Chromaticity Measurements Using Phase Modulated RF and Vector Signal Analyzers
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.
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- Resource Type:
- Technical Report
- Research Org:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
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- Country of Publication:
- United States
- 43 PARTICLE ACCELERATORS; AMPLITUDES; BESSEL FUNCTIONS; BETATRONS; MODULATION; RESOLUTION; SYNCHROTRONS; VECTORS; Accelerators
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