D. Rubin, S.Isaacman, A.Long
May 20, 2005. (updated May 20, 2005)

Lattice with reduced momentum compaction

Introduction

In order to explore the dependence on bunch length and synchrotron tune we introduce an artificial element to adjust momentum compaction without effecting optics. A first order taylor element with zero length is introduced at L3. The nonzero matrix elements are R(i,i)=1, and R(5,6) = 6. The value of R(5,6) was chosen so that when Qz=0.049, sigma_l=13.3mm. (When R(5,6)=0, sigma_l=13.2mm with Qz=0.089.) Alternatively, if Qz=-0.089, sigma_l=7.3mm. We first consider the effect of bunch length. We set Qz=0.089, (the standard for CESR-c) so that sigma_l=7.3mm.

Model

The lattice is hibetainj_20040628_v01_dl6.lat. It is identical to hibetainj_20040628_v01.lat with the addition of the taylor element at L3.

Simulation

The results of the simulation are shown below. The luminosity in the lattice with R(5,6)=6 (hibetainj_20040628_v01_dl6), sigma_l=7.3mm, is compared with standard cesr-c (hibetainj_20040628_v01) and cesr-c no solenoid (bmad_hibetainj_nosol_v01), both with sigma_l=13.2 mm. The horizontal and vertical tunes are (Qx=0.532,Qy=0.594). In all cases the synchrotron tune is -0.089.

The zero current beam size is smallest with wiggler off, yielding biggest tune shift parameter at lowest current. Beyond 1.8mA, the beambeam dynamics of the longer bunches limit tuneshift with solenoid off. Meanwhile, in the short bunch lattice, the tuneshift continues to grow. Presumably it is some kind of synchrobetatron resonance related to the crossing angle, finite bunch length that limits tune shift in the solenoid off lattice. Where that effect is ameliorated, tune shift increases further. In the solenoid on, long bunch case, we get hit by big bunch at low current and synchrobetatron resonances at higher current.

Alternatively, in the reduced momentum compaction optics we can reduce synchrotron tune until the bunch length remains is the same as in the standard cesr-c conditions, namely, 13.3mm. This corresponds to Qz=0.049. The results are shown below. With the lower synchrotron tune, the tune shift saturates at an even higher bunch current than with the short bunch. At low current, low synchrotron tune with long bunch gives the same specific luminosity as the high synchroton tune with the long bunch.