Short Range Wake Field Caused by Electron Cloud in Bending Magnet

A short-range wake field caused by the electron cloud has previously been studied for a drift space. In a bending magnet, the cloud electrons undergo cyclotron motion with a small radius (<1 mm) and at a high frequency (>10 GHz) in the horizontal plane due to the strong magnetic field of order 1 T. In this report, we study the motion of electrons under the combined influence of a strong magnetic dipole field and the electric field of the beam on the time scale of the bunch length, discuss the short-range wake field caused by the electrons, and simulate the emittance growth. As expected, the wake field in a bending magnet is very different from that in a drift space. The dipole field almost completely suppresses any horizontal coherent motion and rms-size blow up, and it also slows down the instability in the vertical direction.