Title: Electron Cloud Trapping In Recycler Combined Function Dipole Magnets,
Abstract: Electron cloud can lead to a fast instability in intense proton and positron
beams in circular accelerators. In the Fermilab Recycler the electron cloud is
confined within its combined function magnets. We show that the field of
combined function magnets traps the electron cloud, present the results of
analytical estimates of trapping, and compare them to numerical simulations of
electron cloud formation. The electron cloud is located at the beam center and
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 multi-turn build-up can be stopped by
injection of a clearing bunch of $10^{10}$ p at any position in the ring.