Difference: ClicAverageTheory (7 vs. 8)

Revision 810 Sep 2012 - FrancisCullinan

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META TOPICPARENT name="ClicBpm"

Theoretical Investigation of Multiple Bunch Signals

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  It can be seen that in both cases, the dominant frequency in the spectrum is at 15 GHz. The signal tends to being periodic at the bunching frequency and oscillates at the cavity resonant frequency between bunches. The extra harmonics of the bunching frequency arise from the sawtooth-like variation in the signal amplitude and there is extra substructure to each peak coming from the start and end of the signal. In the second case, the resonant frequency is strong enough and far enough from an exact multiple of the bunching frequency to be resolved in the spectrum.
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Down-Mixed Signals

The same thing can still be seen with the down-mixed signals. The dominant frequency is now at the nearest multiple of the bunching frequency (15 GHz) minus the local oscillator frequency (14.8 GHz).

 

Mathematical Description

Assuming a uniform train of identical bunches with a single offset and no tilt, the signal coming from the first resonant dipole mode excited in a cavity beam position monitor (BPM) over time t, is given by

 
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