unbunched long. schottky signals
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Page 1Schottky Signals
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:
frequencyf1
∆f
frev
2∆f n∆f
2frev 2f1 nfrev nf1
I(f)
frequency
(n-1)∆f
(n-1)frev
n∆f (n+1)∆f
nfrev
Overlap
Page 2Schottky Signals
Bunched long. Schottky Signals
• Time difference τ to the synchronous particle (frev) due to synchrotron motion of n=1…N particles:
• Schottky signal of the nth particle under phase modulation
– causes sidebands around each h frev for bunched beams
random amplitude
random phase
Lines may broaden due to spread of fs
Page 3Schottky Signals
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