneto-optical response of capped, ferromagnetic Fe, Ni${}_{20}$Fe${}_{80}$, Co, Ni${}_{80}$Fe${}_{20}$, and Ni thin films on ZnO substrates in the spectral range from 300 to 1100 nm. We determined the off-diagonal elements in the magneto-optical dielectric tensor under saturated magnetization conditions in the sample surface plane via a model analysis. The off-diagonal elements depend on the net spin polarization and the electronic band structure of the ferromagnetic thin films. For the pure ferromagnetic metals Fe, Co, and Ni, the converted off-diagonal elements agree well with the reported experimental optical conductivity data. As a result we use the extracted wavelength-dependent magneto-optical coupling constant to predict the wavelength-dependent magneto-optical response of different Ni/Fe multilayer structures.

Vector-magneto-optical generalized ellipsometry

We present the setup of a variable-angle vector-magneto-optical generalized ellipsometer (VMOGE) in the spectral range from 300 to 1100 nm using an octupole magnet, and demonstrate VMOGE measurements of the upper 3 × 4 submatrix of the Mueller matrix in a magnetic field of arbitrary orientation and magnitude up to 0.4 T at room temperature. New "field orbit" measurements can be performed without physically moving the sample, which is useful to study magnetic multilayer or nanostructure samples. A 4 × 4 matrix formalism is employed to model the experimental VMOGE data. Searching the best match model between experimental and calculated VMOGE data, the magneto-optical dielectric tensor ɛ(MO) of each layer in a multilayer sample system can be determined. In this work, we assume that the nonsymmetric terms of ɛ(MO) are induced by an external magnetic field and depend linearly on the sample magnetization. Comparison with vector magnetometer measurements can provide the anisotropic magneto-optical coupling constants Q(x), Q(y), Q(z).

Fulde-Ferrell-Larkin-Ovchinnikov states and quantum oscillations in mesoscopic superconductors and superfluid ultracold Fermi gases

We have studied the distinctive features of the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) instability and phase transitions in two--dimensional (2D) mesoscopic superconductors placed in magnetic field of arbitrary orientation and rotating superfluid Fermi gases with imbalanced state populations. Using a generalized version of the phenomenological Ginzburg-Landau theory we have shown that the FFLO states are strongly modified by the effect of the trapping potential confining the condensate. The phenomenon of the inhomogeneous state formation is determined by the interplay of three length scales: (i) length scale of the FFLO instability; (ii) 2D system size; (iii) length scale associated with the orbital effect caused either by the Fermi condensate rotation or magnetic field component applied perpendicular to the superconducting disc. We have studied this interplay and resulting quantum oscillation effects in both superconducting and superfluid finite -- size systems with FFLO instability and described the hallmarks of the FFLO phenomenon in a restricted geometry. The finite size of the system is shown to affect strongly the conditions of the observability of switching between the states with different vorticities.

Effect of a magnetic field in photodetachment microscopy

The effect of an external static magnetic field of arbitrary orientation with respect to the electric field, on the electron interference ring patterns observed by the photodetachment microscope is studied both experimentally and theoretically. The design of the interaction chamber has been modified to superimpose a controlled uniform magnetic field on the whole volume accessible to the interfering electron. Contrary to a previous study in weaker fields, where the overall dimension of the interferogram was not modified, the effect of the magnetic field here encompasses a regime of magnetic refocusing. A quantitative analysis is carried out using a closed-orbit perturbative calculation of the interference phase at the centre of the ring pattern. The essential result of this work is still the invariance of the extreme interference phase whatever the direction and magnitude of the applied magnetic field, up to values 100 times larger than in the previous experimental study. This property can be applied to revise former electron affinity measurements. Partly due to the previously unsuspected robustness of the electron interferograms vs. magnetic fields, partly thanks to the 2006 CODATA revision of the energy conversion factors, one can update the values of the electron affinities of 16O, 28Si and 32S to 1.4611134(9), 1.3895210(7) and 2.0771040(6) eV respectively.

Stability of layered channel flow of magnetic fluids

The stability of a sheared interface separating a viscous magnetic fluid (ferrofluid) and an ordinary viscous fluid is examined for arbitrary wavelength disturbances using three dimensional linear perturbation theory. The unperturbed state corresponds to a two-layer Poiseuille profile in which a uniform magnetic field of arbitrary orientation is imposed. Coupling between the field and fluid occurs via the magnetic Maxwell stress tensor, formulated here for nonlinear magnetic material, expanding the scope of previous studies of linear media. Neutral curves and stability characteristics at low Reynolds number are presented and analyzed, and are found to depend sensitively on the linear and nonlinear magnetic properties of the material. The stability properties of the flow are shaped by a small set of the least stable modes of the spectrum, a result that evades single mode or potential flow analyses. The gravest modes can be of different character, resembling either interfacial or shear modes, modified by magnetic effects. The commonly cited ferrofluid interface properties of “stabilization by a tangential field” and “destabilization by a normal field” are shown to be invalid here, although the origins of these features can be identified within this problem.

Scattering polarization in the presence of magnetic and electric fields

The polarization of radiation by scattering on an atom embedded in combined external quadrupole electric and uniform magnetic fields is studied theoretically. Limiting cases of scattering under Zeeman effect, and Hanle effect in weak magnetic fields are discussed. The theory is general enough to handle scattering in intermediate magnetic fields (Hanle–Zeeman effect) and for arbitrary orientation of magnetic field. The quadrupolar electric field produces asymmetric line shifts, and causes interesting level-crossing phenomena either in the absence of an ambient magnetic field, or in its presence. It is shown that the quadrupolar electric field produces an additional depolarization in the Q / I profiles and rotation of the plane of polarization in the U / I profile over and above that arising from magnetic field itself. This characteristic may have a diagnostic potential to detect steady-state and time-varying electric fields that surround radiating atoms in solar atmospheric layers.

Buckling and postbuckling of magnetoelastic flat plates carrying an electric current

The basic equations of a fully nonlinear theory of electromagnetically conducting flat plates carrying an electric current and exposed to a magnetic field of arbitrary orientation are derived. The relevant equations have been obtained by considering that both the elastic and electromagnetic media are homogeneous and isotropic. The geometrical nonlinearities are considered in the von-Kármán sense, and the soft ferromagnetic material of the plate is assumed to feature negligible hysteretic losses. Based on the electromagnetic and elastokinetic field equations, by using the standard averaging methods, the 3-D coupled problem is reduced to an equivalent 2-D one, appropriate to the theory of plates. Having in view that the elastic structures carrying an electric current are prone to buckling, by using the presently developed theory, the associated problems of buckling and postbuckling are investigated. In this context, the problem of the electrical current inducing the buckling instability of the plate, and its influence on the postbuckling behavior are analyzed. In the same context, the problem of the natural frequency–electrical current interaction of flat plates, as influenced by a magnetic field is also addressed.

Polarization of line radiation in the presence of external electric quadrupole and uniform magnetic fields: II. Arbitrary orientation of magnetic field

In continuation of our earlier investigation (referred to hereafter as part I) where we considered the mathematically simple case of magnetic field orientation along the Z-axis of the principal axes frame (PAF) of the electric quadrupole field, we take up here the general problem of arbitrary orientation of the magnetic field with respect to the PAF, and investigate the nature of polarized line spectra of an atom making a transition from an upper level with spin J u to a lower level with spin J l. Explicit formulae for the emitted Stokes parameters are obtained and we discuss their physical significance by computing numerically the cases of transitions J u=1→ J l=0 and J u = 3 2 →J l = 1 2 . Specific features or signatures of the polarized line spectra are discussed as functions of the relevant physical parameters. The Stokes parameters are also analyzed in terms of the Zeeman term contributions and the cross-term contributions (which arise due to quantum interference).

Polarization of line radiation in the presence of external electric quadrupole and uniform magnetic fields: II. Arbitrary orientation of magnetic field

Polarization of line radiation in the presence of external electric quadrupole and uniform magnetic fields: II. Arbitrary orientation of magnetic field

Polarization dynamics of two-photon and cascade lasers in the presence of an arbitrarily directed magnetic field

We study theoretically the polarization dynamics of a new type of quantum oscillator that is based on the two-photon stimulated emission process in the presence of a magnetic field of arbitrary orientation. Both cases of cascade (small intermediate-state atomic detuning) and two-photon (large atomic detuning) lasers are considered. The primary goal of this work is to investigate the origin of recently observed polarization instabilities in a two-photon laser (Pfister et al 2001 Phys. Rev. Lett. 86 4512) using a highly simplified model. It is found that the two-photon laser can emit linearly polarized radiation with its plane of polarization orthogonal to the direction of the magnetic field at small magnetic field strengths. It can also emit elliptically polarized radiation over a large range of magnetic field strengths and orientations. When the magnetic field deviates from a direction perpendicular to the laser cavity axis periodic instabilities can appear through a Hopf bifurcation. This dynamic regime could have contributed to the polarization instabilities observed in the experiment.

Interplay of Fulde-Ferrell-Larkin-Ovchinnikov and Vortex states in two-dimensional Superconductors

Clean superconductors with weakly coupled conducting planes have been suggested as promising candidates for observing the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state. We consider here a layered superconductor in a magnetic field of arbitrary orientation with respect to the conducting plane. In this case there is competition of Pauli spin-pair-breaking effects, favoring the FFLO state, and orbital-pair-breaking effects, favoring the Abrikosov vortex state. In previous work, phase transitions to phases with pairing in Landau levels with quantum numbers n > 0 have been predicted. Here, we calculate the actual structure of the stable states below H c2 by minimizing the free energy. We find new order parameter structures differing from both the traditional Abrikosov and FFLO solutions. These include two-dimensional periodic structures with several zeros of the order parameter, as well as quasi-one-dimensional structures consisting of vortex chains separated by FFLO domains. We discuss the limit of high n, where some interesting but yet unsolved questions appear.

Interface Effects in the Model of δ-Potential for 2D Semiconductor Quantum Structures

Here we show that the enhancement of exchange field at the nonmagnetic-semimagnetic semiconductor interface can be described by δ-localized exchange field. In this model, the wave functions of electron, confined in quantum well with semimagnetic barriers can be found analytically for an arbitrary orientation of magnetic field B with respect to growth axis C. Two cases corresponding to B || C and B 1 C are considered. The comparison of present approach with experimental data shows that the proposed method is an efficient tool for interface investigation in 2D quantum structures.

Repolarization of anisotropic muonium in orientationally disordered solids

Muon repolarization in a longitudinal field is calculated for anisotropic muonium with arbitrary orientation of magnetic field to the muonium principal axis. In the absence of superhyperfine interactions, the low-field polarization is shown to be highly dependent on the hyperfine anisotropy. The repolarization is calculated in the quasistatic limit for some different types of orientational averaging, which might result from static or dynamic disorder. Approximate analytical forms for the repolarization curve are obtained and some experimental applications are discussed.