Longitudinal Impedance Research Articles

Space charge and resistive wall impedance computation in the frequency domain using the finite element method

A two-dimensional finite element beam coupling impedance solver for arbitrary transverse geometries and material distribution is presented. The solver is based on open source software and is applicable to space charge and resistive wall longitudinal and transverse impedances. The frequency and the beam velocity can be chosen arbitrarily and also dispersively lossy materials are supported. Space charge impedance, a thin resistive beam pipe, a ferrite ring, and a carbon collimator are presented as application examples.

Using surface impedance for calculating wakefields in flat geometry

Beginning with Maxwell's equations and assuming only that the wall interaction can be approximated by a surface impedance, we derive formulas for the generalized longitudinal and transverse impedance in flat geometry, from which the wakefields can also be obtained. From the generalized impedances, by taking the proper limits, we obtain the normal longitudinal, dipole, and quad impedances in flat geometry. These equations can be applied to any surface impedance, such as the known dc, ac, and anomalous skin models of wall resistance, a model of wall roughness, or one for a pipe with small, periodic corrugations. We show that, for the particular case of dc wall resistance, the longitudinal impedance obtained here agrees with a known result in the literature, a result that was derived from a very general formula by Henke and Napoly.

Mode error analysis of impedance measurement using twin wires**Supported by Natural Science Foundation of China (11175193, 11275221)

Both longitudinal and transverse coupling impedance for some critical components need to be measured for accelerator design. The twin wires method is widely used to measure longitudinal and transverse impedance on the bench. A mode error is induced when the twin wires method is used with a two-port network analyzer. Here, the mode error is analyzed theoretically and an example analysis is given. Moreover, the mode error in the measurement is a few percent when a hybrid with no less than 25 dB isolation and a splitter with no less than 20 dB magnitude error are used.

Analysis of the longitudinal space charge impedance of a round uniform beam inside parallel plates and rectangular chambers

This paper analyzes the longitudinal space charge (LSC) impedances of a round uniform beam inside a rectangular and parallel plate chambers using the image charge method. This analysis is valid for arbitrary wavelengths and the calculation converges fast. The research shows that only a few of the image beams are needed to obtain a relative error less than 0.1%. The beam offset effect is also discussed in the analysis.

Longitudinal impedance tomography for blood pressure characterization of valve deformation

Aorta is formed in a dynamic environment which gives rise to imbalances between many forces that tend to extend the diameter and length. Furthermore, internal forces tend to resist this extension. Impedance tomography can show this imbalance to stimulate the stenosis of aortic valve, growth of the elastic, collagen and to effectively reduce the stresses in the underlying tissue. In blood flow, auscultation noises occurred and in the echocardiography decrease in left ventricular ejection speed can be observed. In this paper, we have modeled an aorta based on anatomical studies to simulate natural, 20% and 30% stenosis as usual heart disease to early diagnosis. Valve deformation causes different impedance tomography in 3D mesh of aorta as blood pressure. Remodeling of aorta and its flow is found when a cylindrical slice of the fully retracted blood aorta is cut longitudinally through the wall.

Longitudinal dynamic response of pile foundation in a nonuniform initial strain field

This paper presents an investigation into the dynamic response of pile and soil due to pile installation in a radially inhomogeneous initial strain field. The radial variation rule for the shear modulus and physical parameters of the soil caused by the initial strain field is deduced. On the basis of the plane strain and complete P-S (pile-soil) contact assumptions, the analytical solution of longitudinal dynamic impedance of the soil is derived by means of subdividing the soil domain into a number of annular vertical zones. The longitudinal impedance of the pile top and velocity response in frequency and time domains, are also obtained. The parametric study of interfacial pressure on the dynamic response of P-S system is undertaken within a relatively lower frequency domain. Comparison results between previous solutions and the present study indicates that the analytical solution derived in this paper is more stable.

Evaluation of the longitudinal parameters of an overhead transmission line with non-homogeneous cross section

This paper presents an accurate method to evaluate the longitudinal parameters of multi-conductor overhead power lines, taking in account skin and proximity effects. This method has the foremost advantage of considering a non-homogeneous ground, composed by separate layers with different conductivities and having surface irregularities, such as hills or valleys. The method splits the system conductors (line and ground) into smaller sub-conductors, with variable rectangular cross-section. The method is validated by comparing the longitudinal impedance results with those obtained using both analytical equations and other numerical methods proposed in the literature. Analytical results presented are concerned to a cylindrical two-wire line and one-phase overhead line. Using the proposed method results are obtained for one-phase overhead line, considering the ground with different conductivity layers and with different topographies.

Impedance of a ceramic break and its resonance structures

A new theory is developed to evaluate longitudinal and transverse impedances of any size of ceramic break that is sandwiched between metal chambers. The theory has been numerically compared with the codes ABCI and CST studio. Excellent agreements are obtained with both codes, in particular with ABCI. The theory successfully reproduces resonance structures of the impedance due to trapped modes inside the ceramic break, which are enhanced by the difference of the dielectric constants between the ceramic and the surrounding space. Moreover, the theory can evaluate the impedance of the ceramic break with titanium nitride coating. We discuss several characteristics of the impedances, especially the difference between the impedances of the ceramic break covered with and without a conductive wall on its outer surface.

Approximate longitudinal space charge impedances of a round beam between parallel plates and inside a rectangular chamber

This paper presents the approximate analytical solutions to the longitudinal space charge (LSC) impedances of a round beam with uniform transverse distribution and sinusoidal line density modulations under two boundary conditions: (a) between parallel plates (b) inside a rectangular chamber, respectively. When the ratio of beam diameter to chamber height is small, the image charge fields of the round beam can be approximated by those of a line charge, the approximate analytical LSC impedances can be obtained by image method. The derived theoretical LSC impedances are valid at any perturbation wavelength and are consistent well with the numerical simulation results in a large range of ratios of beam diameters to chamber heights.

Space charge impedances of a rectangular beam with longitudinal density modulations inside a rectangular chamber

This paper presents the space charge impedances of a rectangular beam inside a rectangular chamber, and the limiting case, e.g., a rectangular beam between parallel plates. The charged beam has uniform density in vertical direction and arbitrary distribution in horizontal direction. The method of separation of variables is used to calculate the space charge potentials, fields, and impedances which are valid in the whole perturbation wavelength spectrum. Comparisons between the theoretical calculations and the numerical simulations are also provided and they match quite well. It is shown that the rectangular beam shape may help to reduce the longitudinal space charge impedances.

Cerebrospinal fluid flow impedance is elevated in Type I Chiari malformation.

Diagnosis of Type I Chiari malformation (CMI) is difficult because the most commonly used diagnostic criterion, cerebellar tonsillar herniation (CTH) greater than 3-5 mm past the foramen magnum, has been found to have little correlation with patient symptom severity. Thus, there is a need to identify new objective measurement(s) to help quantify CMI severity. This study investigated longitudinal impedance (LI) as a parameter to assess CMI in terms of impedance to cerebrospinal fluid motion near the craniovertebral junction. LI was assessed in CMI patients (N = 15) and age-matched healthy controls (N = 8) using computational fluid dynamics based on subject-specific magnetic resonance imaging (MRI) measurements of the cervical spinal subarachnoid space. In addition, CTH was measured for each subject. Mean LI in the CMI group (551 ± 66 dyn/cm5) was significantly higher than in controls (220 ± 17 dyn/cm5, p < 0.001). Mean CTH in the CMI group was 9.0 ± 1.1 mm compared to -0.4 ± 0.5 mm in controls. Regression analysis of LI versus CTH found a weak relationship (R2 = 0.46, p < 0.001), demonstrating that CTH was not a good indicator of the impedance to CSF motion caused by cerebellar herniation. These results showed that CSF flow impedance was elevated in CMI patients and that LI provides different information than a standard CTH measurement. Further research is necessary to determine if LI can be useful in CMI patient diagnosis.

Analytical evaluations of coupling impedances of resistive and magnetic bellows

A theory is developed to calculate both the longitudinal and transverse impedances of magnetic as well as resistive bellows with cylindrical symmetry that is sandwiched between chambers with perfectly conductive metal fittings. Analytical estimations of the impedances are necessary because the skin depth is too small to make sufficiently tiny mesh sizes in current numerical codes. The impedances of bellows made of materials having both large conductivity and permeability are drastically increased owing to magnetic effects, compared with those of bellows made of perfectly conductive materials.

Abcès pulmonaires compliqués : chirurgie ou drainage ?

The influence of torsional stress on the asymmetric magnetoimpedance in a glass-coated negative magnetostrictive amorphous microwire due to bias current is studied theoretically. The longitudinal and off-diagonal impedance components are found assuming a simplified spatial distribution of the magnetoelastic anisotropy induced by the torsional stress. The asymmetry in the field dependence of the impedance components is attributed to the combination of the circular magnetic field produced by the bias current and a helical anisotropy induced by the torsional stress. The asymmetry in the magnetoimpedance and the low-field hysteresis are analyzed as a function of the bias current and torsional stress. It is shown that the application of torsional stress significantly changes the value of the bias current required to suppress the hysteresis effect. The results obtained may be useful for applications in magnetic-field and stress sensors.

Asymmetric magnetoimpedance in amorphous microwires due to bias current: Effect of torsional stress

The influence of torsional stress on the asymmetric magnetoimpedance in a glass-coated negative magnetostrictive amorphous microwire due to bias current is studied theoretically. The longitudinal and off-diagonal impedance components are found assuming a simplified spatial distribution of the magnetoelastic anisotropy induced by the torsional stress. The asymmetry in the field dependence of the impedance components is attributed to the combination of the circular magnetic field produced by the bias current and a helical anisotropy induced by the torsional stress. The asymmetry in the magnetoimpedance and the low-field hysteresis are analyzed as a function of the bias current and torsional stress. It is shown that the application of torsional stress significantly changes the value of the bias current required to suppress the hysteresis effect. The results obtained may be useful for applications in magnetic-field and stress sensors.

Hydrodynamic and Longitudinal Impedance Analysis of Cerebrospinal Fluid Dynamics at the Craniovertebral Junction in Type I Chiari Malformation

Elevated or reduced velocity of cerebrospinal fluid (CSF) at the craniovertebral junction (CVJ) has been associated with type I Chiari malformation (CMI). Thus, quantification of hydrodynamic parameters that describe the CSF dynamics could help assess disease severity and surgical outcome. In this study, we describe the methodology to quantify CSF hydrodynamic parameters near the CVJ and upper cervical spine utilizing subject-specific computational fluid dynamics (CFD) simulations based on in vivo MRI measurements of flow and geometry. Hydrodynamic parameters were computed for a healthy subject and two CMI patients both pre- and post-decompression surgery to determine the differences between cases. For the first time, we present the methods to quantify longitudinal impedance (LI) to CSF motion, a subject-specific hydrodynamic parameter that may have value to help quantify the CSF flow blockage severity in CMI. In addition, the following hydrodynamic parameters were quantified for each case: maximum velocity in systole and diastole, Reynolds and Womersley number, and peak pressure drop during the CSF cardiac flow cycle. The following geometric parameters were quantified: cross-sectional area and hydraulic diameter of the spinal subarachnoid space (SAS). The mean values of the geometric parameters increased post-surgically for the CMI models, but remained smaller than the healthy volunteer. All hydrodynamic parameters, except pressure drop, decreased post-surgically for the CMI patients, but remained greater than in the healthy case. Peak pressure drop alterations were mixed. To our knowledge this study represents the first subject-specific CFD simulation of CMI decompression surgery and quantification of LI in the CSF space. Further study in a larger patient and control group is needed to determine if the presented geometric and/or hydrodynamic parameters are helpful for surgical planning.

Mathematical Analysis for MHD Flow of Blood in Constricted Arteries

Abstract The unsteady oscillatory magneto-hydrodynamic flow of blood in small diameter arteries with mild constriction is analyzed, blood being modelled as a Herschel-Bulkley fluid. Finite difference method is employed for solving the associated initial boundary value problem. Explicit finite difference schemes for velocity distribution, flow rate, skin friction and longitudinal impedance to the flow are obtained. The effects of pressure gradient, yield stress, magnetic field, power law index and maximum depth of the stenosis on the aforesaid flow quantities are discussed through appropriate graphs. It is found that the velocity and flow rate decrease and the skin friction and longitudinal impedance to flow increase with the increase of the magnetic field parameter. It was recorded that the flow rate increases and the skin friction decreases with the increase of the phase angle. It was also noted the skin friction and longitudinal impedance to flow that increase almost linearly with the increase of maximum depth of the stenosis. The estimates of the increase in the longitudinal impedance to flow and skin friction are increased considerably by the presence of the magnetic field.

GMI effect of amorphous microwires with enhanced magnetic softness

We present our results on studies of soft magnetic properties and GMI effect in thin microwires at elevated frequencies paying special attention to tailoring the GMI effect and achievement of high GMI ratio (ΔZ/Z), high magnetic field sensitivity (dZ/dH) with low hysteretic behavior. We measured magnetic field dependence of real part, of the longitudinal wire impedance up to frequency, f, 4 GHz in Co-rich microwires. We observed that the GMI magnetic field dependence can be tailored either controlling magnetoelastic anisotropy of as-prepared microwires or by heat treatment.

Longitudinal Impedance Variability in Patients with Chronically Implanted DBS Devices

BackgroundDeep brain stimulation (DBS) is an effective therapy for advanced movement disorders, but its optimal use is still controversial. One factor that could play a role in the proper delivery of therapeutic stimulation by current DBS devices is the variability of the impedance at the interface between the electrode surface and surrounding tissue. ObjectiveTo analyze variability and trends in the impedance of chronically-implanted DBS electrodes in subjects with movement disorders. MethodsWe reviewed impedance values from medical records of DBS patients at an academic tertiary-care movement disorders center. The standard deviation of data recorded within individual subjects and single contacts were used as measures of longitudinal impedance variability. A generalized linear mixed model (GLMM) determined if a number of effects had significant influences on impedance. ResultsWe analyzed 2863 impedance measurements from 94 subjects. Median variability, for subjects with follow-up from 6 months to 5 years (n = 77), was 194 Ω for individual subjects and 141 Ω for individual contacts, with a range spanning from 18 to over 600 Ω. The GLMM, incorporating all subjects (n = 94), identified time, electrical activity, implanted target, contact position on the electrode and side of implantation as significant predictors of impedance. Age and disease duration at surgery, gender or ethnicity were not significant predictors. ConclusionsOur analysis suggests that a significant amount of impedance variability can be expected in chronically implanted DBS electrodes and indicates a number of factors with possible predictive value. Further studies are needed to link impedance characteristics to clinical outcomes.

Beam-wall interaction in the CERN Proton Synchrotron for the LHC upgrade

Coupling impedances and wakefields are fundamental quantities to characterize the electromagnetic interaction of a particle beam with the surrounding environment. In particular, collective effects, triggered by these self-induced fields, may play an important role in beam stability and machine performance. Within the framework of the LHC Injectors Upgrade project, since a significantly higher beam intensity is planned for the CERN Proton Synchrotron, wakefields are expected to increase their influence on the beam dynamics, and their evaluation is becoming important. In this paper we present the results of recent measurements of the longitudinal broadband coupling impedance by means of the incoherent quadrupole synchrotron frequency shift as a function of beam intensity. A detailed evaluation of the contribution of several machine installations to the total impedance budget is also presented and compared with the measurements.

FORMULATION OF MULTIWIRE MAGNETIC TRANSMISSION-LINE THEORY

Time- and frequency-domain theory of multiwire magnetic transmission lines is presented for the flrst time. The familiar theory of electric multiconductor transmission lines (MTL) is based on the manipulation of two matrices, the longitudinal impedance and the transverse admittance. However, for magnetic MTLs, the key matrices are the transverse impedance and the longitudinal admittance. It is shown how the latter matrices are deflned and how they should be used to determine the modal propagation constants and modal characteristic wave admittances that characterize the various travelling wave modes of magnetic MTLs. The theory is illustrated considering a three-wire system with three-fold symmetry. Simulation results, in the range 0.1GHz to 10GHz, are presented, showing that the magnetic MTL can exhibit superluminal phase velocity and zero attenuation dispersion.