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Unbunched long. Schottky Signals. 2 particles with different f rev : f 1 = f rev +Δf Spectral density of the n th -band of N particles with random initial phase and a revolution frequency spread f rev +Δf /2 :. (n-1)∆f. I(f). n ∆f. n∆f. (n+1)∆f. ∆f. 2∆f. (n-1) f rev. f rev.
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Unbunched long. Schottky Signals • 2 particles with different frev: f1=frev+Δf • Spectral density of the nth-band of N particles with random initial phase and a revolution frequency spread frev+Δf/2: (n-1)∆f I(f) n∆f n∆f (n+1)∆f ∆f 2∆f (n-1)frev frev nfrev 2frev 2f1 nfrev nf1 f1 frequency Overlap frequency
Bunched long. Schottky Signals • Time difference τ to the synchronous particle (frev) due to synchrotron motion of n=1…N particles: • Schottkysignal of the nth particle under phase modulation • causessidebands around each h frevfor bunched beams random amplitude random phase Lines may broaden due to spread of fs
Ion Schottky Signals at the LHC • Observed stable, high level Schottky signals at all ion runs! • Plan to modify the Schottky pickup using the sum signal port long. Schottky signals
