Tangential Magnetic Field Research Articles

Behavior of a ferrofluid layer with stable surface rupture subjected to a tangential magnetic field

The conditions of existence of a stable rupture in a horizontal ferrofluid layer on a liquid base are determined experimentally. The characteristics of ruptures of ferrofluid, kerosene, and water layers are compared to estimate the effect of different physicochemical properties of the liquid pairs used. It is found that switching-on a magnetic field parallel to the ferrofluid layer surface initiates deformation of the rupture and its simultaneous motion along the field. The dependences of the geometric parameters of the rupture on the magnetic field strength and the magnetic susceptibility of ferrofluid are established. The possibility of closing the stable rupture under the action of a magnetic field is demonstrated.

Parametric excitation of surface electron cyclotron O-modes by an external alternating electric field

Using the model of uniform semi-bounded plasma, it is shown that the influence of an external alternating electric field in the range of electron cyclotron frequencies leads to excitation of eigen ordinary polarized waves at the first harmonic of electron cyclotron frequency. The external electric field was assumed to be uniform and monochromatic; electro-dynamical properties of the plasma were described by the kinetic Vlasov–Boltzmann equation in the approach of a weak spatial dispersion of plasma. Two components of these modes’ wave vector oriented across an external magnetic field are taken into consideration. Fields of these electron cyclotron O-modes are described by the Maxwell equations; their phase velocity is assumed to be less than the velocity of light. Nonlinear boundary condition-described discontinuity of the modes’ tangential magnetic field is formulated using the concept of a nonlinear surface electric current. The infinite set of equations for harmonics of these O-modes’ tangential electric field has been derived with the aid of this nonlinear boundary condition. It is solved using a wave packet consisting of the basic harmonic and two nearest satellite harmonics. A simple analytical expression for growth rates of these surface waves’ parametric instability is obtained; the influence of plasma parameters on their excitation is numerically analyzed.

Kink-like mode of a double gradient instability in a compressible plasma current sheet

A linear MHD instability of the electric current sheet, characterized by a small normal magnetic field component, varying along the sheet, is investigated. The tangential magnetic field component is modeled by a hyperbolic function, describing Harris-like variations of the field across the sheet. For this problem, which is formulated in a 3D domain, the conventional compressible ideal MHD equations are applied. By assuming Fourier harmonics along the electric current, the linearized 3D equations are reduced to 2D ones. A finite difference numerical scheme is applied to examine the time evolution of small initial perturbations of the plasma parameters. This work is an extended numerical study of the so called “double gradient instability”, – a possible candidate for the explanation of flapping oscillations in the magnetotail current sheet, which has been analyzed previously in the framework of a simplified analytical approach for an incompressible plasma. The dispersion curve is obtained for the kink-like mode of the instability. It is shown that this curve demonstrates a quantitative agreement with the previous analytical result. The development of the instability is investigated also for various enhanced values of the normal magnetic field component. It is found that the characteristic values of the growth rate of the instability shows a linear dependence on the square root of the parameter, which scales uniformly the normal component of the magnetic field in the current sheet.

Evolution of symmetric reconnection layer in the presence of parallel shear flow

The development of the structure of symmetric reconnection layer in the presence of a shear flow parallel to the antiparallel magnetic field component is studied by using a set of one-dimensional (1D) magnetohydrodynamic (MHD) equations. The Riemann problem is simulated through a second-order conservative TVD (total variation diminishing) scheme, in conjunction with Roe’s averages for the Riemann problem. The simulation results indicate that besides the MHD shocks and expansion waves, there exist some new small-scale structures in the reconnection layer. For the case of zero initial guide magnetic field (i.e., By0 = 0), a pair of intermediate shock and slow shock (SS) is formed in the presence of the parallel shear flow. The critical velocity of initial shear flow Vzc is just the Alfven velocity in the inflow region. As Vz∞ increases to the value larger than Vzc, a new slow expansion wave appears in the position of SS in the case Vz∞ < Vzc, and one of the current densities drops to zero. As plasma β increases, the out-flow region is widened. For By0 ≠ 0, a pair of SSs and an additional pair of time-dependent intermediate shocks (TDISs) are found to be present. Similar to the case of By0 = 0, there exists a critical velocity of initial shear flow Vzc. The value of Vzc is, however, smaller than the Alfven velocity of the inflow region. As plasma β increases, the velocities of SS and TDIS increase, and the out-flow region is widened. However, the velocity of downstream SS increases even faster, making the distance between SS and TDIS smaller. Consequently, the interaction between SS and TDIS in the case of high plasma β influences the property of direction rotation of magnetic field across TDIS. Thereby, a wedge in the hodogram of tangential magnetic field comes into being. When β → ∞, TDISs disappear and the guide magnetic field becomes constant.

Parametric excitation of surface ion cyclotron extraordinary polarized waves by an external alternating electric field

An external alternating electric field in the range of ion–cyclotron frequencies is shown to excite extraordinary polarized surface electromagnetic waves at the second harmonic of ion–cyclotron frequencies. The kinetic model of a uniform semi-bounded plasma is applied. Plasma electrodynamical properties are described by using the Vlasov–Boltzmann kinetic equation in the approach of weak spatial plasma dispersion. Two components of these modes’ wave vector, which are oriented across an external steady magnetic field, are taken into account. Fields of these ion–cyclotron modes are described by Maxwell equations. Their phase velocity is assumed to be much lower than light velocity. The external alternating electric field is assumed to be uniform and monochromatic. The nonlinear boundary condition is formulated for the tangential magnetic field of the studied surface waves (SW). An infinite set of equations is derived for the values of tangential electric field harmonics on the plasma interface. This set is solved using the approach to the wave packet consisting of the main harmonic and two nearest satellite harmonics. Simple analytical expressions for the growth rates of parametric instability of these SW are derived. The influence of plasma parameters on their parametric excitation is numerically analyzed.

Modeled Performance of a Long Baseline Planar SQUID Gradiometer for Biomagnetism

In this paper, the performance of a first order planar SQUID gradiometer with a long baseline, with regard its application to biomagnetism, is presented. In particular, we report on the analysis of the device response to the current dipole which is the most fundamental model used in biomagnetism. The planar gradiometer is arranged to measure the field components. The results have been compared with those of an axial SQUID gradiometer having the same baseline, pickup coil's size and the same SQUID design parameters. The performance study involves the computation of the magnetic flux measured by the sensors in the presence of a current dipole and the minimum detectable dipole as function of both off-axis and on-axis distance from the gradiometer. A comparative study as a function of sensor baseline has been also performed. Furthermore, the spatial resolution has been investigated by computing the response of both sensor type to a pair of current dipoles. The results have shown that the dipole current sensitivity of a planar gradiometer, (which measures the tangential magnetic fields), is better than those of the axial gradiometer suggesting that it is possible to employ planar gradiometers in multichannel systems for biomagnetism.

Enhancement of accelerating field of microwave cavities by magnetic insulation

Limitations on the maximum achievable accelerating gradient of microwave cavities can strongly influence the performance, length, and cost of particle accelerators. Gradient limitations are widely believed to be initiated by electron emission from the cavity surfaces. Here, we show that the deleterious effects of field emission are effectively suppressed by applying a tangential magnetic field to the cavity walls. With the aid of numerical simulations we compute the field strength required to insulate an 805 MHz cavity and estimate the cavity's tolerances to typical experimental errors such as magnet misalignments and positioning errors. Then, we review an experimental program, currently under progress, to further study the concept. Finally, we report on two specific examples that illustrate the feasibility of magnetic insulation into prospective particle accelerator applications.

Numerical study of a magnetically insulated front-end channel for a neutrino factory

A neutrino factory, which can deliver an intense flux of $\ensuremath{\sim}{10}^{21}$ neutrinos per year from a multi-GeV stored muon beam, is seemingly the ideal tool for studying neutrino oscillations and $CP$ violations for leptons. The front end of this facility plays a critical role in determining the number of muons that can be accepted by the downstream accelerators. Delivering peak performance requires transporting the muon beams through long sections of a beam channel containing high-gradient rf cavities and strong focusing solenoids. Here, we propose a novel scheme to improve the performance of the cavities, thereby increasing the number of muons within the acceptance of the accelerator chain. The key element of our new scheme is to apply a tangential magnetic field to the rf surfaces, thus forcing any field-emitted electrons to return to the surface before gaining enough energy to damage the cavity. We incorporate this idea into a new lattice design for a neutrino factory, and detail its performance numerically. Although our proposed front-end channel requires more rf power than conventional pillbox designs, it provides enough beam cooling and muon production to be a feasible option for a neutrino factory.

The Poincaré–Steklov Operator in Hybrid Finite Element-Boundary Integral Equation Formulations

The Poincare-Steklov operator provides a direct relation between the tangential electric and magnetic field at the boundary of a simply connected domain, and a discrete equivalent of the operator can be constructed from the sparse finite element (FE) matrix of that domain by forming the Schur complement to eliminate the interior unknowns. Identifying the FE system matrix as a discretized version of the Poincare-Steklov operator allows us to describe and analyze FE and hybrid finite element-boundary integral equation (FE-BIE) formulations from an operator point of view. We show how this operator notation provides substantial theoretical insight into the analysis of spurious solutions in hybrid FE-BIE methods, and we apply the theory on a TM scattering example to predict the breakdown frequencies of different hybrid formulations.

Desenvolvimento de técnicas micromagnéticas de análise de tensões em risers flexiveis

Em algumas aplicações, a detecção de defeitos não é suficiente para a segurança operacional de componentes e estruturas. Deste modo, as técnicas não destrutivas precisam ser adaptadas para a análise do estado de tensões atuantes no componente. Este trabalho apresenta os esforços despendidos no desenvolvimento de sistemas não destrutivos de análise de tensões, voltados para o monitoramento do estado de tensões atuantes em arames da armadura de tração de Risers flexíveis utilizados para o transporte de petróleo e seus derivados. Combinando técnicas como a Análise Harmônica do Campo Magnético Tangencial, Análise Incremental da Permeabilidade Magnética e Análise Multi-freqüência das Correntes Parasitas os resultados mostraram boa correlação entre os carregamentos aplicados e as medidas micromagnéticas, mostrando a grande aplicabilidade das técnicas magnéticas para a caracterização de materiais de engenharia.

A Novel Skin-Effect Based Surface Impedance Formulation for Broadband Modeling of 3-D Interconnects With Electric Field Integral Equation

The problem of interconnect modeling embedded in multilayered substrate is initially formulated in terms of the volume integral equation (IE) with respect to 3-D conduction current density. One out of three degrees of freedom in volumetric current variation is then eliminated by approximating the current behavior over the coordinate normal to the conductor surface according to the skin-effect. The remaining two degrees of freedom in the volumetric current variation constitute the unknown current distribution on the conductor surface for which a governing surface electric field integral equation is obtained directly from the volume IE via restriction of the volumetric operator's range to the conductor surface. The resultant surface IE features a global to the conductor cross section surface impedance operator, which is shown to approximate the relationship between tangential electric and magnetic field components on the conductor surface. The proposed novel surface IE featuring multilayered media dyadic Green's function is amenable to various discretization schemes including the Rao-Wilton-Glisson method of moments. In this paper the latter is implemented by casting the scattered field operator into Michalski-Zheng's mixed-potential form in conjunction with enforcement of global relationships between the basis and testing functions in conductor cross sections according to the surface impedance operator. Numerical comparisons to alternative conductor loss models show that the method achieves volumetric solution accuracy within the framework of a boundary-element formulation.

Effect of tangential magnetic field on ecton processes in cathode spot of vacuum arc

Emission and erosion processes involved in the final stage of the cathode spot cell operation in vacuum arc in the presence of an external magnetic field have been numerically simulated. It is established that the application of a magnetic field leads to asymmetry in the distributions of current density and heat flux, so that their maxima shift in the “anti-Ampere” direction. For more detailed analysis of the phenomenon of retrograde motion of the cathode spot in a magnetic field, it is necessary to study the behavior of a liquid metal phase in the spot.

Control of ideal and resistive magnetohydrodynamic modes in reversed field pinches with a resistive wall

Numerical studies of magnetohydrodynamic (MHD) instabilities with feedback control in reversed field pinches (RFPs) are presented. Specifically, investigations are performed of the stability of m=1 modes in RFPs with control based on sensing the normal and tangential magnetic fields at the resistive wall and applying two-parameter feedback proportional to these fields. The control scheme is based on that of [J. M. Finn, Phys. Plasmas 13, 082504 (2006)], which is here modified to use a more realistic plasma model. The plasma model now uses full resistive MHD rather than reduced MHD, and it uses three realistic classes of equilibrium parallel current density profiles appropriate to RFPs. Results with these modifications are in qualitative agreement with [J. M. Finn, Phys. Plasmas 13, 082504 (2006)]: the feedback can stabilize tearing modes (with resistive or ideal-wall) and resistive wall ideal modes. The limit for stabilization is again found to be near the threshold for ideal modes with an ideal-wall. In addition to confirming these predictions, the nature of the instabilities limiting the range of feedback stabilization near the ideal-wall ideal-plasma threshold are studied, and the effects of viscosity, resistive wall time, and plasma resistivity are reported.

New printed circuit boards magnetic coils in the vacuum vessel of J-TEXT tokamak for position measurement

Four sets of magnetic diagnostic coils, which are printed on machinable ceramic printed circuit boards (PCB), are designed, fabricated, installed, and tested in the Joint Texas Experimental Tokamak (J-TEXT) vacuum vessel for detecting the plasma radial and vertical displacements relative to the geometric center of the vacuum vessel in Ohmic discharges. Each coordinate is determined by a pair of variable cross-section Rogowski and saddle coils, which measure the tangential and normal magnetic fields (relative to the coil surface). These coils are suitable for mass production and offer advantages in vacuum compatibility and temperature tolerance that are important for J-TEXT. Position measurements using PCB coils are compared with those from soft x-ray image system and match the position well.

Implementation of Collocated Surface Impedance Boundary Conditions in FDTD

Surface impedance boundary conditions (SIBCs) for finite-difference time-domain (FDTD) are implemented with collocated H and E components in which first-order spatial finite difference have been used for the spatial derivatives. Transient error analysis is done for the reflected field for the whole possible range of modeled material conductivity. Magnitude and phase error analysis of the calculated reflection coefficients for wideband pulses is presented as well. The resulting numerical errors are compared with the errors of traditional SIBCs implementation when the tangential magnetic fields on the boundary are approximated with the neighboring FDTD magnetic field component located at half-cell size distance in space and half time step behind in time. It is shown that the collocated fields approach is considerably more accurate for both constant real resistive and dispersive complex lossy dielectric SIBCs, in both magnitude and especially phase. Unlike the traditional approach, it is stable for all values of modeled material conductivity. The collocated fields approach is also applied to SIBCs with coating, and the transient and reflection coefficient errors are studied. It is shown that in contrast to the traditional implementation, it is stable for arbitrarily thin coating and for any substrate conductivity, and requires storage only half of the auxiliary coefficients when computing the convolution integrals.

Magnetospheric feedback in solar wind energy transfer

The solar wind kinetic energy fueling all dynamical processes within the near‐Earth space is extracted in a dynamo process at the magnetopause. This direct energy transfer from the solar wind into the magnetosphere depends on the orientation of the interplanetary magnetic field (IMF) as well as other solar wind parameters, such as the IMF magnitude and solar wind velocity. Using the GUMICS‐4 magnetohydrodynamic (MHD) simulation, we find that the energy input from the solar wind into the magnetosphere depends on this direct driving as well as the magnetopause magnetic properties and their time history in such a way that the energy transfer can continue even after the direct driving conditions turned unfavorable. Such a hysteresis effect introduces discrepancies between the energy input proxies and the energy input measured from GUMICS‐4, especially after strong driving, although otherwise the simulation energy input captures the system dynamics. For the cause of the effect, we propose a simple feedback mechanism based on magnetic flux accumulation in the tail lobes. By ideal MHD theory, the energy conversion at the magnetopause is proportional to the product of normal and tangential magnetic fields, the magnetic stress. During large magnetic flux accumulation, the tangential field at the magnetopause strengthens, enhancing the local instantaneous energy conversion and transfer. Our simulations show that this mechanism supports the energy transfer even under weak driving followed by favorable solar wind conditions and transfer up to 50% more power than without the feedback.

Spectral analysis of coupling between cylindrical cavity resonator and micro-strip line for filter design applications

The method of moments in the spectral domain is employed to analyse coupling between a cylindrical cavity resonator and micro-strip transmission line. By extracting the dyadic Green's function of the structure and matching the tangential magnetic fields on the slot surface, fields in the structure and its scattering parameters are obtained. Parasitic elements are added to the equivalent circuit as a result of coupling which causes an additional anti-resonance in the frequency response. The significant property of the structure is that it exhibits both bandpass and bandstop responses depending on the slot dimensions. Numerical results have been validated by direct comparison to high frequency structure simulator (HFSS) results. As an example, a second-order band-pass filter is designed using the described resonator.

A Fast Method for Scattering From a PEC Strip or PEC Semicircular Cylinder Loaded With Semicircular Dielectric Cylinders

A fast method for determining the fields scattered from a perfect electric conductor (PEC) strip or PEC semicircular cylinder loaded with semicircular dielectric cylinders illuminated by a TE/TM plane wave or an electric/magnetic line source is presented. The method is based on expanding the field on the circle containing the scatterer in terms of a Neumann series, which satisfies the continuity of the tangential electric field. The continuity of the tangential magnetic field is satisfied by using the orthogonality of Gegenbauer polynomials. Some numerical results are presented to demonstrate the efficacy of the proposed solution.

Boundary Element Calculation of Eddy Currents in Cylindrical Structures Containing Cracks

Electromagnetic fields due to excitation coils in boreholes containing cracks have been calculated using a boundary element method formulated in terms of a scalar decomposition of the field. By using a Green's kernel that ensures continuity of the tangential electric and magnetic field at the cylindrical surface, it is only necessary to render the flaw region in a discrete form. The effect of an ideal crack, one with zero opening but acting as a perfect barrier to eddy currents, is here represented by a current dipole layer orientated normal to the crack surface. An integral equation determines the source density on the crack and a numerical solution is found using boundary elements. The coil impedance change due to the crack is then computed using an expression based on a reciprocity principle.

Soft spin modes and magnetic transitions in trilayered nanodisks in the vortex state

We present calculations of spin dynamics of a trilayered cylindrical nanodot with circular cross section, which is made of two permalloy disks with the same diameter (200 nm) and different thicknesses (20 and 10 nm), separated by a nonmagetic 10 nm thick spacer. The calculations are performed within the framework of the dynamical matrix method. Due to the different layer thicknesses, the ground state of this system at zero applied field is the vortex configuration in both layers. This system is the ideal one to investigate the dynamics of vortex modes in multilayered dots: we calculate doublets of gyrotropic, radial, and azimuthal modes, which are in phase and out-of-phase in the two layers. The dependence of these modes on vortex polarity and node number is investigated. The modes are studied as a function of a tangential magnetic field. The transition to the saturated state occurs at different critical fields for the two layers. In the proximity of these critical points, the magnetization discontinuities are related to the occurrence of soft modes.