Surface Resistance Of Superconductors Research Articles

A Superconducting Half-Wave Resonator for Accelerating High Velocity Ions

A computer model for the design of superconducting resonators has been developed which includes feedback effects due to non-linear superconducting surface resistance. These non-linearites may be due to either magnetic field or temperature. We have utilized this model to optimize the design of accelerating resonators for heavy ions. A half-wave structure of this design has been fabricated and is being evaluated with respect to the parameters of the model. Preliminary experimental results agree with the model to within a few percent. The half-wave design is particularly well suited to high frequency, high ß resonators because of its low magnetic field, or to low frequency, very low ß resonators because of its good mechanical stability.

Influence of the inelastic electron-phonon scattering on the superconducting surface resistance

Experimental investigations of the rf losses in superconductors show deviations from the predictions of the weak-coupling theory. In order to explain the observations one has to take into account a number of mechanisms neglected in the weak coupling theory. One of these is the finite lifetime of the electrons due to their interaction with thermally excited phonons described by the strong-coupling theory. We have developed a computer program which calculates the surface impedance of strong-coupling superconductors at finite temperatures. In this paper the main features of the program and numerical calculations of the surface resistance of Sn, Pb, Nb and amorphous Ga are presented.

Superconducting surface resistance of thin amorphous Ga films on metallic substrates

The surface resistance of a metal coated with amorphous superconducting films is investigated. With an improved microwave cryostat and a two layer model considering the influence of the substrate, much thinner films can be used than previously. As an example the surface resistance of amorphous Ga is determined. A set of parametersΔ0/kBTc=2,27;λL=13,4 nm;ξ0=223 nm andl=1,0 nm describes the temperature dependence independent of thickness. As expected a model of free electrons is in agreement with the experimental results. For crystallineβ-GaΔ0/kBTc=1,91;λL=24 nm;ξ0=163 nm and a much larger mean free pathl=22 nm is found.

Comment on the residual rf surface resistance of superconductors

The effect of acoustic generation on the residual rf surface resistance Rs of superconductors has recently been discussed with the use of nonlocal theory. The results obtained are higher than the lowest values of Rs found experimentally. Taking proper account of the nonlocal collision drag force reduces the theoretical values well below the experimental results.

The split-loop resonator as a superconducting heavy ion accelerating element

Ion acceleration tests utilizing a superconducting split-loop resonator at accelerating potentials above 2.7 MV/m have been made on ions up to mass 29 and charge state 12. The velocity acceptance and transit time effects were measured and found to be in good agreement with theoretical estimates. Because of the very low energy content of this resonator, the rf power dissipation at low β is less than 10% of an equivalent reentrant cavity design thus relaxing requirements on the superconducting surface resistance and on the phase stabilizing system.

Anomalous surface resistance of superconductors at finite temperature

A theoretical study of the effect of direct ultrasonic generation on the surface impedance of superconductors at temperatures below the critical temperature Tc is presented. The temperature and frequency dependences of the additional surface resistance due to the ionic motion are analyzed using the Pippard and BCS kernels and parabolic electron energy bands.

On surface resistance of superconductors

In principle, the surface resistance of superconductors forRF can be calculated in the framework of the BCS-theory. However, even in the simplest case (low rf field strengths and Meissner phase), the theory yields complicated expressions, which need a computer for solving; the results are shown as graphs. To avoid the use of these complicated expressions, we discuss these numerical results in a model which allows an understanding of the unusual dependencies on the material parameters of superconductors.

Residual surface resistance of superconductors at microwave frequencies

A microscopic theory of the residual surface resistance is presented and compared with experimental results in superconducting lead and niobium. It is shown that for frequencies above 1 GHz, direct electromagnetic generation of acoustic shear waves can account for the measured residual surface resistance.

Microwave Residual Surface Resistance of Superconductors

Two distinct models account for the microwave residual surface resistance of superconducting cavities with equally good agreement with the measured temperature and frequency dependence. In presenting his phonon-generation model. Passow claimed that Rabinowitz's fluxoid power-loss model of residual resistance does not fit the experimental data, whereas his does. In fact, the two models have essentially the same temperature and frequency dependence. Furthermore, Passow's phonon-generation model cannot explain the observed sensitivity to details of sample preparation and history while the fluxoid model can.

Comments on Superconducting Surface Resistance

The author believes a recent letter by Passow contains several inconsistent and misleading statements.Received 4 May 1972DOI:https://doi.org/10.1103/PhysRevB.7.1188©1973 American Physical Society

Explanation of the Low-Temperature, High-Frequency Residual Surface Resistance of Superconductors

Explanation of the Low-Temperature, High-Frequency Residual Surface Resistance of Superconductors

Superconducting surface resistance of amorphous and crystalline Pb 55Bi 45

Measurements of microwave surface resistance can give information about electronic parameters in the amorphous and the crystalline state. The temperature dependence shows deviations from the BCS-function. Residual absorption in the superconducting state is less than 10 -3 of the normal state.

Surface-resistance measurements in TE011-mode cavities of superconducting indium, lead and an indium-lead alloy at low and high RF magnetic fields

Abstract The superconducting surface resistance of Pb, In and In 0.92 Pb 0.08 was measured between 1.5 K and 4.2 K at low- and high-power levels in TE 011 -mode cavities resonating at 2.85 GHz. A residual surface resistance of 9.4 × 10 -8 ohms was achieved in the lead-plated cavity corresponding to a Q of 8.3 × 10 9 . It is shown that the microscopic theoretical expression for the superconducting surface resistance adequately describes the experimental results for Pb and In, both type-I superconductors, and for In 0.92 Pb 0.08 , a type-II superconductor. In lead and indium-plated cavities, and if heating effects are taken into account, the unloaded Q was observed to be essentially a constant up to the r.f. critical magnetic field B r.f. c , where it abruptly decreased by a factor of 100 or more. This transition is characterized by breakdown oscillation phenomena. A B r.f. c as large as 225 G for In and 750 G for Pb was observed. Measurements as a function of temperature indicated that the r.f. critical magnetic field of In and Pb is in agreement with the d.c. critical magnetic field. The largest measured B r.f. c (≈90 G) on the In alloy disc is a factor of 3 smaller than the lower d.c. critical magnetic field, B c 1 (1.5 K) ≈ 270 G.

Comparison between measured and calculatedRF losses in the superconducting state

Results of experiments and of the BCS-theory on the surface resistance of superconductors are presented. It will be shown that agreement between theory and experiment can be achieved by using revised material parameters.

Superconducting Antennas

A high-efficiency electrically and physically small superconducting antenna is reported. Antenna factors and matching circuit equivalents are developed. Theoretical predictions of efficiency and Q increase are derived on the basis of the superconducting surface resistance of lead. The antenna is a loop supsended through a ground plane and matched through a symmetrical coaxial cavity having a resonant frequency of 400 MHz. The loop is lead-plated and has an open area of approximately 1 cm2. Coupling to the system is achieved through a movable electric-field probe inserted into a slot in the wall of the matching cavity. A normal-state electrically small antenna of this size has a theoretical efficiency of less than 1% due to the fact that the loop resistance is much larger than the equivalent radiation resistance. Upon cooling to 4.2°K, the Q of the system increases to 20 000 from a room-temperature value of 156, indicating limitation by the radiation resistance only. The power radiation efficiency increases by a factor of 500, as measured by a fixed external receiving system. The VSWR of the system is maintained near unity in order to avoid the complications of mismatching.

Automatic Tuning of a Superconducting Cavity Using Optical Feedback

The resonant frequency of a superconducting cavity has been photodielectrically controlled by a feedback loop which contains an optical path. The cavity is an 870-MHz lead-plated quarter-wave reentrant structure. A 19 000 Ω·cm silicon wafer terminates the quarter-wave stub. The loaded Q is approximately 105 indicating the losses in the semiconductor dominate the superconducting surface resistance. The high Q provides a large phase error between the input and output voltage when the driving oscillator drifts or is modulated away from the very stable resonant frequency of the cavity. The error is processed by a wide-bandwidth phase detector that drives a gallium arsenide diode to follow the frequency excursion of the oscillator by photodielectric tuning. The 9000 Å light is the optical feedback signal which corrects the phase error. The system response typically provides a frequency deviation of ±50 kHz at a 0.2 MHz rate. Higher cavity frequency and purer semiconductor samples extend the deviation limits and shorter free-carrier lifetimes increase the speed of response.

Microwave Surface Resistance of Superconducting Niobium

The unloaded Q's of pure Nb cavities in the TE011 mode at 11.2 GHz and in the TM010 mode at 8.4 GHz were measured between 1.2° and 4.2°K to determine whether the residual surface losses in Nb could be made sufficiently low to make it a useful material for practical microwave devices. Three forms of reactor grade Nb were evaluated: recrystallized fully wrought, arc melted, and electron-beam melted. Each of these materials was subjected to additional metallurgical processing including high-temperature vacuum firing and polishing to determine their effects on surface losses. In the TE011 mode, a residual Q of 3.8×1010 was achieved. Also in the TE011 mode, the unloaded Q was observed to be essentially a constant up to the ac critical magnetic field Hcae, where it abruptly decreased by a factor of 100 or more. An Hcae as large as 436 Oe was observed for unstrained Nb. In the TM010 mode, which has electric fields terminating on the surface of the Nb, a residual Q of 2×109 was achieved, the limitation on the maximum field level in the cavity was Hcae, and no power loss associated with electric-field emission was observed up to an electric field of 2.1×105 V/cm, which was the maximum field level obtained in the cavity. The Mattis and Bardeen theoretical expression for the superconducting surface resistance fits the data very well, and the value of the energy gap 2Δ(0) obtained from the fitting procedure is (3.72±0.01) kBTc, which agrees with values of 2Δ(0) obtained by other methods. The surface resistance data are not inconsistent with a double energy-gap model, which has been used to explain specific heat data; however, it was not possible using the data to distinguish between a double energy-gap model and a single energy-gap model with a residual surface resistance. It would be expected that Hcae would be about Hc1 where magnetic flux starts penetrating a type-II superconductor; however, the largest measured Hcae (436 Oe) was in fact about Hc1/4.

Performance of Superconducting Oscillators and Filters

With improved understanding of loss mechanisms in superconducting resonant circuits (SRC), it is possible to design a variety of devices which take advantage of the high Q. Superconducting surface resistance, trapped-flux loss, and residual losses which are annealable can all be related to the superconductor itself. Dielectric dissipation is well enough understood to permit this source of loss to be minimized. Coupling and radiation losses can be made negligible. SRC's are described with a variety of geometries to fill the range from 10 MHz to 10 GHz. Type-I superconductors provide the highest Q's and are readily fabricated by several techniques. The superconducting resonator can be tuned accurately in frequency by temperature control of the surface reactance as well as the dielectric constant of liquid helium. An external magnetic field can be used to tune the bandwidth as well as the resonant frequency. A quarter-wave reentrant cavity is ideally suited for use as an optically tuned frequency-control element. This is accomplished using the photodielectric effect in high-resistivity semiconductor wafers which terminate the stub. Wide-bandwidth optical communication detectors are described using semiconductors with short recombination lifetime. Oscillators have been built which are optically tuned, and others which have frequency stabilities as good as commercial frequency counters. Use of SRC's to study material properties at low temperature is emphasized.

On the magnetic field dependence of the high frequency surface resistance of superconductors

The surface resistance R(H) of a superconductor in a magnetic field H can be smaller than R(0) for frequencies above the energy gap. This effect, recently suggested by Budzinski and Garfunkel, is demonstrated by reducing the gap by means of proximity effects.