Subject: IP Modelling for BBI Compensation
From: "James A. Crittenden"
Date: Tue, 06 Jun 2006 10:09:39 -0400
To: Mike Billing , Dave Rice , David Rubin , mjf7 , Stu Peck , John Sikora , jth@LNS61.LNS.CORNELL.EDU, Jerry Codner , Sasha Temnykh , Maury Tigner

Since our BBI compensation scheme now incorporates compensation
for the main interaction at the IP, I checked the simulated
characteristics of the IP BBI more carefully. I found that
the two parameters, a coupling parameter and a number of
longitudinal slices were set to 1% and a single slice.

The vertical beam size of the strong beam (e+) at the IP
has quadratic contributions from the dispersion,
the radiation integral (about 1.5 microns), and this coupling
assumption. The simulation results I showed last Friday
were for a total size of 4.1 microns.

The operating value determined from the beta function and
the luminosity is 2.5 microns. I obtained this value for
the size in the simulation by reducing the assumed coupling
from 1.0% to 0.3%.

Current dependence for 1.0% coupling:
http://www.lns.cornell.edu/~critten/cesr/injection/notes/6jun06/bunch_1264
Dynamic aperture for 1.0% coupling:
http://www.lns.cornell.edu/~critten/cesr/injection/notes/6jun06/dynap_1264


Current dependence for 0.3% coupling:
http://www.lns.cornell.edu/~critten/cesr/injection/notes/6jun06/bunch_1334
Dynamic aperture for 0.3% coupling:
http://www.lns.cornell.edu/~critten/cesr/injection/notes/6jun06/dynap_1334

Of particular interest was the fact that the vertical beta blowup
compensation using the empirically determined values for the
compensation knobs improved for this more realistic simulation
of the IP parameters. That inspires confidence in the applicability
of the simulation:

1.0% coupling:
http://www.lns.cornell.edu/~critten/cesr/injection/notes/6jun06/bunch_1264/P004.html
0.3% coupling:
http://www.lns.cornell.edu/~critten/cesr/injection/notes/6jun06/bunch_1334/P004.html

The effect of this change in the assumed coupling on the current dependence of the
horizontal quantities and on the dynamic aperture was negligible.

I also checked the effect of increasing the number of longitudinal slices
from 1 to 6:

Current dependence for 0.3% coupling and 6 slices:
/home/critten/public_html/cesr/injection/notes/6jun06/bunch_1336
Dynamic aperture for 0.3% coupling and 6 slices:
/home/critten/public_html/cesr/injection/notes/6jun06/dynap_1336

No significant change in either the current dependence or the dynamic
aperture arising from this more detailed modelling of the IP
is observed.

Finally, I checked the off-energy dynamic aperture in the above studies
in order to address Sasha's concerns expressed during the meeting.
The dynamic aperture narrows from 7 to 4 sigma for a 3.6 sigma
offset in energy:

On-energy:
http://www.lns.cornell.edu/~critten/cesr/injection/notes/6jun06/dynap_1264/P019.html
Energy offset 0.3%, i.e. 3.6 sigma:
http://www.lns.cornell.edu/~critten/cesr/injection/notes/6jun06/dynap_1264/P020.html

This result is not significantly changed for the more accurate modelling of the IP.

The above results concern the proposed local BBI compensation method.
To recall from last Friday's talk, the Qtuning method yields a dynamic aperture
at this current level of 3 sigma. This narrows to 2 sigma for an energy offset
of 3.6 sigma.

All these calculations were done for our present operating lattice
but with the pretzel set to 2850, the operating value rather than
the design value of 3300.
It is reasonable to expect that the dynamic aperture can be
improved by optimizing the lattice for at the operating value of
the pretzel.

-- Jim
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James Crittenden                   Tel. (607) 255-9424
Wilson Synchrotron Laboratory      Fax  (607) 255-8062
Cornell University
Ithaca, New York 14853-8001
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