**Frequency measurement procedure of 350 MHz, =0.175, 2-gap spoke
cavity**

Tsuyoshi Tajima and Alan Shapiro

This memorandum describes how to measure the resonance frequency of the
spoke cavity, but most of the principles and methods can be applied to a
general measurement. It is assumed that a person who can use a network
analyzer will do this measurement with a network analyzer. In Appendix
A2, measurements and results of the 340 MHz, , 2-gap spoke cavity loaned
from ANL are shown as a reference.

# Word Definition

Penetration Distance of a pick-up probe from virtual wall, i.e., the
wall when there is no port. For loop probe, the distance of the furthest
tip of the loop from the virtual wall.

# Procedure

1.  Using an electric coupling on the beam axis.

    1.  Setup of the network analyzer

-   Calibrate the network analyzer and the measurement line after
    connecting an appropriate cable that works at 350 MHz. Since only
    S11 measurement will be done, S11 one-port calibration is enough.

-   Set measurement as s11.

-   Set format to Log-mag.

-   Set the center frequency at 350 MHz and span of 5 MHz. (This span
    should be narrowed to 1 MHz after you find the resonance.)

    1.  Measurement

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-   Prepare an antenna such as the one shown in Fig. A2-1 that
    penetrates about 15 mm into the cavity. The antenna diameter should
    be as small as possible to reduce the perturbation (See Appendix
    A1). When we tested a similar cavity, a convenient size for an N
    connector was 0.064 inches (1.6 mm). If possible, the smaller the
    better.

-   Set a temperature sensor on a cavity body such as shown in Fig. A2-4
    and monitor and log the temperature every time you measure the
    frequency.

-   Measure the frequency, s11 with a span of 1 MHz and auto-scale, and
    cavity temperature. If you change measurement format to Smith chart
    or Polar, you can check if the coupling is over or under couple
    \[2\]. If the signal is weak and the frequency changes, use
    "average" function to get a more accurate frequency. Figure A2-5
    shows an example of what the network analyzer will look like.

-   Shorten the antenna penetration by 3 mm and repeat the measurement.

-   Repeat the measurement by shortening the antenna 3 mm each time
    until the frequency does not change more than 20 kHz. When the
    penetration gets close to zero, you may have to shorten the antenna
    1 -- 2 mm since the signal gets very weak rapidly.

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-   If you plot frequency against penetration, you will get a plot
    similar to Fig. A2-7. Make sure that the frequency gets higher with
    less penetration and approaches to a fixed value.

    1.  Data needed

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-   Measurement date, time and location.

-   The name of the person who did the measurement

-   A table that shows cavity temperature, antenna diameter, antenna
    penetration, frequency (up to 3 digits after decimal point, i.e., 1
    kHz), and s11.

-   Plot of the frequency as a function of antenna penetration. (See
    Fig. A2-7)

-   If it is easy, take data on the temperature dependence similar to
    Fig. A2-6. If not easy, use --7.9 kHz/C to determine the frequency
    at 21 C.

-   Determined frequency (See below).

    1.  Determination of the frequency

> Determine the frequency at 21 C as follows.

-   Take the data with least measurable coupling

-   Add the frequency shift by the temperature difference, i.e.,
    (measurement temperature -- 21) x (rate per degree C such as "-- 7.9
    kHz/C").

    1.  Iteration with trimming of the cylinder length

> If the frequency is different from the requirement, i.e., 349.30 0.2
> MHz at 21 C, you have to trim the cylinder length. (This assumes that
> the cylinder is made such that you can trim to adjust the frequency.)
>
> For this iteration, you need not take the same set of data. You can
> use the shortest antenna with which you can measure the frequency and
> measure the frequency once or twice.

2.  Using a magnetic coupling around the spoke[^1]

This is an alternative to the measurement described above. This is
useful when you do the bead-pull measurement using the beam axis.

You can measure the frequency using the magnetic coupling by inserting a
loop coupler through a radial port. Since there is magnetic field in the
azimuthal direction of spoke, if the loop faces normal to this field,
one can pick up the signal.

1.  Setup of the network analyzer

> This is the same as Section 1.1.

2.  Measurement

> This is similar to Section 1.2 except the following. The loop should
> face the proper direction, i.e., normal to the magnetic field. Also,
> the loop probe should be made such that you can retract it. Figure
> A2-2 shows an example of such a probe. Figure A2-8 shows a frequency
> change as a function of the penetration. Note that the frequency does
> not change as much as it did with the axial antenna due to less
> perturbation.

3.  Data needed

This is the same as 1.3.

4.  Determination of frequency

> This is the same as 1.4.

5.  Iteration with trimming of the cylinder length

> This is the same as 1.5.

# References

\[1\] J. C. Slater, "Microwave Electronics," p. 81, D. Van Nostrand,
Inc. (1950).

\[2\] H. Padamsee et al., "RF Superconductivity for Accelerators," Fig.
8.7 on p. 160, John Wiley and Sons, Inc. 1998.

# Appendices

**A1. Perturbation with a metal object in the cavity.**

The frequency changed due to a metal inside the cavity is described as
follows \[1\].

$f^{2} = f_{0^{2}}\left\{ 1 + \int_{}^{}{(H_{0^{2}} - E_{0^{2}})\text{dv}} \right\}$
, (A.1)

where *f~0~* is the resonant frequency without an object inside the
cavity. The second term in the brackets is an integral over the volume
removed by the object. As you can see in (A. 1), if you put a bead on
the beam axis in the acceleration gap, frequency becomes lower since
there is no magnetic field. In other words, you can measure the relative
field strength by measuring the frequency shifts at different locations
of the bead. This is so-called a bead-pull method.

**A2. Measurements on the 340 MHz, = 0.29, 2-gap ANL spoke cavity**

Since we have a similar cavity that was loaned from Argonne National
Laboratory (ANL), we tried to measure this cavity to get some data and
write this document.

Table 1 summarizes the frequency shifts with temperature change. The
data on the frequency at 4 K was taken from the data during the cold
temperature test on 3/29/01. The rate of change around room temperature
was measured by placing the cavity outside the lab, i.e., colder than
inside the room. Since the temperature was not precisely controlled,
this data may be quite different from that obtained using a temperature
controlled room.

Table 1: Frequency shift of ANL 340-MHz, 2-gap spoke cavity.

  ----------------------------------------------------------- -----------
  Frequency shift from 295 K (22 C) in air to 4 K under       \+ 402 kHz
  vacuum[^2]                                                  

  Frequency shift around room temperature                     -7.9 kHz/C
  ----------------------------------------------------------- -----------

![](media/image1.png){width="4.300694444444445in"
height="2.573611111111111in"}

Fig. A2-1: Antenna-type probe connected with an N-type connector. This
will be inserted through an axial port.

![](media/image2.png){width="5.997916666666667in"
height="2.951388888888889in"}

Fig. A2-2: Loop-type probe. The loop size is an ellipse of 50 mm x 23
mm. This will be inserted through a radial port. To obtain maximum
signal, the rotation angle of the loop should be such that the cavity
magnetic field lines are normal to the loop. This loop can be retracted
using the bolt and nuts.

![](media/image3.png){width="4.7375in" height="3.5430555555555556in"}

Fig. A2-3: Frequency measurement setup. S11 measurement with a network
analyzer using an antenna probe inserted through an axial port. Other
ports should be properly closed with an aluminum foil or a blank flange.

![](media/image4.png){width="5.058333333333334in"
height="3.7576388888888888in"}

Fig. A2-4: Measurement with an antenna-type probe inserted through an
axial port. A temperature sensor is taped on an outside surface near the
spoke with a copper tape. Temperature of the cavity has to be monitored
since the resonant frequency changes with temperature as shown in Fig.
A2-6.

![](media/image5.png){width="5.260416666666667in"
height="4.188888888888889in"}

Fig. A2-5: A S11 plot using loop-type probe inserted through the side
port.

![](media/image6.wmf)Fig. A2-6: Temperature dependence of the frequency.

![](media/image7.wmf)Fig. A2-7: Frequency as a function of antenna
penetration.

![](media/image8.wmf)Fig. A2-8: Frequency as a function of loop
penetration.

[^1]: This measurement might not be carried out well with LANL 2-gap
    spoke cavities since the diameter of the radial port is large and
    the electro-magnetic field does not attenuate rapidly in the port.

[^2]: This includes the frequency shifts due to air, evacuation and
    cooldown.