Proceedings of IBIC2012, Tsukuba, JapanTUPB49ELECTRON CLOUD DENSITY MEASUREMENTS
USING RESONANT TE WAVES AT CESRTA∗
J.P. Sikora† , M.G. Billing, D.O. Duggins, Y. Li, D.L. Rubin,R.M. Schwartz, K.G. Sonnad, CLASSE, Ithaca, New York, USA
S. De Santis, LBNL, Berkeley, California, USA
Abstract

INTRODUCTION
In August 2012, four sections of test beam-pipe were assembled and installed in the CESRTA storage ring. Eachchamber is instrumented with a Time Resolved Retarding
Field Analyzer (TR-RFA) to evaluate the mitigation properties of the different geometries and surface coatings. The
TR-RFA detects the flux of cloud electrons into the beampipe wall [1].
There are two different cross sections of round beampipe, one smooth and the other with triangular grooves on
the top and bottom inside surfaces as shown in Fig. 1. With
these two cross sections, one pair has been made with asurface of bare aluminum. The other pair have a coating ofTitanium Nitride (TiN) on the inner surface. The chambers
are assembled together and when installed, each chamber
will be centered in one of four chicane dipole magnets.
Having established the basic technique for the resonant
TE wave measurement of EC density [2, 3, 4, 5], we investigated the possibility of using this technique to makeindependent EC density measurements on each of the four
test chambers. Each resonance has its own characteristic
standing wave pattern and the TE Wave measurements are
localized to the region of the standing wave. So the choice∗ This work is supported by the US National Science Foundation PHY0734867, PHY-1002467 and the US Department of Energy DE-FC0208ER41538, DE-SC0006505.
† jps13@cornell.edu

Figure 1: A cross section of grooved beam-pipe is shown
above with a Time Resolved RFA assembly on the uppersurface.
of the resonances used in a measurement determines wherethe cloud is sampled along the length of the beam-pipe.

BENCH MEASUREMENTS
A bead pull is a common technique for measuring thefields in resonant cavities [6]. If a small dielectric bead is
positioned in a cavity, there will be a shift in its resonant
frequency that is proportional to E 2 of the standing wave
at the location of the bead.
Previous bench measurements had been made using various combinations of grooved and smooth sections of beampipe. These measurements showed that the first two resonances were mostly confined to a grooved section if it is between smooth sections of beam-pipe [4]. This is due to thefact that the cutoff frequency of the grooved pipe is lower
than that of the smooth pipe. This result influenced thedecision to alternate grooved and smooth beam-pipe whenassembling the actual vacuum chambers.

Bead Pull of the Assembly
Before it was installed in the storage ring, a bead pullmeasurement was made on the four chamber assembly(Fig. 2). For the measurement, short sections of smoothbeam-pipe were added to the ends of the assembly andthe flanges at the far ends had aluminum plates covering
the openings in order to produce reflections. A 0.3 cm3nylon bead was positioned inside the beam-pipe using athin mono-filament fishing line. At each position along thelength of the beam-pipe, the frequency shift was measured
by recording the peak response on a spectrum analyzer.
The electrodes of three Beam Position Monitor (BPM)flanges in the assembly were used to couple microwaves inISBN 978-3-95450-119-9
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1c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○The Cornell Electron Storage Ring has been reconfigured as a test accelerator (CESRTA) with beam energies
ranging from 2 GeV to 5 GeV of either positrons or electrons. Research at CESRTA includes the study of thegrowth, decay and mitigation of electron clouds in the storage ring. Electron Cloud (EC) densities can be measured
by resonantly exciting the beam-pipe with microwaves
where standing waves are established between discontinuities. The EC density that is within the standing waves willchange the beam-pipe’s resonant frequency. When the EC
density is not uniform, it is especially important to know
the standing wave pattern in order to know exactly wherethe EC density is being sampled by the microwaves. We
present our current understanding of this technique in thecontext of new test sections of beam-pipe installed in August 2012. This includes bench measurements of standing
waves in the beam-pipe, simulations of this geometry andrecent EC density measurements with beam.

TUPB49

Proceedings of IBIC2012, Tsukuba, Japanc 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Figure 2: A sketch of the L3 chamber assembly is shown
above. For the bead pull measurement, 63 cm extensions
were added at either end with shorting plates on the end
flanges.
and out of the chamber. For simplicity, only single buttons
were used. For example, a vertical measurement would usea button on the top of the beam-pipe for excitation and abutton on the bottom for receiving. For each BPM andplane, six to eight resonances were chosen from the spectrum for a measurement series.
Some of the bead pull measurement results are shown inFigs. 3, 4 and 5. Figures 3 and 4 used horizontal excitation
and receiving at the BPMs indicated. As expected fromprevious bench measurements with grooved beam-pipe, thestanding waves were localized in the grooved sections near
1.95 GHz. The two frequencies correspond to a one-halfand a two-halves wavelength resonance along the length ofthese sections.
A response in the smooth chambers is shown in Fig. 5,
where vertical buttons were used for excitation and receiving. The standing waves of the two frequencies are notas well confined, in that there is significant field in bothsmooth chambers and to a lesser extent in the TiN groovedchamber. So extracting separate EC densities for the twosmooth chambers will not be as straightforward as withthe grooved chambers. Measurements would need to bemade at both frequencies shown in Fig. 5, as well as one
frequency from each of the plots of Fig. 3 and 4. Thesemeasurements, when combined with a bit of linear algebra,
should give the separate EC densities for the four chambers.
In order to understand why the smooth sections hadstanding waves within them, we made careful measurements of the inner diameters. Both the flanges and theextrusions have a nominal inner diameter of 89 mm. It
turned out that the smooth beam-pipe aluminum extrusions
had an inner diameter about 0.5 mm larger than the machined flanges. So the smooth beam-pipe, with a cutoff frequency roughly 10 MHz lower than the flanges surroundingit, could also contain a local resonance.

DATA WITH BEAM
In an accelerator, the presence of an electron cloud
will shift the frequency of the resonance according toEq. 1 [7, 8, 9]. This, along with some simplifying assumptions: a train of bunches will produce a periodic EC density; the duration of the cloud is long compared to theFigure 3: A bead pull measurement shows that the standing
waves of two resonances near 1.9 GHz are primarily in theTiN grooved chamber.

Figure 4: The bare aluminum grooved chamber also shows
two resonances.

Figure 5: Resonances in the smooth chambers are mutuallycoupled and very close in frequency.
damping time of the resonance and that external magnetic
fields can be ignored – allows a calculation of the EC
density from the phase modulation sidebands that are produced [2].
Z
ne E02 dV
∆ω
e2
VZ=.
(1)
ω2ε0 me ω 2
E02 dVV

The TE wave data taking system in L3 was reconfigured
to make use of the information from the bead pull that sug-ISBN 978-3-95450-119-92

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Proceedings of IBIC2012, Tsukuba, Japangested 13 resonances of interest. The modulation sidebands
from four of these resonances were used to calculate the EC
densities given in Fig. 6. The frequencies correspond to
the n=1 and n=2 resonances of the bare aluminum and TiNgrooved chambers. As expected, the aluminum grooved
chamber shows a higher EC density than TiN. Also, theEC densities for both resonances (n = 1, 2) are in good
agreement in the TiN chamber. The agreement between theresonances is not as good for the bare aluminum grooved
chamber, but they are nevertheless within 10% . Furtheranalysis is needed to compare the two chambers since theamount of synchrotron light in the aluminum chamber isless than in the TiN chamber. This needs to be quantified.

TUPB49Figure 7: The simulation of a resonance in grooved chamber between two smooth chambers is shown near the n=1
resonance.
and simulation will continue in parallel in order to improve
our understanding of this technique.

We would like to thank to Seth Veitzer at Tech-X Corp.
and the VORPAL Development Team for their help withVORPAL simulations. We are also grateful for the supportof Yulin Li and the vacuum group at Cornell in setting up
bead pull measurements on beam-pipe.
Figure 6: Data taken with a 10 bunch train of 5.3 GeV
positrons with currents up to 6 mA (9.6 × 1010 particles)
per bunch.

SIMULATION OF A GROOVED
BEAM-PIPE
In addition to bead pull measurements, there has been aparallel effort to use simulations of the TE wave resonance.
This will become increasingly important with more complex beam-pipe geometries, including the round groovedpipe. Figure 7 shows the result of a VORPAL [10] simulation of grooved beam-pipe with smooth beam-pipe adjacent
to it.
To find resonances, the driving frequency is changed andthe magnitude and phase outputs of the simulation are examined. The resonant frequency will be that in which themagnitude is at a maximum and phase difference from thedrive phase is close to zero or ±π.

CONCLUSIONS AND FUTURE WORKThe use of bead pull measurements on beam-pipe has
greatly improved our understanding of localized resonances. The independent measurement of EC densities inchambers less than a meter long seems to be straightforward when lower cutoff frequencies allow standing waves
to be set up. This method is unique in that it measures theEC density in the volume of the beam-pipe, rather than theflux of electrons into the beam-pipe wall. Work on analysis

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[2] J. P. Sikora, et al., “ Resonant TE Wave Measurements ofElectron Cloud Densities at CESRTA”, in Proc. of IPAC’11,San Sebastián, August 2011, TUPC170, p.1434, (2011).
[3] S. De Santis, et al.,“Analysis of Resonant TE Wave Modulation Signals for Electron Cloud Measurements”, in Proc.
of IPAC’12, New Orleans, May 2012, MOPPR073, (2012).
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[5] J.P. Sikora, et al., “TE Wave Measurement and Modeling”,
in Proc. of ECloud12 (CERN Yellow Paper), La Biodola,Italy, June 2012, (2012).
[6] L.C. Maier and J.C. Slater,“Field Strength Measurement inResonant Cavities”, Journal of Applied Physics 23, p.68,(1952).
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[8] M. A. Heald and C. B. Wharton, Plasma Diagnostics withMicrowaves, John Wiley and Sons, New York (1965).
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ISBN 978-3-95450-119-9
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3c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○ACKNOWLEDGEMENTS