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Title: Chromaticity Measurements Using Phase Modulated RF and Vector Signal Analyzers

Abstract

Chromaticity measurements are usually done by changing the energy of the beam by a known amount and measuring the change in betatron tune with a spectrum analyzer. The energy change is done by adjusting the RF frequency. The change in RF frequency is made large enough so that the change in betatron tune can be seen. If synchrotron motion is present in the beam, then measuring the change in betatron tune can be difficult. This note will outline a method to measure the change in betatron tune by phase-modulating the RF and measuring the phase modulated betatron spectrum Extremely small resolution bandwidths are available on modern vector signal analyzers. A small resolution bandwidth is equivalent to measuring the chromaticity many times and averaging the results. This would permit much smaller shifts in betatron tunes to be measured. The phase-modulated signal consists of sidebands whose amplitudes are given by Bessel functions. The complication of the Bessel functions can be removed if the vector signal analyzer is capable of phase demodulation. The sign of the chromaticity can be determined by observing the modulation spectrum at both betatron sidebands.

Authors:
;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
984578
Report Number(s):
FERMILAB-PBAR-NOTE-656
TRN: US1005993
DOE Contract Number:
AC02-07CH11359
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; AMPLITUDES; BESSEL FUNCTIONS; BETATRONS; MODULATION; RESOLUTION; SYNCHROTRONS; VECTORS; Accelerators

Citation Formats

McGinnis, Dave, and /Fermilab. Chromaticity Measurements Using Phase Modulated RF and Vector Signal Analyzers. United States: N. p., 2001. Web. doi:10.2172/984578.
McGinnis, Dave, & /Fermilab. Chromaticity Measurements Using Phase Modulated RF and Vector Signal Analyzers. United States. doi:10.2172/984578.
McGinnis, Dave, and /Fermilab. Fri . "Chromaticity Measurements Using Phase Modulated RF and Vector Signal Analyzers". United States. doi:10.2172/984578. https://www.osti.gov/servlets/purl/984578.
@article{osti_984578,
title = {Chromaticity Measurements Using Phase Modulated RF and Vector Signal Analyzers},
author = {McGinnis, Dave and /Fermilab},
abstractNote = {Chromaticity measurements are usually done by changing the energy of the beam by a known amount and measuring the change in betatron tune with a spectrum analyzer. The energy change is done by adjusting the RF frequency. The change in RF frequency is made large enough so that the change in betatron tune can be seen. If synchrotron motion is present in the beam, then measuring the change in betatron tune can be difficult. This note will outline a method to measure the change in betatron tune by phase-modulating the RF and measuring the phase modulated betatron spectrum Extremely small resolution bandwidths are available on modern vector signal analyzers. A small resolution bandwidth is equivalent to measuring the chromaticity many times and averaging the results. This would permit much smaller shifts in betatron tunes to be measured. The phase-modulated signal consists of sidebands whose amplitudes are given by Bessel functions. The complication of the Bessel functions can be removed if the vector signal analyzer is capable of phase demodulation. The sign of the chromaticity can be determined by observing the modulation spectrum at both betatron sidebands.},
doi = {10.2172/984578},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Feb 16 00:00:00 EST 2001},
month = {Fri Feb 16 00:00:00 EST 2001}
}

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