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212 R. GROSS AND A. MARX Chapter 4RF-SQUID:• A rf-SQUID is formed by a superconducting loop of inductance L intersected by a single Josephsonjunction with critical current I c .• The variation of the flux Φ threading the SQUID loop as a function of the applied flux Φ ext isgiven byΦ= Φ ext− β (L,rfΦ 0 Φ 0 2π sin 2π Φ )Φ 0.• The rf-SQUID is operated by inductively coupling it to a resonant tank circuit and measuringthe voltage V T of the tank circuit (with inductance L T , resonance frequency ω rf , quality factorQ) as a function of the external flux Φ ext .• The performance of the rf-SQUID is determined by the flux-to-voltage transfer functionH≡( ∂VT∣∂Φ ext)I rf =const∣ ≃ ω rfL TMand the equivalent flux noise or noise energyS Φ ≈ (LI c) 2ε≈ω rf( πη 2 Φ 2 02L( 2πkB TI c Φ 0) 4/3+ 2πηk B T effamp) 1.ω rfIn order to make the noise energy small one has to increase the tank frequency ω rf .rf-SQUIDs have a noise energy of the order of 100¯h.Best• Since the V T (Φ ext ) dependence of rf-SQUIDs is nonlinear and periodic, the SQUID is usuallyoperated in a flux-locked-loop, acting as a null detector.SQUID Based Instruments:• SQUID based instruments usually consist of an antenna transferring an input signal into amagnetic flux threading the SQUID loop, the autonomous SQUID acting as a flux-to-voltageconverter, and the read out electronics.• Depending on the antenna, SQUIDs can be used as magnetometers, gradiometers of differentorder, susceptometers, voltmeters, ammeters, or rf-amplifiers.• The magnetic field resolution of best SQUID magnetometers are of the order of a few fT/ √ Hzat a frequency of 1 Hz.• First and higher order gradiometers are used for suppression of perturbing magnetic field fluctuationscaused by the environment.© <strong>Walther</strong>-Meißner-<strong>Institut</strong>
Section 4.5 APPLIED SUPERCONDUCTIVITY 213Applications of SQUIDs:• In medical technology important applications of SQUIDs are magnetocardiography and magnetoencephalography.Multichannel SQUID systems are used to measure the magnetic fielddistribution due to currents flowing inside the body.• SQUID sensors can be used for nondestructive evaluation of materials, in particular for thedetection of structural or material flaws deep inside of a specimen.• SQUID microscopy allows the imaging of the distribution of weak magnetic fields in variousmaterials and devices such as superconducting and magnetic films and electronic circuits witha spatial resolution of a few µm.• Further fields of application of SQUID systems are gravity wave detection and geophysics.2005
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Applied Superconductivity:Josephson
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List of Tables5.1 Switching delay a
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APPLIED SUPERCONDUCTIVITY 155Since
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