Calculations of Emittance and Damping Time Effects in the SLC Damping Rings’ - .-x-r i

In a recent NDR machine experiment the transverse emittance was studied as a function of store time and tune. To explain the observed transverse emittance damping time constants, the magnetic measurement data of the longitudinal field of the bending magnets had to be taken intoaccount. The variation of the transverse emittances with tune due to misalignments and the associated anome lous~disper&ii is studied as well as the effect of synchro betatron coupling due to dispersion in the RF cavities. _Damping rings reduce the transverse phase space of electron and positron beams to suitably small values near the. injector so that the bunches can collide with high luminosity. The Stanford Linear Collider (SLC) operates at 120 Hz (60 Hz at long store) and electron bunches stay for about 2 (4) damping times in the North Damping Ring (NDR). Any deviation -from the design equilibrium emittance or design damping time may degrade the performance of the Collider. We recalculate the theoretically expected transverse damping time constants using the measured field of the bending magnet. Experimental data show a tune dependance of the emittance in the damping ring [l]. We investigate two potential sources of this tune dependence: (a) random misalignments of magnets which increase the emittance and disturb the lattice functions and (b) synchro betatron coupling caused by dispersion at the RF cavities. I. EMITTANCESAND DAMPING FOR DIFFERENT BENDING MAGNET MODELS -We compare hard edge (the field at the ends of the magnet rises from zero to the peak value discontinuously) and soft edge models using the magnetic measurement data of the dipole fringe fields. Table 1 contains the synchrotron integrals [2]. The longitudinal profile of the dipole fringe field reduces the second and the third as well as the fifth synchrotron integrals [3]. Figure 1 shows a half cell in the arc of the damping ring. The dipole field stretches out over the permanent sextupoles to the adjacent quadrupoles. The transverse damping time increases by about 12 % compared to the hard edge model. The rect ngular bending magnets with parallel pole faces cancel t i fclurth synchrotron integral in the hard It edge approximation. For the soft edge model, the fourth synchrotron integral becomes negative, the horizontal damping partition slightly larger than 1.0 and the horizontal damping time is about 1 % shorter than the vertical. l Work Supported by the Department of Energy Contract DE-AC03-76SF00515 II. EMITTANCE IN THE PRESENCE OF MISALIGNMENTS F We have simulated the effects of misalignment errors ‘-‘ on the equilibrium emittance and the damping partitions. Random misalignments were generated using gaussian distributions cutoff at f2u. Two cases were considered with_ rms values for the the various elements listed in Table 2. These values are reasonable based on the original design tolerances. ::. -40 -20 0 20 40 Length w.r.t. Center of BEND in [cm] Figure 1: Field of the Main Dipole in a DR Half-Cell Table 1. Beam parameters for the damping ring without errors and two different fringe field models Energy = 1.153 GeV Characteristic hard edge soft edge