From: Vladimir Shiltsev [shiltsev@fnal.gov]
Sent: Sunday, November 28, 2004 10:30 PM
To: Frank Zimmermann
Subject: RE: draft PAC2005 abstract on SPS BBLR studies

Frank,

I can not explain powers at all... my naive model says that kick K which drives resonance of the power n is about
I/gamma/(R+Asin(phi)) \approx (I/gamma)*A^n/R^(n+1). Speed of acquiring the amplitude is about S=dA/dN where dN=1/dQ=1/|Q-Qr|, while dA (max amplitude)=Kick/(Q^2-Qr^2)=Kick/dQ, so S is independent of dQ and S=Kick.
Lifetime 1/tau=S/A=(I/gamma)*A^(n-1)/R^(n+1).

Dependence 1/R^3 found at TeV says that n=2 (i.e taht half-integer resonance drives losses... I can hardly agree with that as n=7 order resonances seem to be dominating).

1/R^5 found at SPS says n=4 (fourth-otder resonance... why not n-6 or smth else

so, S (speed) must be tune dependent (isn't that natural) - but I don't know how to explain that and what is form of dependence.

Q to you: is 1/R^5 found without tuneshift compensation - y/n?

As for TEL results - R varied over less than order of magintude, so, 1/R^3 only fits losses in the range R=1mm (beam size) and R=5mm (p-pbar
distance)

VS

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