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Two-port CW measurements on RF cavities: Notes on self-consistency assessment and indirect methods

Walter H. Hartung, Wei Chang, Sang-Hoon Kim, Taro Konomi, Ting Xu

Abstract

In the case of a radio-frequency (RF) cavity with a mismatched input coupler, a direct calculation of the power dissipation in the cavity and the intrinsic quality factor from continuous-wave (CW) measurements may have uncertainty due to systematic errors. Formulae for an indirect calculation of these quantities are derived for the case of a cavity with two couplers of fixed coupling strength. In this approach, the signal from the pickup coupler is used to infer the amplitude of the "emitted wave" from the input coupler. A graphical method for self-consistency assessment is evaluated. The impact of frequency offsets is considered. Applications of these methods are presented, drawing on cold tests of superconducting cavities produced for the Facility for Rare Isotope Beams.

Two-port CW measurements on RF cavities: Notes on self-consistency assessment and indirect methods

Abstract

In the case of a radio-frequency (RF) cavity with a mismatched input coupler, a direct calculation of the power dissipation in the cavity and the intrinsic quality factor from continuous-wave (CW) measurements may have uncertainty due to systematic errors. Formulae for an indirect calculation of these quantities are derived for the case of a cavity with two couplers of fixed coupling strength. In this approach, the signal from the pickup coupler is used to infer the amplitude of the "emitted wave" from the input coupler. A graphical method for self-consistency assessment is evaluated. The impact of frequency offsets is considered. Applications of these methods are presented, drawing on cold tests of superconducting cavities produced for the Facility for Rare Isotope Beams.
Paper Structure (33 sections, 58 equations, 13 figures, 2 tables)

This paper contains 33 sections, 58 equations, 13 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Background
  3. CW Measurement Basics
  4. RF Power and Field Level Calibration
  5. CW Analysis
  6. Direct Method Using Pf - Pr - Pt
  7. Indirect Method Using Pt/Pf: Brute Force Derivation
  8. Indirect Method Using Pt/Pf: Emitted Wave Derivation
  9. Indirect Method: Additional Formulae, Comments
  10. Graphical Assessment Method: Derivation
  11. Graphical Assessment Method: Vertices and Limiting Cases
  12. Weak Input Coupling
  13. Unity Input Coupling
  14. Strong Input Coupling
  15. Detuning
  16. ...and 18 more sections

Figures (13)

  • Figure 1: The "Duality Triangle." In CW measurements, the calculated values of $|S_{11}|$ and $|R_{21}|$ should fall on the lower or upper green line segments.
  • Figure 2: Calculated scattering parameters as a function of normalized drive frequency for a cavity with $Q_0 = 10^3$: (a) $|S_{11}|$ and (b) $|R_{21}|$.
  • Figure 3: (a) Polar plot of $S_{11}$ and (b) curves traced out in the $|S_{11}|$-$|R_{21}|$ plane as a function of drive frequency. (c) Polar plot of $S_{11}$ and (d) curves traces out in the $|S_{11}|$-$|R_{21}|$ plane as a function of $\beta_1$.
  • Figure 4: CW measurements on FRIB HWRs as a function of loop phase: (a) polar plot of $S_{11}$ and (b) $|S_{11}|$ vs $|R_{21}|$ at 2 different bath temperatures (S53-028, December 2017); (c) polar plot of $S_{11}$ and (d) $|S_{11}|$ vs $|R_{21}|$ for 3 different coupler positions (S53-121, October 2018).
  • Figure 5: Calculated $Q_0$ values via the indirect method as a function of (a) relative detuning in parts per billion and (b) detuning normalized to the bandwidth $\Delta f$, with an actual $Q_0$ of $2 \!\cdot\! 10^{9}$; black line: $Q_0$ calculated via the direct method.
  • ...and 8 more figures