On October 9/10, 2005 MAP and EPT investigated the effect of VNOSEING 1 on the luminosity
from each bunch in operating conditions in a 9x5 configuration:
<a href=
"https://wiki.lepp.cornell.edu/cesr/bin/view/Bunch/BSMLog#October_2005"> MS 9/10 Oct 05</a>
VNOSEING 1 is a knob designed to vary alpha* and therefor the position of the beam waist.
Minimizing the function beta(s) = beta* - 2 x alpha* x S + gamma* x S^2,
one can derive
S(waist) = alpha*/gamma* = alpha* x beta* / (1 + alpha*^2 )
and
beta (waist) = beta* x ( 1 - alpha*^2/(1 + alpha*^2) )
Since the observed luminosity likely comes from the beam sizes at the waist rather than
those at the nominal IP, it is of interest to calculate the BBI effects on the position
of the waist and on the beam sizes at the waist.
I have performed such calculations for the lattice 4160_fromdlr4200 which was in
use at the time of the machine studies. Lattice characterists as seen by a test electron
are calculated for a given positron bunch current; each electron bunch sees a different
lattice because of the different distribution of parasitic crossings.
The horizontal and vertical electron tunes are held constant as a function of positron current by
compensating the BBI effects with the quad strengths.
<a href=
"http://www.lns.cornell.edu/~critten/cesr/injection/notes/21oct05/bunch_944">IP BBI on</a>
In order to distinguish the effect of the parasitic crossings alone, I have also performed
this calculation with the BBI at the IP turned off:
<a href=
"http://www.lns.cornell.edu/~critten/cesr/injection/notes/21oct05/bunch_943">IP BBI off</a>
Here is an admittedly subjective set of conclusions that can be drawn from this plethora of plots.
The variation of the following quantities are described with reference to a positron bunch
current varying between zero and 2 mA/bunch.
1) The horizontal crossing angle between the two beams decreases from 6.0 to 5.7 mrad, similarly
for all the bunches.
2) The vertical crossing angle decreases from 60 microradians by an amount ranging from zero to
50 microradians depending on the bunch.
3) The horizontal alpha* varies very differently bunch-to-bunch. At zero current it is about -0.15,
varying to zero for bunch 1 and to -0.4 for bunch 5.
4) The vertical alpha* varies similarly for all bunches, from -0.08 to -0.16.
5) The S position of the horizontal waist varies from -10 cm at zero current for all bunches to
zero at 2 mA/bunch for bunch 1 and in the opposite direction to -30 cm for bunch 5.
6) The S position of the vertical waist varies from -1 mm to -1.5 mm similarly for all bunches.
7) The horizontal beta* varies from 90 cm to 55-70 cm, depending on the bunch.
8) The vertical beta* decreases from about 1.2 cm to 1.0 cm similarly for all bunches.
9) The contribution to the beam size at the waist and at the nominal IP from the energy spread
is small (percent level), so the beam sizes are determined by the variation in beta function
and emittance.
10) The variation in beam size at the nominal IP and at the waist are fairly similar, with the
possible exception of bunch 5.
11) The horizontal beam size at the horizontal waist varies from 0.33 mm to about 0.30 mm
similarly for all bunches.
12) The vertical beam size at the vertical waist varies from 1.41 to 1.35 or 1.38 depending on
the bunch. The beam sizes of all bunches coincide at a particular value of positron bunch
current: 0.5 mA/bunch.
A brief look at such a calculation for another of the lattices used during the scan indicates
that this set of conclusions would be quite different. It appears that the lattice design process
does not constrain the above quantities at the level of their variation with positron bunch current.
========================================================
James Crittenden Tel. (607) 255-9424
Wilson Synchrotron Laboratory Fax (607) 255-8062
Cornell University
Ithaca, New York 14853-8001
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