James Maniscalco

A Computational Method for More Accurate Measurements of the Surface Resistance in SRF Cavities

The principal loss mechanism for superconducting RF cavities in normal operation is Ohmic heating due to the microwave surface resistance in the superconducting surface. The typical method for calculating this field-dependent surface resistance Rs(H) from RF measurements of quality factor Q0 implicitly returns a weighted average of Rs over the surface as a function of peak surface magnetic field H, not the true value of Rs as a function of the local magnitude of H. In this work we present a computational method to convert a measured Q0 vs. Hpeak to a more accurate Rs vs. Hlocal, given knowledge about cavity geometry and field distribution. INTRODUCTION In superconducting radio-frequency accelerator physics (SRF), the signature figure of merit of accelerating cavities is the intrinsic quality factor Q0. As for any harmonic resonator, this quality factor indicates the amount of power P needed to sustain an energy U stored in the cavity’s electromagnetic field, shown here with resonant frequency ω: Q0 = ωU P = ω 2 ∫ | H |2 dV P (1) Thus a cavity with a higher quality factor needs less power to maintain a given field magnitude. For state-of-the-art SRF cavities in typical operation, losses arise almost exclusively from Ohmic power dissipation on the RF surface: P = 1 2 ∫ | H |Rs(H) dS (2) Understanding and improving this surface resistance is a key factor in improving SRF technology and studying new SRF surfaces and surface treatments. Further, this resistance can depend strongly on the magnitude of the surface magnetic field, as it does for many materials currently under investigation (see for example impurity-doped niobium [1,2], Nb3Sn [3], and thin film niobium [4]). As such, it is highly desirable to measure Rs as a function of H for SRF cavities. For simplicity, in order to extract Rs from experimental measurements of Q0, researchers calculate a “geometry factor”1 G from Eqs. 1 and 2: G = ω ∫ | H |2 dV ∫ | H |2 dS (3) ∗ This work was supported by the U.S. National Science Foundation under Award No. PHY-1549132, the Center for Bright Beams. Travel to IPAC 2018 supported by NSF, APS-DPB, and TRIUMF. † jtm288@cornell.edu 1 For a full treatment of standard practices, see H. Padamsee’s textbook [5]. This allows the following approximate form of Q0: Q0(Hpk) = G Rs(Hpk) (4) Here, Hpk is the peak surface magnetic field. The definition in Eq. 4 implicitly assumes that the surface resistance and magnetic field are constant across the surface of the cavity, allowing Rs(H) to be pulled out of the integral in Eq. 3. To be more accurate, it is better to rewrite Eq. 4 noting that the surface resistance is actually a weighted average: Q0(Hpk) = G Rav(Hpk) (5) Rearranging Eqs. 1 to 5 demonstrates this averaging: Rav(Hpk) = G Q0(Hpk) = ∫ | H |Rs(H) dS ∫ | H |2 dS (6) Given knowledge about the field distribution and the geometry of the cavity, it is possible to derive the observed Rav(Hpk) from a theoretical model of Rs(H). On the other hand, “undoing” the averaging is not easy to do analytically without at least a parameterized functional form for Rs(H). However, it is possible to approximate this reversal process (i.e. to calculate Rs(H) from an observed Rav(Hpk)) numerically, given the aforementioned knowledge about the cavity geometry and field distribution. In this work, we describe such a method using linear algebra. MATHEMATICAL PROCESS The right-hand side of Eq. 6 can be approached as an averaging operator A acting on a function Rs(H) that transforms the actual surface resistance into the observed Rav(Hpk). To calculate the fundamental, local2 resistance Rs(H) from the observed Rav(Hpk), we need to find the inverse of the averaging function: Rs(H) = A(A(Rs(H))) (7) One way to calculate this inverse function is by discretizing the problem. We can find a good approximate solution by representing Rs(H) as a vector R, with each entry of R denoting the surface resistance at a given field value Hi; the index i goes from 1 to N , R has N entries, and A has dimensions N × N . In our case we will set the Hi values to be 2 N.B.: “local” here does not imply that this method can find localized areas of heating; instead, it assumes a defect-free surface where the function Rs(H) is the same everywhere. 9th International Particle Accelerator Conference IPAC2018, Vancouver, BC, Canada JACoW Publishing ISBN: 978-3-95450-184-7 doi:10.18429/JACoW-IPAC2018-WEPMF042 WEPMF042 2458 Co nt en tf ro m th is w or k m ay be us ed un de rt he te rm so ft he CC BY 3. 0 lic en ce (© 20 18 ). A ny di str ib ut io n of th is w or k m us tm ai nt ai n at tri bu tio n to th e au th or (s ), tit le of th e w or k, pu bl ish er ,a nd D O I. 07 Accelerator Technology T07 Superconducting RF spaced evenly between Hpk/N and Hpk. Then the operation looks as follows: Rav = AR (8) The averaging operator A is a positive lower-triangular matrix. To calculate the jth entry of the ith row (with 1 ≤ j ≤ i) of A, one should first separate the cavity surface into i sections Sj/i , each the union of the areas of the surface where the field H is approximately equal to Hj = j Hpk1/i. Then the integral in Eq. 6 can be split into a sum of integrals over the sections Sj/i: Rav,i = 1 ∫ | H |2 dS i ∑

Developing a Setup to Measure Field Dependence of BCS Surface Resistance

The temperature-dependent part of the microwave surface resistance of superconducting radio-frequency (SRF) cavities has been shown experimentally to depend on the strength of the applied magnetic surface field. Several theories have recently been proposed to describe this phenomenon. In this paper we present work on the development of a microwave cavity setup for measuring the field-dependence with an applied DC magnetic field.

Surface Analysis and Material Property Studies of Nb3Sn on Niobium for Use in SRF Cavities

Studies of superconducting Nb3Sn cavities and samples at Cornell University and Argonne National Lab have shown that current state-of-the-art Nb3Sn cavities are limited by material properties and imperfections. In particular, the presence of regions within the Nb3Sn layer that are deficient in tin are suspected to be the cause of the lower than expected peak accelerating gradient. In this paper we present results from a material study of the Nb3Sn layer fabricated using the vapour deposition method, with data collected using AFM, SEM, TEM, EDX, and XRD methods as well as with pulsed RF testing.

Niobium Impurity-Doping Studies at Cornell and CM Cool-Down Dynamic Effect on Q0

As part of a multi-laboratory research initiative on high Q0 niobium cavities for LCLS-II and other future CW SRF accelerators, Cornell has conducted an extensive research program during the last two years on impurity-doping of niobium cavities and related material characterization. Here we give an overview of these activities, and present results from single-cell studies, from vertical performance testing of nitrogen-doped nine-cell cavities, and from cryomodule testing of nitrogen-doped nine-cell cavities. We show that 2K quality factors at 16 MV/m well above the nominal LCLS-II specification of 2.7 × 10 can be reached reliably by nitrogen doping of the RF penetration layer. We demonstrate that the nitrogen furnace pressure is not a critical parameter in the doping process. We show that higher nitrogen doping levels generally result in reduced quench fields, with substantial variations in the quench field between cavities treated similarly. We propose that this can be explained by the reduced lower critical field Hc1 in N-doped cavities and the typical variation in the occurrence of defects on a cavity surface. We report on the results from five cryomodule tests of nitrogen-doped 9-cell cavities, and show that fast cooldown with helium mass flow rates above 2 g/s is reliable in expelling ambient magnetic fields, and that no significant change in performance occurs when a nitrogen-doped cavity is installed in a cryomodule with auxiliary components.

Understanding the Field Dependence of the Surface Resistance in Nitrogen-Doped Cavities

An important limiting factor in the performance of superconducting radio frequency (SRF) cavities in medium and high field gradients is the intrinsic quality factor and, thus, the surface resistance of the cavity [1]. The exact dependence of the surface resistance on the magnitude of the RF field is not well understood. We present an analysis of experimental data of LT1-3 and LT1-4, 1.3 GHz single-cell nitrogen-doped cavities prepared and tested at Cornell [2]. Most interestingly, the cavities display anti-Q slopes in the medium field region (i.e. Rs decreases with increasing accelerating field). We extract the temperature dependent surface resistances of the cavities, analyze field dependencies, and compare with theoretical predictions. These comparisons and analyses provide new insights into the field dependence of the surface resistance and improve our understanding of the mechanisms behind this effect.