Anomalous Impedance Research Articles

Anomalous fractal scaling in two-dimensional electric networks

Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a two-dimensional LC circuit network. We find this anomalous impedance contribution to sensitively depend on the number of nodes N in a curious erratic manner and experimentally demonstrate its robustness against perturbations from the contact and parasitic impedance of individual components. This impedance anomaly is traced back to a generalized resonance condition reminiscent of Harper’s equation for electronic lattice transport in a magnetic field, even though our circuit network does not involve magnetic translation symmetry. It exhibits an emergent fractal parametric structure of anomalous impedance peaks for different N that cannot be reconciled with a continuum theory and does not correspond to regular waveguide resonant behavior. This anomalous fractal scaling extends to the transport properties of generic systems described by a network Laplacian whenever a resonance frequency scale is simultaneously present.

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits such as one- and two-dimensional Su-Schrieffer-Heeger circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite $LC$ circuits. Through the method of images, we study how resonance modes in a multidimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally reduced expressions for the impedance in three dimensions and above.

On the representation of dense plasma focus as a circuit element

The dense plasma focus is a plasma discharge powered by a capacitor bank. Standard diagnostics include the measurement of the time derivative of the current through and the voltage across its connections with the capacitor bank. Interpretation of this diagnostic data often involves some assumptions regarding the representation of the dense plasma focus as a time varying inductance. One of the characteristic features of the current derivative waveform is a relatively sharp dip and an associated sharp voltage spike. This has often been interpreted as a result of a rapid rise in the time varying inductance of the plasma. Sometimes, an anomalous plasma impedance is invoked. This Letter discusses instances where such interpretation creates conceptual difficulties. A first principles approach to the representation of the dense plasma focus as a circuit element reveals some fundamental problems with the traditional representation of plasma focus as a time varying inductance. The anomalous impedance is shown to be necessary to account for the difference in the motional impedance implied by a time-varying inductance in the circuit element representation and a first principles description based on Poynting's theorem. Dynamo effects that convert post-stagnation local motion of plasma into three-dimensional magnetic fields are shown to contribute to the effective inductance of the plasma focus and resolve the observed conceptual difficulties.

Theory of generalized Gerischer impedance for quasi-reversible charge transfer at rough and finite fractal electrodes

A theoretical model for the generalized Gerischer impedance at an irregular interface under quasi-reversible heterogeneous charge transfer reaction has been developed. The dynamic impedance response is predicted to depend on three phenomenological components, viz. diffusion, charge transfer reaction and bulk homogeneous kinetics as well as roughness. The theory has been developed for both deterministic and stochastic electrode roughness. Statistical properties of the stochastic electrode roughness are characterized through their power spectral density. The impedance response is influenced by the finite self-affine fractal roughness which is analyzed in detail. Three governing phenomenological length scales are diffusion length, charge transfer length and reaction layer thickness. The anomalous impedance response of the finite fractal electrode is due to the synergistic effect of the phenomenological lengths and finite-fractal morphological parameters, namely, fractal dimension (DH), lower cut-off length (ℓ) and topothesy length (ℓτ). The impedance response has three distinct characteristic frequency regimes: the low frequency bulk kinetics controlled regime, roughness dependent intermediate frequency region and heterogeneous charge transfer controlled high frequency regime. A contrasting diffusive behavior is predicted, wherein the system switches from sub-diffusive to super-diffusive response with increase in electrode roughness. This theory unravels the influence of both bulk and interfacial kinetics on the impedance response of a rough electrode.

Electrical impedance response of gamma irradiated gelatin based solid polymer electrolytes analyzed using a generalized calculus formalism

The electrical impedance response of gelatin based solid polymer electrolyte to gamma irradiation is investigated by impedance spectroscopy. An analysis based on Poisson–Nernst–Plank model, incorporating fractional time derivatives is carried out. A detailed derivation for anomalous impedance function is given. The model involves boundary conditions with convolution of the fractional time derivative of ion density and adsorption desorption relaxation kinetics. A fractional diffusion–drift equation is used to solve the bulk behavior of the mobile charges in the electrolyte. The complex adsorption–desorption process at the electrode–electrolyte interface produces an anomalous effect in the system. The model gives a good fit for the observed impedance data for this biopolymer based solid electrolyte in a wide range of frequencies. We have compared different parameters based upon this model for both irradiated and unirradiated samples.

The impact of plasma dynamics on the self-magnetic-pinch diode impedance

The self-magnetic-pinch diode is being developed as an intense electron beam source for pulsed-power-driven x-ray radiography. The basic operation of this diode has long been understood in the context of pinched diodes, including the dynamic effect that the diode impedance decreases during the pulse due to electrode plasma formation and expansion. Experiments being conducted at Sandia National Laboratories' RITS-6 accelerator are helping to characterize these plasmas using time-resolved and time-integrated camera systems in the x-ray and visible. These diagnostics are analyzed in conjunction with particle-in-cell simulations of anode plasma formation and evolution. The results confirm the long-standing theory of critical-current operation with the addition of a time-dependent anode-cathode gap length. The results may suggest that anomalous impedance collapse is driven by increased plasma radial drift, leading to larger-than-average ion vr × Bθ acceleration into the gap.

Three-dimensional resistivity modelling of a seismogenic area in an oblique subduction zone in the western Kurile arc: Constraints from anomalous magnetotelluric phases

Abstract Wide-band magnetotelluric surveys were performed at 44 sites in the inland earthquake zone on the western margin of the Kurile arc, where strain accumulation has been observed since a high-magnitude interplate earthquake in 2003 (Tokachi-oki earthquake, M 8.0). We estimated the three-dimensional (3-D) resistivity distribution based on magnetotelluric impedance tensors, which contained anomalously large impedance phases. Although anomalous impedance phases have previously been considered a major impediment for magnetotelluric studies, we found that the anomalous phase can be used to constrain the resistivity distribution. The 3-D resistivity model showed that the earthquake zone consists of resistive areas (> 300 Ω-m), whereas the fore-arc and back-arc areas consist of regional conductive layers (

Anomalous surface impedance in a normal-metal/superconductor junction with a spin-active interface

We discuss the surface impedance (Z=R-iX) of a normal-metal/superconductor proximity structure taking into account the spin-dependent potential at the junction interface. Because of the spin mixing transport at the interface, odd-frequency spin-triplet s-wave Cooper pairs penetrate into the normal metal and cause the anomalous response to electromagnetic fields. At low temperature, the local impedance at a surface of the normal metal shows the nonmonotonic temperature dependence and the anomalous relation R>X. We also discuss a possibility of observing such anomalous impedance in experiments.

Characterization and investigation of the anomalous behavior of the immersed-Bz diode during operation at 4 to 5 MV

The immersed-Bz diode is being developed as a high-brightness, flash x-ray radiography source at Sandia National Laboratories. This diode is a foil-less electron-beam diode with a long, thin, needlelike cathode which is inserted into the bore of a solenoid. The solenoidal magnetic field guides the electron beam emitted from the cathode to the anode while maintaining a small beam radius. The electron beam strikes a thin, high-atomic-number anode and produces forward-directed bremsstrahlung. In addition, electron beam heating of the anode produces surface plasmas allowing ion emission. Two different operating regimes for this diode have been identified: A nominal operating regime where the total diode current is characterized as classically bipolar with stable impedance [see D. C. Rovang et al., Phys. Plasmas 14, 113107 (2007)] and an anomalous operating regime characterized by a rapid impedance collapse where the total diode current greatly exceeds the bipolar limit. The operating regimes are approximately separated by cathode diameters greater than 3mm for the nominal regime and less than 3mm for the anomalous impedance collapse regime. Results from a comprehensive series of experiments conducted at 4–5MV characterizing the transition from this nominal operating regime to the anomalous operating regime as the cathode diameter is reduced are presented. Results from experiments investigating the effects of anode-cathode gap, anode material, and cryogenic modification of the anode surface are also presented. Although these investigations were unsuccessful in completely mitigating the anomalous behavior, insight gained from these experiments has elucidated several key physics issues that are discussed.

Anomalous impedance and anomalous ion heating due to gyrorelaxation through magnetohydrodynamic fluctuations

The ion viscosity associated with the gyrorelaxation dominates the dissipation of fluctuations in a fast reconnection process, where the magnetic compression becomes finite. The kink instability, which drives the fast reconnection, yields a spontaneous ν×B electric field that diminshes the toroidal current. The enhanced impedance of the discharge, which appears as an anomalous resistance of the discharge, is related to the ion gyrorelaxation dissipation. The viscosity contributes to the energy dissipation, while the helicity remains constant. This model of anomalous resistance applies to a turbulent discharge with an appreciable dynamo effect, and explains a part of the high resistance in an ultralow q discharge.

Anomalous impedance and roughness at a metallic electrode

Anomalous impedance and roughness at a metallic electrode

Anomalous impedance and roughness at a metallic electrode

We study the frequency dependence of the electrical impedance at a rough metallic electrode. Using the Rayleigh-Fano approximation to treat the boundary conditions at a rough surface, we get an impedance which depends on the roughness correlation function and exhibits anomalous behaviour under suitable condition. Explicit forms are considered and discussed.

On the increase in permittivity of ferroelectrics during switching

Relations are derived for the anomalous impedance of ferroelectrics during switching on the basis of the phenomenological description of the process of switching in a constant field. It is shown that these expressions represent the characteristic properties of anomalous impedance, known from experiment, qualitatively quite well.