Fast Instability Caused by Electron Cloud in Combined Function Magnets
  One of the factors which may limit the intensity in the Fermilab Recycler is a fast transverse instability. It develops within a hundred turns and, in certain conditions, may lead to a beam loss. The high rate of the instability suggest that its cause is electron cloud. We studied the phenomena by observing the dynamics of stable and unstable beam, simulating numerically the build-up of the electron cloud, and developed an analytical model of an electron cloud driven instability with the electrons trapped in combined function di-poles. We found that beam motion can be stabilized by a clearing bunch, which confirms the electron cloud nature of the instability. The clearing suggest electron cloud trapping in Recycler combined function mag-nets. Numerical simulations show that up to 1% of the particles can be trapped by the magnetic field. Since the process of electron cloud build-up is exponential, once trapped this amount of electrons significantly increases the density of the cloud on the next revolution. In a Recycler combined function dipole this multi-turn accumulation allows the electron cloud reaching final intensities orders of magnitude greater than in a pure dipole. The estimated resulting instability growth rate of about 30 revolutions and the mode fre-quency of 0.4 MHz are consistent with experimental observations and agree with the simulation in the PEI code. The created instability model allows investigating the beam stability for the future intensity upgrades. 
S. A. Antipov, P. Adamson, A. Burov, S. Nagaitsev, M.-J. Yang
physics.acc-ph