D. Rubin, S.Isaacman, A.Long, & J. Robinson
March 7, 2005.

Correcting IR coupling with Compensating Solenoid and Tune Shift Limit

Introduction

The energy dependence of the solenoid compensation with the Phase III IR optics dilutes the vertical equilibrium emittance, compromises off energy dynamic aperture and limits the beambeam tune shift parameter. See D.Rubin/3/7/05 for details. We find that the energy dependence can be very nearly eliminated by including a compensating solenoid in a configuration very similar to that developed for the DAPHNE collider. In our model, the CESR compensating solenoid is located in the straight adjacent to the IR quad cryostat. The integrated field of the solenoid is set equal in magnitude but of opposite sign to the integrated field of the CLEO solenoid over half if its length. We suppose that the compensating solenoid has a length of 0.95m, extending between 3.75 and 4.7m from the IP, and with Bz~1.85T. (We assume that the field of the CLEO solenoid is 1T with effective length 3.51m.)

Design Constraints

Having fixed the strength of the compensating solenoid, four skew variables are required to guarantee that the transport from machine arc to interaction point is block diagonal. We explore two possibilities, one in which the rotation angle of the permanent magnet (Q00) is fixed and another in which it is a free parameters. (Access to Q00 for the purpose of realignment requires removal of the superconducting magnets and some weeks of down time.)

Fixed angle Q00

We begin with the fixed Q00 solution. We use the superimposed skew windings on sc_Q01 and sc_Q02, and skew quads sk_Q02 and sk_Q04 as the four skew variables. The strengths of the skew quads are shown in the table. The lattice that incorporates this compensation scheme is /home/dlr/lat/bmad_c_020305.lat.

Skew Quadrupole       k
 sc_sk_q01           1.154e-01
 sc_sk_q02           3.044e-02
 sk_q02             -2.518e-02
 sk_q04              7.628e-03

The transformation of coupling parameters through the compensation region for the lattice bmad_c_020305 are computed and can be compared with the transformation in the standard IR . The C12 and C22 elements of the coupling matrix are plotted. C12 corresponds to the ratio of vertical to horizontal emittance, and c22 corresponds approximately to the tilt of the beam. We find that the variation in c12 in the IR with compensating solenoid is significantly smaller than in the standard IR. The c22 parameter indicates the tilt of the beam first in one direction through the compensating solenoid and then back the other way in the CLEO solenoid.

The off energy dynamic aperture in the optics with compensating solenoid, da_bmad_c_020305 is significantly more expansive than in the standard cesr-c optics. (Dashed lines indicate physical aperture for corresponding energy.)

Optimized Q00 tilt angle

We now imagine that the angle of the permanent magnet is one of the four skew variables available to satsify the decoupling constraint. The superimposed skew windings on sc_Q01 and sc_Q02, and skew quad sk_Q02 complete the quartet. The strengths of the skew quads and the tilt angle of Q00 are shown in the table. The lattice that incorporates this compensation scheme is /home/dlr/lat/bmad_c_q0_040305.lat.

Skew Quadrupole       k
 sc_sk_q01          -7.237e-02
 sc_sk_q02           1.551e-01
 sk_q02              3.294e-04

 Q00(tilt)           33.325mrad (1.9 degrees)

The transformation of coupling parameters through the compensation region for the lattice bmad_c_ir_q0_040305 show essentially no evolution of c12 throughout the insert.

The off energy dynamic aperture in the optics with compensating solenoid, and optimally tilted Q00 da_bmad_c_q0_040305 approaches the physical aperture.

Beam beam limit

The current dependent of the luminosity and vertical tune shift parameter are computed with the weak-strong beam beam simulation for four configurations:

standard cesr-c phase III optics - hibetainj_200406287_v01.lat
solenoid off optics - bmad_hibetainj_nosol_v01.lat
compensating solenoid but fixed Q00 tilt (theta = 4.2 deg) - bmad_c_020305.lat
compensating solenoid and optimally tilted Q00 (theta = 1.9 deg)

and summarized in the plots of luminosity and tuneshift vs current. We also plot luminosity and tuneshift comparing only the cesr-c phase III optics and the optics with anti-solenoid and permanent magnet tilted 1.9deg. In the optics with compensating solenoid and q0 tilted to 1.9 degrees, we very nearly achieve the pristine solenoid off luminosity and a specific luminosity that is nearly double standard cesr-c.

Beam size

We also determine the vertical beam size and even better vs current as part of the beam beam simulation. Extrapolation to zero current suggests that the single equilibrium beam size is significantly smaller in the solenoid off optics than in the cesr-c phase III optics.

Conclusion

The beambeam tune shift in the cesr-c phase III optics is limited by the energy dependence of the solenoid compensation. With the implementation of a compensating solenoid (length ~95cm and B-field ~1.85T), placed in the straight reserved for the round beam quad, (3.75 to 4.7m from the IP), and realignment of the permanent magnet (Q0) quadrupole tilt angle from 4.5 to 1.9 degrees, the solenoid compensation is very nearly energy independent. The beambeam simulation indicates that in such a configuration we achieve a vertical tuneshift of ~0.04.