An electron cloud instability might limit the intensity in the Fermilab Recycler after the PIP-II upgrade. A multibunch instability typically develops in the horizontal plane within a hundred turns and, in certain conditions, leads to beam loss. Recent studies have indicated that the instability is caused by an electron cloud, trapped in the Recycler index dipole magnets. We developed an analytical model of an electron cloud driven instability with the electrons trapped in combined function dipoles. The resulting instability growth rate of about 30 revolutions is consistent with experimental observations and qualitatively agrees with the simulation in the PEI code. The model allows an estimation of the instability rate for the future intensity upgrades.
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