SKIFFS: Superconducting Kinetic Inductance Field-Frequency Sensors for Sensitive Magnetometry in Moderate Background Magnetic Fields
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Determination of the Magnetic Permeability, Electrical Conductivity
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TII.2018.2885406, IEEE Transactions on Industrial Informatics TII-18-2870 1 Determination of the magnetic permeability, electrical conductivity, and thickness of ferrite metallic plates using a multi-frequency electromagnetic sensing system Mingyang Lu, Yuedong Xie, Wenqian Zhu, Anthony Peyton, and Wuliang Yin, Senior Member, IEEE Abstract—In this paper, an inverse method was developed by the sensor are not only dependent on the magnetic which can, in principle, reconstruct arbitrary permeability, permeability of the strip but is also an unwanted function of the conductivity, thickness, and lift-off with a multi-frequency electrical conductivity and thickness of the strip and the electromagnetic sensor from inductance spectroscopic distance between the strip steel and the sensor (lift-off). The measurements. confounding cross-sensitivities to these parameters need to be Both the finite element method and the Dodd & Deeds rejected by the processing algorithms applied to inductance formulation are used to solve the forward problem during the spectra. inversion process. For the inverse solution, a modified Newton– Raphson method was used to adjust each set of parameters In recent years, the eddy current technique (ECT) [2-5] and (permeability, conductivity, thickness, and lift-off) to fit the alternating current potential drop (ACPD) technique [6-8] inductances (measured or simulated) in a least-squared sense were the two primary electromagnetic non-destructive testing because of its known convergence properties. The approximate techniques (NDT) [9-21] on metals’ permeability Jacobian matrix (sensitivity matrix) for each set of the parameter measurements. -
Nonlinear Dynamics of Josephson Junction Chains
Nonlinear dynamics of Josephson Junction Chains and Superconducting Resonators ADEM ERGUL¨ Doctoral Thesis in Physics Stockholm, Sweden 2013 KTH-Royal Institute of Technology TRITA FYS 2013:52 School of Engineering Sciences ISSN 0280-316X Department of Applied Physics ISRN KTH/FYS/- -13:52- -SE SE-100 44 Stockholm ISBN 978-91-7501-869-0 SWEDEN Akademisk avhandling som med tillst˚and av Kungliga Tekniska H¨ogskolan framl¨agges till offentlig granskning f¨or avl¨aggande av teknologie doktorsexamen i fysik torsda- gen den 28 november 2013 klockan 13:00 i sal FA32, AlbaNova Universitetscentrum, Kungliga Tekniska H¨ogskolan, Roslagstullsbacken 21, Stockholm. Opponent: Prof. Per Delsing Huvudhandledare: Prof. David B. Haviland © ADEM ERGUL,¨ 2013 Tryck: Universitetsservice US AB iii Abstract This thesis presents the results of the experimental studies on two kind of Superconducting circuits: one-dimensional Josephson junction chains and superconducting coplanar waveguide (CPW) resonators. One-dimensional Josephson junction chains are constructed by connecting many Supercon- ducting quantum interference devices (SQUIDs) in series. We have stud- ied DC transport properties of the SQUID chains and model their nonlinear dynamics with Thermally Activated Phase-Slips (TAPS). Experimental and simulated results showed qualitative agreement revealing the existence of a uniform phase-slipping and phase-sticking process which results in a voltage- independent current on the dissipative branch of the current-voltage char- acteristics (IVC). By modulating the effective Josephson coupling energy of the SQUIDs (EJ ) with an external magnetic field, we found that the ra- tio EJ /EC is a decisive factor in determining the qualitative shape of the IVC. A quantum phase transition between incoherent Quantum Phase Slip, QPS (supercurrent branch with a finite slope) to coherent QPS (IVC with well-developed Coulomb blockade) via an intermediate state (supercurrent branch with a remnant of Coulomb blockade) is observed as the EJ /EC ra- tio is tuned. -
Units in Electromagnetism (PDF)
Units in electromagnetism Almost all textbooks on electricity and magnetism (including Griffiths’s book) use the same set of units | the so-called rationalized or Giorgi units. These have the advantage of common use. On the other hand there are all sorts of \0"s and \µ0"s to memorize. Could anyone think of a system that doesn't have all this junk to memorize? Yes, Carl Friedrich Gauss could. This problem describes the Gaussian system of units. [In working this problem, keep in mind the distinction between \dimensions" (like length, time, and charge) and \units" (like meters, seconds, and coulombs).] a. In the Gaussian system, the measure of charge is q q~ = p : 4π0 Write down Coulomb's law in the Gaussian system. Show that in this system, the dimensions ofq ~ are [length]3=2[mass]1=2[time]−1: There is no need, in this system, for a unit of charge like the coulomb, which is independent of the units of mass, length, and time. b. The electric field in the Gaussian system is given by F~ E~~ = : q~ How is this measure of electric field (E~~) related to the standard (Giorgi) field (E~ )? What are the dimensions of E~~? c. The magnetic field in the Gaussian system is given by r4π B~~ = B~ : µ0 What are the dimensions of B~~ and how do they compare to the dimensions of E~~? d. In the Giorgi system, the Lorentz force law is F~ = q(E~ + ~v × B~ ): p What is the Lorentz force law expressed in the Gaussian system? Recall that c = 1= 0µ0. -
On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch
Andre Koch Torres Assis On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch Abstract The electrostatic, electrodynamic and electromagnetic systems of units utilized during last century by Ampère, Gauss, Weber, Maxwell and all the others are analyzed. It is shown how the constant c was introduced in physics by Weber's force of 1846. It is shown that it has the unit of velocity and is the ratio of the electromagnetic and electrostatic units of charge. Weber and Kohlrausch's experiment of 1855 to determine c is quoted, emphasizing that they were the first to measure this quantity and obtained the same value as that of light velocity in vacuum. It is shown how Kirchhoff in 1857 and Weber (1857-64) independently of one another obtained the fact that an electromagnetic signal propagates at light velocity along a thin wire of negligible resistivity. They obtained the telegraphy equation utilizing Weber’s action at a distance force. This was accomplished before the development of Maxwell’s electromagnetic theory of light and before Heaviside’s work. 1. Introduction In this work the introduction of the constant c in electromagnetism by Wilhelm Weber in 1846 is analyzed. It is the ratio of electromagnetic and electrostatic units of charge, one of the most fundamental constants of nature. The meaning of this constant is discussed, the first measurement performed by Weber and Kohlrausch in 1855, and the derivation of the telegraphy equation by Kirchhoff and Weber in 1857. Initially the basic systems of units utilized during last century for describing electromagnetic quantities is presented, along with a short review of Weber’s electrodynamics. -
Chapter 32 Inductance and Magnetic Materials
Chapter 32 Inductance and Magnetic Materials The appearance of an induced emf in one circuit due to changes in the magnetic field produced by a nearby circuit is called mutual induction. The response of the circuit is characterized by their mutual inductance. Can we find an induced emf due to its own magnetic field changes? Yes! The appearance of an induced emf in a circuit associated with changes in its own magnet field is called self-induction. The corresponding property is called self-inductance. A circuit element, such as a coil, that is designed specifically to have self-inductance is called an inductor. 1 32.1 Inductance Close: As the flux through the coil changes, there is an induced emf that opposites this change. The self induced emf try to prevent the rise in the current. As a result, the current does not reach its final value instantly, but instead rises gradually as in right figure. Open: When the switch is opened, the flux rapidly decreases. This time the self- induced emf tries to maintain the flux. When the current in the windings of an electromagnet is shut off, the self-induced emf can be large enough to produce a spark across the switch contacts. 2 32.1 Inductance (II) Since the self-induction and mutual induction occur simultaneously, both contribute to the flux and to the induced emf in each coil. The flux through coil 1 is the sum of two terms: N1Φ1 = N1(Φ11 + Φ12 ) The net emf induced in coil 1 due to changes in I1 and I2 is d V = −N (Φ + Φ ) emf 1 dt 11 12 3 Self-Inductance It is convenient to express the induced emf in terms of a current rather than the magnetic flux through it. -
Relative Permeability Measurements for Metal-Detector Research
NATL INST. OF STAND & TECH MIST 1""""""""" PUBUCATI0N8 National Institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Technical Note 1532 Relative Permeability Measurements for Metal-Detector Research Michael D. Janezic James Baker-Jarvis /oo NIST Technical Note 1532 Relative Permeability Measurements For Metal-Detector Research Michael D. Janezic James Baker-Jarvis Radio-Frequency Technology Division Electronics and Electrical Engineering Laboratory National Institute of Standards and Technology Boulder, CO 80305 April 2004 U.S. Department of Commerce Donald L. Evans, Secretary Technology Administration Phillip J. Bond, Under Secretary for Technology National Institute of Standards and Technology Arden L. Bement, Jr., Director National Institute of Standards U.S. Government Printing Office For sale by the and Technology Washington: 2004 Superintendent of Documents Technical Note 1532 U.S. Government Printing Office Natl. Inst. Stand. Technol. Stop SSOP Tech. Note 1532 Washington, DC 20402-0001 1 6 Pages (April 2004) Phone: (202) 512-1 800 CODEN: NTNOEF Fax: (202) 512-2250 Internet: bookstore.gpo.gov Contents 1 Introduction 1 2 Overview and Definitions 2 3 Toroid Meeisurement Technique 4 3.0.1 Relative Permeability Model Excluding Toroid Conductivity 4 3.0.2 Relative Permittivity Model Including Toroid Conductivity 5 4 Measurements of Relative Permeability 7 5 Conclusions 11 6 References 12 Relative Permeability Measurements for Metal-Detector Research Michael D. Janezic and James Baker- Jarvis Electromagnetics Division, National Institute of Standards and Technology, Boulder, CO 80305 We examine a measurement method for characterizing the low-frequency relative per- meability of ferromagnetic metals commonly used in the manufacture of weapons. -
Chapter 6 Inductance, Capacitance, and Mutual Inductance
Chapter 6 Inductance, Capacitance, and Mutual Inductance 6.1 The inductor 6.2 The capacitor 6.3 Series-parallel combinations of inductance and capacitance 6.4 Mutual inductance 6.5 Closer look at mutual inductance 1 Overview In addition to voltage sources, current sources, resistors, here we will discuss the remaining 2 types of basic elements: inductors, capacitors. Inductors and capacitors cannot generate nor dissipate but store energy. Their current-voltage (i-v) relations involve with integral and derivative of time, thus more complicated than resistors. 2 Key points di Why the i-v relation of an inductor isv L ? dt dv Why the i-v relation of a capacitor isi C ? dt Why the energies stored in an inductor and a capacitor are: 1 1 w Li, 2 , 2 Cv respectively? 2 2 3 Section 6.1 The Inductor 1. Physics 2. i-v relation and behaviors 3. Power and energy 4 Fundamentals An inductor of inductance L is symbolized by a solenoidal coil. Typical inductance L ranges from 10 H to 10 mH. The i-v relation of an inductor (under the passive sign convention) is: di v L , dt 5 Physics of self-inductance (1) Consider an N1 -turn coil C1 carrying current I1 . The resulting magnetic fieldB 1() r 1 N 1(Biot- I will pass through Savart law) C1 itself, causing a flux linkage 1 , where B1() r 1 N 1 , 1 B1 r1() d s1 P 1, 1 N I S 1 P1 is the permeance. 2 1 PNI 1 11. 6 Physics of self-inductance (2) The ratio of flux linkage to the driving current is defined as the self inductance of the loop: 1 2 L1NP 1 1, I1 which describes how easy a coil current can introduce magnetic flux over the coil itself. -
On-Chip Intercalated-Graphene Inductors for Next-Generation Radio Frequency Electronics
ARTICLES https://doi.org/10.1038/s41928-017-0010-z On-chip intercalated-graphene inductors for next-generation radio frequency electronics Jiahao Kang 1, Yuji Matsumoto2, Xiang Li3, Junkai Jiang1, Xuejun Xie1, Keisuke Kawamoto2, Munehiro Kenmoku2, Jae Hwan Chu1, Wei Liu1, Junfa Mao3, Kazuyoshi Ueno2 and Kaustav Banerjee 1* On-chip metal inductors that revolutionized radio frequency electronics in the 1990s suffer from an inherent limitation in their scalability in state-of-the-art radio frequency integrated circuits. This is because the inductance density values for con- ventional metal inductors, which result from magnetic inductance alone, are limited by the laws of electromagnetic induc- tion. Here, we report inductors made of intercalated graphene that uniquely exploit the relatively large kinetic inductance and high conductivity of the material to achieve both small form-factors and high inductance values, a combination that has proved difficult to attain so far. Our two-turn spiral inductors based on bromine-intercalated multilayer graphene exhibit a 1.5-fold higher inductance density, leading to a one-third area reduction, compared to conventional inductors, while pro- viding undiminished Q-factors of up to 12. This purely material-enabled technique provides an attractive solution to the longstanding scaling problem of on-chip inductors and opens an unconventional path for the development of ultra-compact wireless communication systems. he Internet of Things (IoT) promises unprecedented connec- the conductor in the Drude model for a.c. electrical conductivity. tivity between people and 50 billion things by 20201,2, with a Hence, the magnetic inductance is determined by the geometrical/ potential economic impact of US$2.7 trillion to US$6.2 tril- structural design of the inductor, while kinetic inductance is purely T 1,3 lion per year by 2025 . -
Single-Photon Detection, Kinetic Inductance, and Non-Equilibrium Dynamics in Niobium and Niobium Nitride Superconducting Nanowires
Abstract Single-Photon Detection, Kinetic Inductance, and Non-Equilibrium Dynamics in Niobium and Niobium Nitride Superconducting Nanowires Anthony Joseph Annunziata 2010 This thesis is a study of superconducting niobium and niobium nitride nanowires used as single optical and near-infrared photon detectors. The nanowires are biased in the zero-voltage state with a current just below their critical current and at a temperature well below their critical temperature. In this state, an absorbed photon induces localized heating at the point of absorption. This suppresses the critical current in that location, creating a resistive region in the nanowire. The resistive region can grow under Joule heating and can self-reset to the zero-voltage state without the dc bias current being reduced. This study is twofold. First, niobium is investigated as an alternate detector material to niobium nitride. This study compares the performance niobium nanowire detectors of several geometries and fabricated in two different ways to the performance of niobium nitride nanowire detectors. Niobium detectors are found to have longer reset times and are more difficult to bias in a regime where they self-reset to the zero voltage state after detecting a photon. This makes niobium a less suitable material than niobium nitride for these detectors. In the second part of this study, the reset dynamics of these detectors are studied. Thermal relaxation is studied using a combination of experiments and numerical simulations. It is found that the thermal relaxation time for a niobium nanowire depends significantly on the amount of energy dissipated into the hotspot during the detection event. -
P451/551 Lab: Superconducting Quantum Interference Devices
P451/551 Lab: Superconducting Quantum Interference Devices (SQUIDs) AN INTRODUCTION TO SUPERCONDUCTIVITY AND SQUIDS Superconductivity was first discovered in 1911 in a sample of mercury metal whose resistance fell to zero at a temperature of four degrees above absolute zero. The phenomenon of superconductivity has been the subject of both scientific research and application development ever since. The ability to perform experiments at temperatures close to absolute zero was rare in the first half of this century and superconductivity research proceeded in relatively few laboratories. The first experiments only revealed the zero resistance property of superconductors, and more than twenty years passed before the ability of superconductors to expel magnetic flux (the Meissner Effect) was first observed. Magnetic flux quantization – the key to SQUID operation – was predicted theoretically only in 1950 and was finally observed in 1961. The Josephson effects were predicted and experimentally verified a few years after that. SQUIDs were first studied in the mid-1960’s, soon after the first Josephson junctions were made. Practical superconducting wire for use in moving machines and magnets also became available in the 1960's. For the next twenty years, the field of superconductivity slowly progressed toward practical applications and to a more profound understanding of the underlying phenomena. A great revolution in superconductivity came in 1986 when the era of high-temperature superconductivity began. The existence of superconductivity at liquid nitrogen temperatures has opened the door to applications that are simpler and more convenient than were ever possible before. The superconducting ground state is one in which electrons pair up with one another such that each resultant pair has the same net momentum (which is zero if no current is flowing). -
Capacitor and Inductors
Capacitors and inductors We continue with our analysis of linear circuits by introducing two new passive and linear elements: the capacitor and the inductor. All the methods developed so far for the analysis of linear resistive circuits are applicable to circuits that contain capacitors and inductors. Unlike the resistor which dissipates energy, ideal capacitors and inductors store energy rather than dissipating it. Capacitor: In both digital and analog electronic circuits a capacitor is a fundamental element. It enables the filtering of signals and it provides a fundamental memory element. The capacitor is an element that stores energy in an electric field. The circuit symbol and associated electrical variables for the capacitor is shown on Figure 1. i C + v - Figure 1. Circuit symbol for capacitor The capacitor may be modeled as two conducting plates separated by a dielectric as shown on Figure 2. When a voltage v is applied across the plates, a charge +q accumulates on one plate and a charge –q on the other. insulator plate of area A q+ - and thickness s + - E + - + - q v s d Figure 2. Capacitor model 6.071/22.071 Spring 2006, Chaniotakis and Cory 1 If the plates have an area A and are separated by a distance d, the electric field generated across the plates is q E = (1.1) εΑ and the voltage across the capacitor plates is qd vE==d (1.2) ε A The current flowing into the capacitor is the rate of change of the charge across the dq capacitor plates i = . And thus we have, dt dq d ⎛⎞εεA A dv dv iv==⎜⎟= =C (1.3) dt dt ⎝⎠d d dt dt The constant of proportionality C is referred to as the capacitance of the capacitor. -
Lumped Element Kinetic Inductance Detectors
18th International Symposium on Space Terahertz Technology Lumped Element Kinetic Inductance Detectors Simon Doyle a, Jack Naylon b, Philip Mauskopf a, Adrian Porch b, and Chris Dunscombe a a Department of Physics and Astronomy, Cardiff University, Queens Buildings, The Parade Cardiff CF24 3AA b Department of Electrical Engineering, Cardiff University, Queens buildings, The Parade Cardiff CF24 3AA ABSTRACT Kinetic Inductance Detectors (KIDs) provide a promising solution to the problem of producing large format arrays of ultra sensitive detectors for astronomy. Traditionally KIDs have been constructed from superconducting quarter-wavelength or half-wavelength resonator elements capacitivly coupled to a co-planar feed line. Photons are detected by measuring the change in quasi-particle density caused by the splitting of Cooper pairs in the superconducting resonant element. This change in quasi-particle density alters the kinetic inductance, and hence the resonant frequency of the resonant element. This arrangement requires the quasi-particles generated by photon absorption to be concentrated at positions of high current density in the resonator. This is usually achieved through antenna coupling or quasi-particle trapping. For these detectors to work at wavelengths shorter than around 500 μm where antenna coupling can introduce a significant loss of efficiency, then a direct absorption method needs to be considered. One solution to this problem is the Lumped Element KID (LEKID), which shows no current variation along its length and can be arranged into a photon absorbing area coupled to free space and therefore requiring no antennas or quasi-particle trapping. This paper outlines the relevant microwave theory of a LEKID, along with theoretical performance for these devices.