Abstract
The interaction between a low-density electron cloud in a circular particle accelerator with a circulating charged particle beam is considered. The particle beam's space charge attracts the cloud, enhancing the cloud density near the beam axis. It is shown that this enhanced charge and the image charges associated with the cloud charge and the conducting wall of the accelerator may have important consequences for the dynamics of the beam propagation. The tune shift due to the electron cloud is obtained analytically and compared to a new numerical model (QuickPIC) that is described here. Sample numerical results are presented and their significance for current and planned experiments is discussed.
Highlights
Electron clouds have been shown to be associated with limitations in particle accelerators performance in several of the world’s largest circular proton and positron machines [1]
If the average secondary emission yield of the chamber material is greater than unity, the primary electrons accelerated in the field of the passing bunch can reach the pipe wall with a high enough energy to produce more electrons
We show that (i) the cloud space charge force is the dominant force in contributing to the coherent tune shift. (ii) The cloud compression on the axis of the beam along with its image charges on the conducting walls of the accelerator may not contribute to the coherent tune shift, but instead, play an important role in configuring the steady state beam dynamics
Summary
Electron clouds have been shown to be associated with limitations in particle accelerators performance in several of the world’s largest circular proton and positron machines [1]. : In these equations Qx and Qy are, respectively, the horizontal and vertical tunes; Qx and Qy represent the chromatic shifts proportional to the particle relative momentum offset p=p0; !0 is the angular revolution frequency of the beam in the circular accelerator (which for ultrarelativistic beams can be written as c=R0, R0 being the average machine radius); Fcl Fclx ; Fcly ; Fclz is the total force exerted by the cloud on each beam particle; p0 is the nominal particle momentum; is the relativistic factor; is the slippage factor, which can be positive if the machine is operating above transition energy, causing more energetic particles to move backwards within the bucket and vice versa. Rms horizontal spot size (mm) rms vertical spot size (mm) rms bunch length (cm) Horizontal box size (mm) Vertical box size (mm) Bunch population Horizontal emittance (m) Vertical emittance (m) Momentum spread Beam momentum (GeV=c) Circumference (km) Horizontal betatron tune Vertical betatron tune Synchrotron tune Electron cloud density (cmÿ3)
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