D. Rubin, S.Isaacman, A.Long
March 17, 2005.

Dependence of luminosity on vertical alpha* (SCMATING 1)

Introduction

We compute the dependence of luminosity on SCMATING 1 (alpha *). We find that a 1% change in alpha* corresponds to a 10% change in specific luminosity, and that the optimum luminosity is achieved for Delta(alpha*)=0.01, (and not 0).

SCMATING 1 calibration

SCMATING 1 is a group element that varies quadrupoles near the IR to shift the beta minimum longitudinally. A change of 1 unit in SCMATING 1 corresponds approximately to Delta alpha* ~ 1. The shift in the position of the beta minimum is Delta(s)=(alpha)(beta*). If beta*=0.012m, then 1 unit of SCMATING 1 => Delta(s) = 1.2cm, etc.

Lattice

All calculations are in the standard cesr-c 12 wiggler lattice hibetainj_20040628_v01.lat

Model

The model is defined as follows:

Beginning with design optics, set SCMATING 1
Include long range parasitic beambeam interactions
Close pretzel, (zero horizontal differential displacement of beams using pretzing 13)
Close vertical, (zero vertical differental angle and displacement of beams using VNOSEING 1, VCROSING 5
Set horizontal, vertical, synchrotron tunes
Iterate closure and tune
Include beambeam interaction at IP
Compute alpha*
Begin tracking

Calibration

Alpha* is computed for the positron beam after all beambeam interactions are incuded, beams are in collision and tunes are set. The correspondence between alpha* and the value of the SCMATING 1 command is nominally one to one in the design lattice. In our model we find that the slope is unity but that there is a significant offset as shown in the plot

Luminosity

The dependence of luminosity on SCMATING 1 is shown here We find that the luminosity peaks for a SCMATING 1 command of 0.01 or a shift in alpha* of 0.01, and that the 0.01 shift in alpha corresponds to a 10% change in luminosity. Exploration of the dependence of luminosity on alpha on a coarser scale indicates that the peak at alpha=0.01 is unique.