Transverse Coupled Bunch Mode Growth Due to Photoelectron Trapping in the Cesr Vacuum Chamber

An anomalous damping or growth of transverse coupled bunch modes is observed in CESR. The growth rates and tune shifts of these modes are a highly nonlinear function of current. The effect is associated with the operation of the distributed ion pumps and disappears when the pumps are not powered. We show that this effect is due to the presence of electrons trapped in the CESR chamber by the field of the dipole magnets and the electrostatic leakage field of the distributed ion pumps. Photoelectrons are introduced into the chamber by synchrotron radiation and can be ejected from the chamber by the passage of an e or e bunch. The transverse position of the beam thus modulates the trapped photoelectron charge density, which in turn deflects the beam, creating growth or damping and a tune shift for each coupled bunch mode. We have simulated this process numerically. 1 ANOMALOUS INSTABILITY 1.1 Distributed ion pumps CESR contains distributed ion pumps (DIPs) in all of the bending magnets. A series of slots allows gas to flow from the beam chamber to the pump chamber. The slots also allow the DC electric field produced by the DIP anode to leak into the beam chamber. A numerical computation of the leakage field [1] shows that at the center of the beam chamber the dipole and quadrupole components of the electric field are 320 V/m and 2.1 ×10 V/m, respectively for an anode voltage of 7.3 kV. Higher-order multipole fields are also present. Distributed ion pumps in the CESR hard bend magnets have additional copper shields with offset slots, which shield the beam chamber from the DIP field. 1.2 Characteristics of the instability An anomalous transverse coupled bunch instability ("anomalous antidamping") is observed in CESR [2]. Unlike an instability caused by the coupling impedance of the vacuum chamber, the growth rates and tune shifts are strongly nonlinear functions of beam current. The absolute value of the growth rate is largest at the intermediate currents encountered during CESR injection, and becomes dramatically smaller at higher currents. The growth rates are very reproducible for positrons, over a period of years, and do not depend on the residual gas pressure. The instability occurs for electrons as well as positrons, but is not as severe or as reproducible for electrons as it is for positrons. The instability is much stronger in the horizontal than in the vertical direction. Coupled bunch modes at positive frequencies are damped; those at negative frequencies are antidamped (tend to grow). The absolute value of the growth rate is largest for the lowest frequency mode and decreases with mode frequency. The current at which the absolute value of the growth rate reaches its maximum value has a mild dependence on the number of bunches, unless the bunches are closely spaced, as shown in Table 1. Table 1: Bunch current at maximum instability growth rate for different bunch patterns. Number of trains Bunches per train Minimum bunch spacing Bunch current at |αmax| 1 1 2562 ns 7±1 mA